- componentAn integer corresponding to the direction in order parameter space this kernel acts in (e.g. for unrotated functionals 0 for q_x, 1 for q_y, 2 for q_z).
C++ Type:unsigned int
Controllable:No
Description:An integer corresponding to the direction in order parameter space this kernel acts in (e.g. for unrotated functionals 0 for q_x, 1 for q_y, 2 for q_z).
- polar_xThe x component of the polarization
C++ Type:std::vector<VariableName>
Controllable:No
Description:The x component of the polarization
- polar_yThe y component of the polarization
C++ Type:std::vector<VariableName>
Controllable:No
Description:The y component of the polarization
- variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on
WallEnergyDerivative
buildconstruction:Undocumented Class
The WallEnergyDerivative has not been documented. The content listed below should be used as a starting point for documenting the class, which includes the typical automatic documentation associated with a MooseObject; however, what is contained is ultimately determined by what is necessary to make the documentation clear for users.
Calculates a residual contribution due to the variation w.r.t polarization of the gradient energy. This Kernel needs to be used in conjunction with Wall2EnergyDerivative!
Overview
This object computes the residual and jacobian contributions due to the variation of the free energy density associated with the Lifshitz invariants (gradients). We split the computation into two Kernels. The gradient free energy density for a parent phase cubic perovskite is (in Voight notation),
which can be written in general as,
The governing time-dependent Landau-Ginzburg-Devonshire (TDLGD) equation of relaxation of the ferroelectric order is given by,
which means we need to compute . Multiplying by the test function and integrating over the volume, we have after moving over to the other side,
The variational derivative of the free energy is as follows,
Focusing on , neglecting the time derivative, and writing in index notation we have
In the first term, we use the relation
with the shape function of the finite element method. The second term of can be written as
via integration by parts. The surface terms vanish and we are left with the residual contribution for due to the Lifshitz invariants,
where the first term is computed in WallEnergyDerivative and the second is calculated in Wall2EnergyDerivative. We hand code into the problem for cubic parent phase perovskites such as . This term can be reworked in general for lower symmetry ferroelectric materials if needed. In general, due to the fact that the second term scales on the order of , its influence to the evolution of the TDLGD problem is quite weak. Now we compute the jacobian contributions,
Example Input File Syntax
Input Parameters
- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements
- polar_zThe z component of the polarization
C++ Type:std::vector<VariableName>
Controllable:No
Description:The z component of the polarization
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
Optional Parameters
- absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill
Tagging Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
Input Files
- (test/tests/electrooptics/BTO_monodomain_T298K_REF.i)
- (test/tests/msca/BFO_P0A0.i)
- (test/tests/topology/A_skyrm.i)
- (tutorial/ferroelectric_domain_wall.i)
- (test/tests/ics/PTOtest_fluc.i)
- (test/tests/coupled/PTOtest_3D.i)
- (tutorial/BFO_dwP1A1_100.i)
- (examples/other/skyrm.i)
- (examples/domain_walls/BTO_wall_T298K.i)
- (examples/monodomain/BTO_monodomain_Tdef.i)
- (test/tests/coupled/PTOtest_2D.i)
- (tutorial/multidomain.i)
- (test/tests/electrooptics/BTO_monodomain_T298K_REFnoEO.i)
- (test/tests/relaxor/coor.i)
- (test/tests/thermal/thermal_test.i)
- (test/tests/dispersion/genDomain_PzEz.i)
- (test/tests/dispersion/genDomain_PyEz.i)
- (test/tests/film/PTO_film3_T298K.i)
- (examples/films/PZTfilm_e12_T298K_E0.i)
- (test/tests/auxkernels/surface_charge.i)
- (test/tests/dispersion/perturbBTO_PyEz.i)
- (examples/monodomain/PZT_monodomain_Tdef.i)
- (examples/other/PTO_E0.i)
- (test/tests/pbc/pbc.i)
- (test/tests/electrostatics/Ferro_para_superlattice.i)
- (test/tests/film/PTO_film3_T298K_noP.i)
- (test/tests/electrostatics/FE_8nmFilm_Die_4nmLayer_U0.i)
- (examples/domain_walls/BTO_90wall_T298K.i)
- (test/tests/msca/BFO_dwP1A1_100.i)
- (test/tests/domain_wall/test_BTO_domain_wall.i)
- (tutorial/film.i)
- (examples/other/PZT_nanowire_test.i)
- (test/tests/pbc/bcc_pbc.i)
- (test/tests/dispersion/perturbBTO_PzEz.i)
- (examples/monodomain/PTO_monodomain_Tdef.i)
- (test/tests/auxkernels/microforce.i)
- (examples/films/PTOfilm_e12_T298K_E0.i)
- (tutorial/BFO_homogeneous_PA.i)
(test/tests/electrooptics/BTO_monodomain_T298K_REF.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 2
ny = 2
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
[./stripe1]
type = ParsedFunction
value = 0.01*cos(0.08975979010256552*(x)) # 0.08975979010256552 = 2pi/(xmax-xmin)
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.01
max = 0.02
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
######################################
##
## Principle change in refractive and
## refractive index components
##
######################################
[./dpn_1]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_2]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_3]
order = CONSTANT
family = MONOMIAL
[../]
[./den_1]
order = CONSTANT
family = MONOMIAL
[../]
[./den_2]
order = CONSTANT
family = MONOMIAL
[../]
[./den_3]
order = CONSTANT
family = MONOMIAL
[../]
[./n_1]
order = CONSTANT
family = MONOMIAL
[../]
[./n_2]
order = CONSTANT
family = MONOMIAL
[../]
[./n_3]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./dn_p1]
type = PolarOpticChangeInRefractiveIndex
component = 0
variable = dpn_1
execute_on = 'timestep_end'
[../]
[./dn_p2]
type = PolarOpticChangeInRefractiveIndex
component = 1
variable = dpn_2
execute_on = 'timestep_end'
[../]
[./dn_p3]
type = PolarOpticChangeInRefractiveIndex
component = 2
variable = dpn_3
execute_on = 'timestep_end'
[../]
[./dn_e1]
type = ElastoChangeInRefractiveIndex
component = 0
variable = den_1
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./dn_e2]
type = ElastoChangeInRefractiveIndex
component = 1
variable = den_2
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./dn_e3]
type = ElastoChangeInRefractiveIndex
component = 2
variable = den_3
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./n_1_c]
type = ReworkedRefractiveIndex
variable = n_1
elasto = true
electro = false
polar = true
component = 0
var1 = dpn_1
var2 = den_1
execute_on = 'timestep_end'
[../]
[./n_2_c]
type = ReworkedRefractiveIndex
variable = n_2
elasto = true
electro = false
polar = true
component = 1
var1 = dpn_2
var2 = den_2
execute_on = 'timestep_end'
[../]
[./n_3_c]
type = ReworkedRefractiveIndex
variable = n_3
elasto = true
electro = false
polar = true
component = 2
var1 = dpn_3
var2 = den_3
execute_on = 'timestep_end'
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.11 0.045 0.045 -0.11 0.045 -0.11 -0.029 -0.029 -0.029'
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./ref_index]
############################################
##
## Cubic refractive index BTO
## (need correct value)
##
############################################
type = GenericConstantMaterial
prop_names = 'n1 n2 n3 n4 n5 n6'
prop_values = '2.4272 2.4272 2.4272 0.0 0.0 0.0'
[../]
[./po_tensor]
############################################
##
## PO tensor coefficients from
## Bernasconi and Günter
## J. Appl. Phys., 78, 2651 (1995)
##
############################################
type = GenericConstantMaterial
prop_names = 'g1111 g1122 g1212'
prop_values = '0.15 0.038 0.07'
[../]
[./eo_tensor]
############################################
##
## Elastoptic tensor coefficients from
## Bernasconi and Günter
## J. Appl. Phys., 78, 2651 (1995)
##
############################################
type = GenericConstantMaterial
prop_names = 'p1111 p1122 p1212'
prop_values = '0.37 0.11 -0.30'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
permittivity = 0.08854187
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
num_steps = 5
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = test_bire
elemental_as_nodal = true
[../]
[]
(test/tests/msca/BFO_P0A0.i)
Nx = 5
Ny = 5
Nz = 5
xMax = 2.0
yMax = 2.0
zMax = 2.0
g11 = 12e-3
g12 = -3.0e-3
g44 = 3.0e-3
h11 = 2.0e-4
h12 = -0.2e-3
h44 = 0.8e-3
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${Nx}
ny = ${Ny}
nz = ${Nz}
xmin = 0.0
xmax = ${xMax}
ymin = 0.0
ymax = ${yMax}
zmin = 0.0
zmax = ${zMax}
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
antiphase_A_x = antiphase_A_x
antiphase_A_y = antiphase_A_y
antiphase_A_z = antiphase_A_z
displacements = 'u_x u_y u_z'
potential_E_int = potential_E_int
[]
[Functions]
[./constPm]
type = ParsedFunction
value = -0.54
[../]
[./constPp]
type = ParsedFunction
value = 0.54
[../]
[./constAm]
type = ParsedFunction
value = -7.37
[../]
[./constAp]
type = ParsedFunction
value = 7.37
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPm
[../]
[../]
[./antiphase_A_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAm
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e21]
order = CONSTANT
family = MONOMIAL
[../]
[./e02]
order = CONSTANT
family = MONOMIAL
[../]
[./e20]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e21]
type = RankTwoAux
variable = e21
rank_two_tensor = total_strain
index_i = 2
index_j = 1
[../]
[./e20]
type = RankTwoAux
variable = e20
rank_two_tensor = total_strain
index_i = 2
index_j = 0
[../]
[./e02]
type = RankTwoAux
variable = e02
rank_two_tensor = total_strain
index_i = 0
index_j = 2
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[Kernels]
[./TensorMechanics]
[../]
[./rotostr_ux]
type = RotostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./rotostr_uy]
type = RotostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./rotostr_uz]
type = RotostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
### Operators for the polar field: ###
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
[./walled_a_x]
type = AFDWallEnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled_a_y]
type = AFDWallEnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled_a_z]
type = AFDWallEnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./walled2_a_x]
type = AFDWall2EnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled2_a_y]
type = AFDWall2EnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled2_a_z]
type = AFDWall2EnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./roto_polar_coupled_x]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_x
component = 0
[../]
[./roto_polar_coupled_y]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_y
component = 1
[../]
[./roto_polar_coupled_z]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_z
component = 2
[../]
[./roto_dis_coupled_x]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_x
component = 0
[../]
[./roto_dis_coupled_y]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_y
component = 1
[../]
[./roto_dis_coupled_z]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
#Operators for the AFD field
[./rbed_x]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_x
component = 0
[../]
[./rbed_y]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_y
component = 1
[../]
[./rbed_z]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_z
component = 2
[../]
[./rotostr_dis_coupled_x]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_y]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_z]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./a_x_time]
type = TimeDerivativeScaled
variable = antiphase_A_x
time_scale = 0.01
block = '0'
[../]
[./a_y_time]
type = TimeDerivativeScaled
variable = antiphase_A_y
time_scale = 0.01
block = '0'
[../]
[./a_z_time]
type = TimeDerivativeScaled
variable = antiphase_A_z
time_scale = 0.01
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-2.81296 1.72351 2.24147 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_A]
type = GenericConstantMaterial
prop_names = 'beta1 beta11 beta12 beta111 beta112 beta123 beta1111 beta1112 beta1122 beta1123'
prop_values = '-0.0137763 0.0000349266 0.0000498846 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./P_A_couple]
type = GenericConstantMaterial
prop_names = 't1111 t1122 t1212 t42111111 t24111111 t42111122 t24112222 t42112233 t24112233 t42112211 t24111122 t42111212 t42123312 t24121112 t24121233 t6211111111 t2611111111 t6211111122 t2611222222 t4411111111 t4411112222'
prop_values = '0.012516 0.0180504 -0.036155 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '1.0 ${g11} ${g12} ${g44} 0.0'
[../]
[./Landau_H]
type = GenericConstantMaterial
prop_names = 'H110 H11_H110 H12_H110 H44_H110 H44P_H110'
prop_values = '1.0 ${h11} ${h12} ${h44} 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '295.179 117.567 74.0701'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.0603833 0.0111245 -0.0175686'
[../]
[./mat_R]
type = GenericConstantMaterial
prop_names = 'R11 R12 R44'
prop_values = '-0.0000878064 0.0000295306 0.0000627962'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-30.4162 -5.01496 -10.4105'
#the point is the following: use a slightly different definition of Q_ij than Hlinka
[../]
[./mat_r]
type = GenericConstantMaterial
prop_names = 'r11 r12 r44'
prop_values = '-0.0379499 0.00373096 0.0372105'
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '295.179 117.567 117.567 295.179 117.567 295.179 74.0701 74.0701 74.0701'
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Postprocessors]
[./dt]
type = TimestepSize
[../]
[./FbP]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FbA]
type = RotoBulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FcPA]
type = RotoPolarCoupledEnergyEighth
execute_on = 'timestep_end'
[../]
[./FgP]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./FgA]
type = AFDWallEnergy
execute_on = 'timestep_end'
[../]
[./FcPu]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./FcAu]
type = RotostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./Felu]
type = ElasticEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'FbP FbA FgP FgA FcPA FcPu FcAu Felu Fele'
pp_coefs = ' 1 1 1 1 1 1 1 1 1'
execute_on = 'timestep_end'
##########################################
#
# NOTE: Ferret output is in attojoules
#
##########################################
[../]
[./perc_change]
type = EnergyRatePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
dt = dt
[../]
[]
[BCs]
[./Periodic]
[./x]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z antiphase_A_x antiphase_A_y antiphase_A_z'
[../]
[./xyz]
auto_direction = 'x y z'
variable = 'potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalBFOMaterialRVEUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-7'
[../]
[]
#=
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 121 1e-8 1e-7 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 10.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 25 #usually 10
linear_iteration_ratio = 100
dt = 0.08
growth_factor = 1.1
[../]
num_steps = 2
[]
#=
[Outputs]
print_linear_residuals = false
perf_graph_live = false
[./out]
type = Exodus
file_base = BFO_P0A0
elemental_as_nodal = true
[../]
[]
(test/tests/topology/A_skyrm.i)
[Mesh]
file = exodus_disk_r8_h1.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
vol = vol
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
[]
[Functions]
[./parsed_function_x_skyrm]
type = ParsedFunction
value = '-(0.738217-0.00686984*(x^2+y^2)^(0.5)+0.00644497*(x^2+y^2)-0.0188174*(x^2+y^2)^(1.5)+0.00441745*(x^2+y^2)^2-0.000274842*(x^2+y^2)^(5/2))*sin(-0.028395+0.267482*(x^2+y^2)^(0.5)-0.146762*(x^2+y^2)+0.0632932*(x^2+y^2)^(1.5)-0.00790942*(x^2+y^2)^(2)+0.000294936*(x^2+y^2)^(5/2))*sin(atan(y/x))'
[../]
[./parsed_function_y_skyrm]
type = ParsedFunction
value = '(0.738217-0.00686984*(x^2+y^2)^(0.5)+0.00644497*(x^2+y^2)-0.0188174*(x^2+y^2)^(1.5)+0.00441745*(x^2+y^2)^2-0.000274842*(x^2+y^2)^(5/2))*sin(-0.028395+0.267482*(x^2+y^2)^(0.5)-0.146762*(x^2+y^2)+0.0632932*(x^2+y^2)^(1.5)-0.00790942*(x^2+y^2)^(2)+0.000294936*(x^2+y^2)^(5/2))*cos(atan(y/x))'
[../]
[./parsed_function_z_skyrm]
type = ParsedFunction
value = '(0.738217-0.00686984*(x^2+y^2)^(0.5)+0.00644497*(x^2+y^2)-0.0188174*(x^2+y^2)^(1.5)+0.00441745*(x^2+y^2)^2-0.000274842*(x^2+y^2)^(5/2))*cos(-0.028395+0.267482*(x^2+y^2)^(0.5)-0.146762*(x^2+y^2)+0.0632932*(x^2+y^2)^(1.5)-0.00790942*(x^2+y^2)^(2)+0.000294936*(x^2+y^2)^(5/2))'
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = parsed_function_x_skyrm
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = parsed_function_y_skyrm
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = parsed_function_z_skyrm
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.110448 0.0451767 -0.115654'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -6.28'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
u_x = u_x
u_y = u_y
u_z = u_z
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
u_x = u_x
u_y = u_y
u_z = u_z
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
u_x = u_x
u_y = u_y
u_z = u_z
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./top_electrode_top]
type = DirichletBC
variable = 'potential_E_int'
value = 0.0001
boundary = '2'
[../]
[./top_electrode_bottom]
type = DirichletBC
variable = 'potential_E_int'
value = 0.0001
boundary = '3'
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fb]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
u_x = u_x
u_y = u_y
u_z = u_z
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 1e-5
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-4'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 8.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
growth_factor = 1.25
linear_iteration_ratio = 1000
dt = 0.000008
[../]
verbose = true
num_steps = 1
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_bto_skyrm_disk
elemental_as_nodal = true
[../]
[]
(tutorial/ferroelectric_domain_wall.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
nx = 480
ny = 1
nz = 1
xmin = -60.0
xmax = 60.0
ymin = -0.25
ymax = 0.25
zmin = -0.25
zmax = 0.25
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-60.0 -0.25 -0.25'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
[./stripe1]
type = ParsedFunction
value = 0.1*cos(0.05235987755*(x)) #2pi/L = 0.10471975512
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'stripe1'
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.11 -0.045 0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '14.2 -0.74 1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '0.11 -0.045 -0.045 0.11 -0.045 0.11 0.029 0.029 0.029'
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total
## energy decomposed into linear combinations
## of the different physics.
##
###############################################
[./Fb]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the
## energy difference between subsequent time
## steps is lower than 1e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
growth_factor = 1.2
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
############################################
##
## Output options
##
############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_ferroelectric_domain_wall
elemental_as_nodal = true
execute_on = 'timestep_end'
interval = 2
[../]
[]
(test/tests/ics/PTOtest_fluc.i)
[Mesh]
type = GeneratedMesh
dim = 3
nx = 10
ny = 10
nz = 7
xmin = -4
xmax = 4
ymin = -4
ymax = 4
zmin = -3
zmax = 3
elem_type = HEX8
[]
[GlobalParams]
len_scale = 1.0
alpha1 = -0.1722883
alpha11 = -0.07253
alpha111 = 0.26
alpha12 = 0.75
alpha112 = 0.61
alpha123 = -3.67
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
displacements = 'disp_x disp_y disp_z'
prefactor = 0.01 #negative = tension, positive = compression
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FluctuationsIC
epsilon = 1.0e-5
q1 = '354 1005 645'
q2 = '715 1065 1132'
q3 = '391 305 1106'
q4 = '1053 1116 627'
h = 0.22
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FluctuationsIC
epsilon = 1.0e-5
q1 = '354 850 10'
q2 = '715 28 5'
q3 = '391 305 1106'
q4 = '653 1116 627'
h = 0.15
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FluctuationsIC
epsilon = 1.0e-5
q1 = '860 165 645'
q2 = '715 665 1332'
q3 = '361 15 706'
q4 = '253 1116 627'
h = 0.05
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[./disp_z]
order = FIRST
family = LAGRANGE
[../]
[]
[Materials]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
[../]
[./eigen_strain_zz] #Use for stress-free strain (ie epitaxial)
type = ComputeEigenstrain
block = '0'
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1 0 0 0 1 0 0 0 0'
eigenstrain_name = eigenstrain
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '380. 150. 150. 380. 150. 380. 110. 110. 110.'
[../]
[./strain_1]
type = ComputeSmallStrain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.089 0.026 0.026 -0.089 0.026 -0.089 -0.03375 -0.03375 -0.03375'
C_ijkl = '380. 150. 150. 380. 150. 380. 110. 110. 110.'
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
[./TensorMechanics]
[../]
[./bed_x]
type = BulkEnergyDerivativeSixth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeSixth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeSixth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./ferroelectriccouplingp_xx]
type = FerroelectricCouplingP
variable = polar_x
component = 0
[../]
[./ferroelectriccouplingp_yy]
type = FerroelectricCouplingP
variable = polar_y
component = 1
[../]
[./ferroelectriccouplingp_zz]
type = FerroelectricCouplingP
variable = polar_z
component = 2
[../]
[./ferroelectriccouplingX_xx]
type = FerroelectricCouplingX
variable = disp_x
component = 0
[../]
[./ferroelectriccouplingX_yy]
type = FerroelectricCouplingX
variable = disp_y
component = 1
[../]
[./ferroelectriccouplingX_zz]
type = FerroelectricCouplingX
variable = disp_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./disp_x_front]
type = DirichletBC
boundary = 'front'
value = 0.0
variable = disp_x
[../]
[./disp_y_front]
type = DirichletBC
boundary = 'front'
value = 0.0
variable = disp_y
[../]
[./disp_z_front]
type = DirichletBC
boundary = 'front'
value = 0.0
variable = disp_z
[../]
[./potential_E_int_front]
type = DirichletBC
boundary = 'front'
value = 0.0001
variable = potential_E_int
[../]
[./potential_E_int_back]
type = DirichletBC
boundary = 'back'
value = 0.0001
variable = potential_E_int
[../]
[./disp_x_back]
type = DirichletBC
boundary = 'back'
value = 0.0
variable = disp_x
[../]
[./disp_y_back]
type = DirichletBC
boundary = 'back'
value = 0.0
variable = disp_y
[../]
[./disp_z_back]
type = DirichletBC
boundary = 'back'
value = 0.0
variable = disp_z
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergy
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
[../]
[./Fcoupled]
type = ElectrostrictiveEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_rtol -ksp_rtol -pc_type'
petsc_options_value = ' 121 1e-6 1e-8 bjacobi'
[../]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 0.1
num_steps = 5
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
file_base = outPTO_test_fluct
elemental_as_nodal = true
interval = 1
[../]
[]
(test/tests/coupled/PTOtest_3D.i)
[Mesh]
type = GeneratedMesh
dim = 3
nx = 6
ny = 6
nz = 4
xmin = -1.5
xmax = 1.5
ymin = -1.5
ymax = 1.5
zmin = -1
zmax = 1
elem_type = HEX8
[]
[GlobalParams]
len_scale = 1.0
alpha1 = -0.1722883 # (3.766(T-765.1)*10^5) C^{-2} nm^2 (T = 293 K)
alpha11 = -0.07253
alpha111 = 0.26
alpha12 = 0.75
alpha112 = 0.61
alpha123 = -3.67
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
displacements = 'disp_x disp_y disp_z'
prefactor = 0.01 #negative = tension,positive = compression
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[./disp_z]
order = FIRST
family = LAGRANGE
[../]
[]
[Materials]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
[../]
[./eigen_strain_zz] #Use for stress-free strain (ie epitaxial)
type = ComputeEigenstrain
block = '0'
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1 0 0 0 1 0 0 0 0'
eigenstrain_name = eigenstrain
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '380. 150. 150. 380. 150. 380. 110. 110. 110.'
[../]
[./strain_1]
type = ComputeSmallStrain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.089 0.026 0.026 -0.089 0.026 -0.089 -0.03375 -0.03375 -0.03375'
C_ijkl = '380. 150. 150. 380. 150. 380. 110. 110. 110.'
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
#Elastic problem
[./TensorMechanics]
[../]
[./bed_x]
type = BulkEnergyDerivativeSixth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeSixth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeSixth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./ferroelectriccouplingp_xx]
type = FerroelectricCouplingP
variable = polar_x
component = 0
[../]
[./ferroelectriccouplingp_yy]
type = FerroelectricCouplingP
variable = polar_y
component = 1
[../]
[./ferroelectriccouplingp_zz]
type = FerroelectricCouplingP
variable = polar_z
component = 2
[../]
[./ferroelectriccouplingX_xx]
type = FerroelectricCouplingX
variable = disp_x
component = 0
[../]
[./ferroelectriccouplingX_yy]
type = FerroelectricCouplingX
variable = disp_y
component = 1
[../]
[./ferroelectriccouplingX_zz]
type = FerroelectricCouplingX
variable = disp_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./potential_E_int_front]
type = DirichletBC
boundary = 'front'
value = 0.0001
variable = potential_E_int
[../]
[./potential_E_int_back]
type = DirichletBC
boundary = 'back'
value = 0.0001
variable = potential_E_int
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergy
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
[../]
[./Fcoupled]
type = ElectrostrictiveEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type'
petsc_options_value = ' 121 1e-10 1e-8 1e-6 bjacobi'
[../]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 0.35
num_steps = 15
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
file_base = outPTOchunk_test
elemental_as_nodal = true
interval = 1
[../]
[]
(tutorial/BFO_dwP1A1_100.i)
Nx = 250
Ny = 1
Nz = 1
xMax = 31.41592653589793
yMax = 1.0
zMax = 1.0
freq = 0.2
g11 = 12e-3
g12 = -3.0e-3
g44 = 3.0e-3
h11 = 2.0e-4
h12 = -0.2e-3
h44 = 0.8e-3
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${Nx}
ny = ${Ny}
nz = ${Nz}
xmin = 0.0
xmax = ${xMax}
ymin = 0.0
ymax = ${yMax}
zmin = 0.0
zmax = ${zMax}
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
antiphase_A_x = antiphase_A_x
antiphase_A_y = antiphase_A_y
antiphase_A_z = antiphase_A_z
displacements = 'u_x u_y u_z'
potential_E_int = potential_E_int
[]
[Functions]
[./stripeP1]
type = ParsedFunction
value = 0.54*cos(${freq}*(x))
[../]
[./stripeP2]
type = ParsedFunction
value = -0.54*cos(${freq}*(x))
[../]
[./stripeA1]
type = ParsedFunction
value = 7.37*cos(${freq}*(x))
[../]
[./stripeA2]
type = ParsedFunction
value = -7.37*cos(${freq}*(x))
[../]
[./constPm]
type = ParsedFunction
value = -0.54
[../]
[./constPp]
type = ParsedFunction
value = 0.54
[../]
[./constAm]
type = ParsedFunction
value = -7.37
[../]
[./constAp]
type = ParsedFunction
value = 7.37
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = stripeP1
[../]
[../]
[./antiphase_A_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = stripeA1
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e21]
order = CONSTANT
family = MONOMIAL
[../]
[./e02]
order = CONSTANT
family = MONOMIAL
[../]
[./e20]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Kernels]
[./TensorMechanics]
[../]
[./rotostr_ux]
type = RotostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./rotostr_uy]
type = RotostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./rotostr_uz]
type = RotostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
### Operators for the polar field: ###
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
[./walled_a_x]
type = AFDWallEnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled_a_y]
type = AFDWallEnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled_a_z]
type = AFDWallEnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./walled2_a_x]
type = AFDWall2EnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled2_a_y]
type = AFDWall2EnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled2_a_z]
type = AFDWall2EnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./roto_polar_coupled_x]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_x
component = 0
[../]
[./roto_polar_coupled_y]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_y
component = 1
[../]
[./roto_polar_coupled_z]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_z
component = 2
[../]
[./roto_dis_coupled_x]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_x
component = 0
[../]
[./roto_dis_coupled_y]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_y
component = 1
[../]
[./roto_dis_coupled_z]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
#Operators for the AFD field
[./rbed_x]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_x
component = 0
[../]
[./rbed_y]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_y
component = 1
[../]
[./rbed_z]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_z
component = 2
[../]
[./rotostr_dis_coupled_x]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_y]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_z]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./a_x_time]
type = TimeDerivativeScaled
variable = antiphase_A_x
time_scale = 0.01
block = '0'
[../]
[./a_y_time]
type = TimeDerivativeScaled
variable = antiphase_A_y
time_scale = 0.01
block = '0'
[../]
[./a_z_time]
type = TimeDerivativeScaled
variable = antiphase_A_z
time_scale = 0.01
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e21]
type = RankTwoAux
variable = e21
rank_two_tensor = total_strain
index_i = 2
index_j = 1
[../]
[./e20]
type = RankTwoAux
variable = e20
rank_two_tensor = total_strain
index_i = 2
index_j = 0
[../]
[./e02]
type = RankTwoAux
variable = e02
rank_two_tensor = total_strain
index_i = 0
index_j = 2
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-2.81296 1.72351 2.24147 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_A]
type = GenericConstantMaterial
prop_names = 'beta1 beta11 beta12 beta111 beta112 beta123 beta1111 beta1112 beta1122 beta1123'
prop_values = '-0.0137763 0.0000349266 0.0000498846 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./P_A_couple]
type = GenericConstantMaterial
prop_names = 't1111 t1122 t1212 t42111111 t24111111 t42111122 t24112222 t42112233 t24112233 t42112211 t24111122 t42111212 t42123312 t24121112 t24121233 t6211111111 t2611111111 t6211111122 t2611222222 t4411111111 t4411112222'
prop_values = '0.012516 0.0180504 -0.036155 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '1.0 ${g11} ${g12} ${g44} 0.0'
[../]
[./Landau_H]
type = GenericConstantMaterial
prop_names = 'H110 H11_H110 H12_H110 H44_H110 H44P_H110'
prop_values = '1.0 ${h11} ${h12} ${h44} 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '295.179 117.567 74.0701'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.0603833 0.0111245 -0.0175686'
[../]
[./mat_R]
type = GenericConstantMaterial
prop_names = 'R11 R12 R44'
prop_values = '-0.0000878064 0.0000295306 0.0000627962'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-30.4162 -5.01496 -10.4105'
[../]
[./mat_r]
type = GenericConstantMaterial
prop_names = 'r11 r12 r44'
prop_values = '-0.0379499 0.00373096 0.0372105'
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '295.179 117.567 117.567 295.179 117.567 295.179 74.0701 74.0701 74.0701'
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Postprocessors]
[./dt]
type = TimestepSize
[../]
[./FbP]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FbA]
type = RotoBulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FcPA]
type = RotoPolarCoupledEnergyEighth
execute_on = 'timestep_end'
[../]
[./FgP]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./FgA]
type = AFDWallEnergy
execute_on = 'timestep_end'
[../]
[./FcPu]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./FcAu]
type = RotostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./Felu]
type = ElasticEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'FbP FbA FgP FgA FcPA FcPu FcAu Felu Fele'
pp_coefs = ' 1 1 1 1 1 1 1 1 1'
execute_on = 'timestep_end'
##########################################
#
# NOTE: Ferret output is in attojoules
#
##########################################
[../]
[./perc_change]
type = EnergyRatePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
dt = dt
[../]
[./elapsed]
type = PerfGraphData
section_name = "Root" # for profiling the problem
data_type = total
[../]
[]
[BCs]
[./Periodic]
[./x]
auto_direction = 'x'
variable = 'u_x u_y u_z polar_x polar_y polar_z antiphase_A_x antiphase_A_y antiphase_A_z'
[../]
[./xyz]
auto_direction = 'x y z'
variable = 'potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalBFOMaterialRVEUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-7'
[../]
[]
#=
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 121 1e-8 1e-7 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 10.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 25 #usually 10
linear_iteration_ratio = 100
dt = 0.08
growth_factor = 1.1
[../]
num_steps = 1000
[]
[Outputs]
print_linear_residuals = false
perf_graph_live = false
[./out]
type = Exodus
file_base = BFO_dwP1A1_100
elemental_as_nodal = true
[../]
[]
(examples/other/skyrm.i)
[Mesh]
file = exodus_disk_r8_h1.e
[]
[MeshModifiers]
[./centernodeset_1]
type = AddExtraNodeset
new_boundary = 'center_node_1'
coord = '0.0 0.0 -0.5'
[../]
[./centernodeset_2]
type = AddExtraNodeset
new_boundary = 'center_node_2'
coord = '0.0 0.0 0.5'
[../]
[./centernodeset_3]
type = AddExtraNodeset
new_boundary = 'center_node_3'
coord = '0.0 0.0 0.166667'
[../]
[./centernodeset_4]
type = AddExtraNodeset
new_boundary = 'center_node_4'
coord = '0.0 0.0 -0.166667'
[../]
[]
[GlobalParams]
len_scale = 1.0
alpha1 = -0.09179 #room temp PTO
alpha11 = 0.0706
alpha111 = 0.0
alpha12 = 0.1412
alpha112 = 0.0
alpha123 = 0.0
G110 = 0.141
G11_G110 = 0.0 #this is here to somehow prevent P_z "ringing" problems on the side...
G12_G110 = 0.0 #perhaps this allows for div P =0?
G44_G110 = 1.0
G44P_G110 = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
lambda = 0.01
K = -0.01
[]
[Functions]
#This is a skyrmion.
[./parsed_function_x]
type = ParsedFunction
value = '-(0.738217-0.00686984*(x^2+y^2)^(0.5)+0.00644497*(x^2+y^2)-0.0188174*(x^2+y^2)^(1.5)+0.00441745*(x^2+y^2)^2-0.000274842*(x^2+y^2)^(5/2))*sin(-0.028395+0.267482*(x^2+y^2)^(0.5)-0.146762*(x^2+y^2)+0.0632932*(x^2+y^2)^(1.5)-0.00790942*(x^2+y^2)^(2)+0.000294936*(x^2+y^2)^(5/2))*sin(atan(y/x))'
[../]
[./parsed_function_y]
type = ParsedFunction
value = '(0.738217-0.00686984*(x^2+y^2)^(0.5)+0.00644497*(x^2+y^2)-0.0188174*(x^2+y^2)^(1.5)+0.00441745*(x^2+y^2)^2-0.000274842*(x^2+y^2)^(5/2))*sin(-0.028395+0.267482*(x^2+y^2)^(0.5)-0.146762*(x^2+y^2)+0.0632932*(x^2+y^2)^(1.5)-0.00790942*(x^2+y^2)^(2)+0.000294936*(x^2+y^2)^(5/2))*cos(atan(y/x))'
[../]
[./parsed_function_z]
type = ParsedFunction
value = '(0.738217-0.00686984*(x^2+y^2)^(0.5)+0.00644497*(x^2+y^2)-0.0188174*(x^2+y^2)^(1.5)+0.00441745*(x^2+y^2)^2-0.000274842*(x^2+y^2)^(5/2))*cos(-0.028395+0.267482*(x^2+y^2)^(0.5)-0.146762*(x^2+y^2)+0.0632932*(x^2+y^2)^(1.5)-0.00790942*(x^2+y^2)^(2)+0.000294936*(x^2+y^2)^(5/2))'
[../]
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = parsed_function_x
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = parsed_function_y
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = parsed_function_z
[../]
[../]
[]
[Kernels]
#Bulk energy density
[./bed_x]
type = BulkEnergyDerivativeSixth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeSixth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeSixth
variable = polar_z
component = 2
[../]
##Wall energy penalty
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./anis_x]
type = AnisotropyEnergy
variable = polar_x
component = 0
[../]
[./anis_y]
type = AnisotropyEnergy
variable = polar_y
component = 1
[../]
##Electrostatics
#PdotE
#[./polar_electric_px]
# type = PolarElectricPStrong
# variable = polar_x
# component = 0
#[../]
#[./polar_electric_py]
# type = PolarElectricPStrong
# variable = polar_y
# component = 1
#[../]
#[./polar_electric_pz] # when K > 0, turning this block off will get the two band state
# type = PolarElectricPStrong
# variable = polar_z
# component = 2
#[../]
##Poisson problem:
#[./FE_E_int]
# type = Electrostatics
# variable = potential_int
# block = '1'
# permittivity = 3.54
#[../]
#[./polar_x_electric_E]
# type = PolarElectricEStrong
# variable = potential_int
#[../]
[./depol_z]
type = DepolEnergy
permitivitty = 0.00885
variable = polar_z
avePz = avePz
[../]
##Time dependence
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./center_pol_x]
type = DirichletBC
variable = 'polar_x'
value = 0.0
boundary = 'center_node_1 center_node_2 center_node_3 center_node_4'
[../]
[./center_pol_y]
type = DirichletBC
variable = 'polar_y'
value = 0.0
boundary = 'center_node_1 center_node_2 center_node_3 center_node_4'
[../]
# [./center_pol_z]
# type = DirichletBC
# variable = 'polar_z'
# value = 0.65
# boundary = 'center_node_1 center_node_2 center_node_3 center_node_4'
# [../]
[./side_neumann_x]
variable = 'polar_x'
type = NeumannBC
value = 0.0
boundary = '1'
[../]
[./side_neumann_y]
variable = 'polar_y'
type = NeumannBC
value = 0.0
boundary = '1'
[../]
[./side_Neumann_z]
variable = 'polar_z'
type = NeumannBC
value = 0.0
boundary = '1'
[../]
[]
[Postprocessors]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'initial linear nonlinear timestep_begin timestep_end'
[../]
[./Fbulk]
type = BulkEnergy
execute_on = 'timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./total_energy]
type = TotalEnergy
Fbulk = Fbulk
Fwall = Fbulk
execute_on = 'timestep_end'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type'
petsc_options_value = ' 250 1e-10 1e-8 1e-6 bjacobi '
[../]
[]
[Executioner]
type = Transient
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.1
#iteration_window = 3
optimal_iterations = 6 #should be 5 probably
growth_factor = 1.4
linear_iteration_ratio = 1000
cutback_factor = 0.9
[../]
solve_type = 'NEWTON' #"PJFNK, JFNK, NEWTON"
scheme = 'implicit-euler' #"implicit-euler, explicit-euler, crank-nicolson, bdf2, rk-2"
dtmin = 1e-13
dtmax = 0.7
num_steps = 500
[]
[Outputs]
print_linear_residuals = false
print_perf_log = true
[./out]
type = Exodus
execute_on = 'timestep_end'
file_base = out_ic_skyrm
elemental_as_nodal = true
[../]
[]
(examples/domain_walls/BTO_wall_T298K.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
nx = 60
ny = 2
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -30.0
xmax = 30.0
ymin = -1.0
ymax = 1.0
zmin = -1.0
zmax = 1.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
vol = vol
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
[./stripe1]
type = ParsedFunction
value = 0.1*cos(0.10471975512*(x+2)) #2pi/L = 0.10471975512
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'stripe1'
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.11 0.045 0.045 -0.11 0.045 -0.11 -0.029 -0.029 -0.029'
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fb]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'initial timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_bto_wall_T298K_2
elemental_as_nodal = true
[../]
[./console]
type = Console
time_precision = 3
[../]
[]
(examples/monodomain/BTO_monodomain_Tdef.i)
a1temp = a1def
a11temp = a11def
a111temp = a111def
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 8
ny = 8
nz = 8
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -2.0
xmax = 2.0
ymin = -2.0
ymax = 2.0
zmin = -2.0
zmax = 2.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
vol = vol
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.075
max = 0.1
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.075
max = 0.1
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.075
max = 0.1
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs00]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs11]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./eigs00]
type = LocalABO3EigenstressAux
variable = eigs00
index_i = 0
index_j = 0
[../]
[./eigs11]
type = LocalABO3EigenstressAux
variable = eigs11
index_i = 1
index_j = 1
[../]
[./eigs22]
type = LocalABO3EigenstressAux
variable = eigs22
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${a1temp} ${a11temp} 0.323 ${a111temp} 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrains_name = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./avePx]
type = ElementAverageValue
variable = polar_x
execute_on = 'timestep_end'
[../]
[./avePy]
type = ElementAverageValue
variable = polar_y
execute_on = 'timestep_end'
[../]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'timestep_end'
[../]
[./ave_e00]
type = ElementAverageValue
variable = e00
execute_on = 'timestep_end'
[../]
[./ave_e11]
type = ElementAverageValue
variable = e11
execute_on = 'timestep_end'
[../]
[./ave_e22]
type = ElementAverageValue
variable = e22
execute_on = 'timestep_end'
[../]
[./Fb]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is smallhotkey for tilde
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-6 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./outCSV]
type = CSV
file_base = out_bto_monodomain_Tdef
[../]
[]
(test/tests/coupled/PTOtest_2D.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 32
ny = 32
xmin = -8
xmax = 8
ymin = -8
ymax = 8
[]
[GlobalParams]
len_scale = 1.0
alpha1 = -0.1722883 # (3.766(T-765.1)*10^5) C^{-2} nm^2 (T = 293 K)
alpha11 = -0.07253
alpha111 = 0.26
alpha12 = 0.75
alpha112 = 0.61
alpha123 = -3.67
polar_x = polar_x
polar_y = polar_y
potential_E_int = potential_E_int
disp_x = disp_x
disp_y = disp_y
displacements = 'disp_x disp_y'
prefactor = 0.0
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 5
legacy_generator = true
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 5
legacy_generator = true
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[]
[Materials]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
[../]
[./eigen_strain_zz] #Use for stress-free strain (ie epitaxial)
type = ComputeEigenstrain
block = '0'
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1 0 0 0 1 0 0 0 0'
eigenstrain_name = eigenstrain
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '380. 150. 150. 380. 150. 380. 110. 110. 110.'
[../]
[./strain_1]
type = ComputeSmallStrain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.089 0.026 0.026 -0.089 0.026 -0.089 -0.03375 -0.03375 -0.03375'
C_ijkl = '380. 150. 150. 380. 150. 380. 110. 110. 110.'
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
#Elastic problem
[./TensorMechanics]
[../]
[./bed_x]
type = BulkEnergyDerivativeSixth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeSixth
variable = polar_y
component = 1
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./ferroelectriccouplingp_xx]
type = FerroelectricCouplingP
variable = polar_x
component = 0
[../]
[./ferroelectriccouplingp_yy]
type = FerroelectricCouplingP
variable = polar_y
component = 1
[../]
[./ferroelectriccouplingX_xx]
type = FerroelectricCouplingX
variable = disp_x
component = 0
[../]
[./ferroelectriccouplingX_yy]
type = FerroelectricCouplingX
variable = disp_y
component = 1
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[]
[BCs]
[./potential_E_int_front]
type = DirichletBC
boundary = 'top'
value = 0.0001
variable = potential_E_int
[../]
[./potential_E_int_back]
type = DirichletBC
boundary = 'bottom'
value = 0.0001
variable = potential_E_int
[../]
[./disp_x_back]
type = DirichletBC
boundary = 'top'
value = 0.0
variable = disp_x
[../]
[./disp_y_back]
type = DirichletBC
boundary = 'top'
value = 0.0
variable = disp_y
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergy
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
[../]
[./Fcoupled]
type = ElectrostrictiveEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type'
petsc_options_value = ' 121 1e-10 1e-8 1e-6 bjacobi'
[../]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
#dt = 0.5
dtmin = 1e-13
dtmax = 0.1
num_steps = 10
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
file_base = outPTOchunk_test_2D
elemental_as_nodal = true
interval = 1
[../]
[]
(tutorial/multidomain.i)
[Mesh]
type = GeneratedMesh
dim = 3
nx = 32
ny = 32
nz = 6
xmin = -15
xmax = 15
ymin = -15
ymax = 15
zmin = -2
zmax = 2
elem_type = HEX8
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_int
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.0001
max = 0.0001
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.0001
max = 0.0001
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.0001
max = 0.0001
[../]
[../]
[./potential_int]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
#---------------------------------------#
# #
# Bulk (homogeneous) free energy #
# #
#---------------------------------------#
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
#---------------------------------------#
# #
# Gradient free energy #
# #
#---------------------------------------#
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
#---------------------------------------#
# #
# Poissons equation and P*E #
# #
#---------------------------------------#
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
#---------------------------------------#
# #
# Time dependence of Pj #
# #
#---------------------------------------#
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[Materials]
## Use coefficients for lead-titanate in this convienient unit system (aC, kg, sec, nm)
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
## This does not influence results much.
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[BCs]
[]
[Postprocessors]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'timestep_end'
[../]
[./FbP]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./FgP]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'FbP FgP'
pp_coefs = ' 1 1'
execute_on = 'timestep_end'
##########################################
#
# NOTE: Ferret output is in attojoules
#
##########################################
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
[../]
[]
[UserObjects]
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-4'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type'
petsc_options_value = ' 120 1e-10 1e-8 1e-4 bjacobi'
[../]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmax = 0.7
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
execute_on = 'timestep_end'
file_base = out_multidomain
elemental_as_nodal = true
interval = 1
[../]
[./outcsv]
type = CSV
file_base = out_multidomain
execute_on = 'timestep_end'
[../]
[]
(test/tests/electrooptics/BTO_monodomain_T298K_REFnoEO.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 2
ny = 2
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
[./stripe1]
type = ParsedFunction
value = 0.01*cos(0.08975979010256552*(x)) # 0.08975979010256552 = 2pi/(xmax-xmin)
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.01
max = 0.02
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
######################################
##
## Principle change in refractive and
## refractive index components
##
######################################
[./dpn_1]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_2]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_3]
order = CONSTANT
family = MONOMIAL
[../]
[./den_1]
order = CONSTANT
family = MONOMIAL
[../]
[./den_2]
order = CONSTANT
family = MONOMIAL
[../]
[./den_3]
order = CONSTANT
family = MONOMIAL
[../]
[./n_1]
order = CONSTANT
family = MONOMIAL
[../]
[./n_2]
order = CONSTANT
family = MONOMIAL
[../]
[./n_3]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./dn_p1]
type = PolarOpticChangeInRefractiveIndex
component = 0
variable = dpn_1
execute_on = 'timestep_end'
[../]
[./dn_p2]
type = PolarOpticChangeInRefractiveIndex
component = 1
variable = dpn_2
execute_on = 'timestep_end'
[../]
[./dn_p3]
type = PolarOpticChangeInRefractiveIndex
component = 2
variable = dpn_3
execute_on = 'timestep_end'
[../]
[./dn_e1]
type = ElastoChangeInRefractiveIndex
component = 0
variable = den_1
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./dn_e2]
type = ElastoChangeInRefractiveIndex
component = 1
variable = den_2
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./dn_e3]
type = ElastoChangeInRefractiveIndex
component = 2
variable = den_3
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./n_1_c]
type = ReworkedRefractiveIndex
variable = n_1
elasto = false
electro = false
polar = true
component = 0
var1 = dpn_1
execute_on = 'timestep_end'
[../]
[./n_2_c]
type = ReworkedRefractiveIndex
variable = n_2
elasto = false
electro = false
polar = true
component = 1
var1 = dpn_2
execute_on = 'timestep_end'
[../]
[./n_3_c]
type = ReworkedRefractiveIndex
variable = n_3
elasto = false
electro = false
polar = true
component = 2
var1 = dpn_3
execute_on = 'timestep_end'
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.11 0.045 0.045 -0.11 0.045 -0.11 -0.029 -0.029 -0.029'
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./ref_index]
############################################
##
## Cubic refractive index BTO
## (need correct value)
##
############################################
type = GenericConstantMaterial
prop_names = 'n1 n2 n3 n4 n5 n6'
prop_values = '2.4272 2.4272 2.4272 0.0 0.0 0.0'
[../]
[./po_tensor]
############################################
##
## PO tensor coefficients from
## Bernasconi and Günter
## J. Appl. Phys., 78, 2651 (1995)
##
############################################
type = GenericConstantMaterial
prop_names = 'g1111 g1122 g1212'
prop_values = '0.15 0.038 0.07'
[../]
[./eo_tensor]
############################################
##
## Elastoptic tensor coefficients from
## Bernasconi and Günter
## J. Appl. Phys., 78, 2651 (1995)
##
############################################
type = GenericConstantMaterial
prop_names = 'p1111 p1122 p1212'
prop_values = '0.37 0.11 -0.30'
[../]
[./eps]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
num_steps = 5
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = test_bire_no_EO
elemental_as_nodal = true
[../]
[]
(test/tests/relaxor/coor.i)
[Mesh]
type = GeneratedMesh
dim = 2
############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y
##
############################################
nx = 60
ny = 60
############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y
##
############################################
xmin = -15
xmax = 15
ymin = -15
ymax = 15
[]
[GlobalParams]
len_scale = 1.0
############################################
##
## BST Landau coefficients from
## Y.H. Huang and L.-Q. Chen et al
## Appl. Phys. Lett. 112, 102901 (2018)
##
############################################
#----------------#
# Units #
#----------------#
T = 210 # Kelvin
#concentration dependent coefficients
alpha01 = 0.08 # nm^2 nN / aC^2
alpha011 = -0.1154 # nm^6 nN / aC^4
alpha012 = 0.653 # nm^6 nN / aC^4
alpha0111 = -2.106 # nm^10 nN / aC^6
alpha0112 = 4.091 # nm^10 nN / aC^6
alpha0123 = -6.688 # nm^10 nN / aC^6
#fixed coefficients
alpha1111 = 75.9 # nm^14 nN / aC^8
alpha1112 = -21.93 # nm^14 nN / aC^8
alpha1122 = -22.21 # nm^14 nN / aC^8
alpha1123 = 24.16 # nm^14 nN / aC^8
# coupling constants
b1 = -1.75
b2 = 1.05
b3 = 0.483
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
############################################
##
## Fourier Noise implementation from
## D. Schwen (INL) - see paper
##
############################################
x = conc
lambda = 5.0 # correlation length for random field (nm)
range = 0.01 # variation of the Sr concentration (plus or minus)
mid = 0.4 # nominal value of the Sr concentration field
potential_E_int = potential_int
seed = 1 #NOTE THAT THE SAME MESH GRID MUST BE USED WITH THE SAME PROCESSOR GROUPING ALWAYS TO COMPARE DOMAIN STRUCTURE EVOLUTION
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
[../]
[./potential_int]
order = FIRST
family = LAGRANGE
[../]
[]
[Functions]
[./fn]
type = SDFourierNoise
# Note that FourierNoise automatically makes concentration periodic which in turn makes the Landau coefficients periodic.
# This then makes the polarization periodic.
[../]
##############################
##
## Define the electric field
## expression to be used below
##
##############################
#[./bc_func_1]
# type = ParsedFunction
# value = 'amplitude*sin(freq*t)'
# vars = 'freq amplitude'
# vals = '${freq} ${amplitude}'
#[../]
[]
[AuxVariables]
[./conc]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = fn
[../]
[../]
#[./Ey]
# order = CONSTANT
# family = MONOMIAL
#[../]
[./fb]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
# [./cEy]
# type = ElecFieldAux
# component = 2
# variable = Ey
# [../]
[./fbk]
type = SDBulkEnergyDensity
variable = fb
[../]
[]
[Materials]
############################################
##
## Gradient coefficients (assumed BTO) from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '1.0 0.51 -0.02 0.02 0.0'
[../]
[./permitivitty_1]
#NOTE: This is a static permittivity contribution from core-electrons.
# This effectively screens the electrostatic interactions.
# For BTO, this value is about 7*e_0, where e_0 is the permitivitty of the vacuum.
# See the brief discussion before sec. IV on pp. 4 of Phys. Rev. B. 74, 104014, (2006)
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.0637501464'
[../]
[]
[Kernels]
#########################################
##
## Landau's problem (no elastic coupling:
##
#########################################
[./bed_x]
type = InhomogeneousBulkEnergyDerivP
variable = polar_x
component = 0
[../]
[./bed_y]
type = InhomogeneousBulkEnergyDerivP
variable = polar_y
component = 1
[../]
[./bed_z]
type = InhomogeneousBulkEnergyDerivP
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
#########################################
##
## Poisson's equation and P*E interaction
##
#########################################
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
#########################################
##
## Time dependence
##
#########################################
[./polar_x_time]
type = TimeDerivativeScaled
variable = polar_x
# Time scale estimate for BTO, from Hlinka (2007)
# We use seconds here
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
##############################
##
## Boundary Condition System
##
## This corresponds to a small
## ac field along the direction
## of the spontaneous polarization
## that was ostensibly put there
## by a strong dc bias.
##
##############################
[./top_pot]
type = DirichletBC
variable = potential_int
boundary = 'top'
value = 0.0
[../]
[./back_pot]
type = DirichletBC
variable = potential_int
boundary = 'bottom'
value = 0.0
[../]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'polar_x polar_y polar_z'
[../]
[../]
[]
[Postprocessors]
[./Fgrad]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Fsdbulk]
type = InhomogeneousBulkEnergy
execute_on = 'initial timestep_end'
block = '0'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fgrad Fsdbulk'
pp_coefs = ' 1 1 '
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-5'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -ksp_rtol -pc_type'
petsc_options_value = ' 121 1e-10 1e-8 bjacobi'
[../]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmin = 1e-10
dt = 3.0
dtmax = 10.0
num_steps = 2
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
file_base = out_test
elemental_as_nodal = true
[../]
[./outCSV]
type = CSV
new_row_tolerance = 1e-16
file_base = out_test
[../]
[]
(test/tests/thermal/thermal_test.i)
[Mesh]
type = GeneratedMesh
dim = 3
nx = 3
ny = 3
nz = 23
xmin = -1
xmax = 1
ymin = -1
ymax = 1
zmin = -8
zmax = 8
elem_type = HEX8
[]
[GlobalParams]
len_scale = 1.0
alpha0 = 0.0003766
Tc = 765.1
alpha11 = -0.07253
alpha111 = 0.26
alpha12 = 0.75
alpha112 = 0.61
alpha123 = -3.67
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
temperature = temperature
[]
[Materials]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.15 0.6 0.0 0.3 0.3'
[../]
[]
[Variables]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-2
max = 0.1e-2
seed = 5
legacy_generator = true
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-2
max = 0.1e-2
seed = 5
legacy_generator = true
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-2
max = 0.1e-2
seed = 5
legacy_generator = true
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./temperature]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
#Bulk energy density
[./bed_x]
type = BulkEnergyDerivativeSixthCoupledT
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeSixthCoupledT
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeSixthCoupledT
variable = polar_z
component = 2
[../]
##Wall energy penalty
[./walled_x]
type=WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type=WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type=WallEnergyDerivative
variable = polar_z
component = 2
[../]
##Electrostatics
[./polar_x_electric_E]
type=PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type=Electrostatics
variable = potential_E_int
block = '0'
[../]
[./polar_electric_px]
type=PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type=PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type=PolarElectricPStrong
variable = polar_z
component = 2
[../]
#temperature kernel
[./t_dif]
type = Diffusion
variable = temperature
[../]
##Time dependence
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./potential_cube5]
type = DirichletBC
boundary = 'front'
value = 0.002
variable = potential_E_int
[../]
[./potential_cube6]
type = DirichletBC
boundary = 'back'
value = 0.002
variable = potential_E_int
[../]
[./t5]
type = DirichletBC
boundary = 'front'
value = 0.0
variable = temperature
[../]
[./t6]
type = DirichletBC
boundary = 'back'
value = 825
variable = temperature
[../]
[]
[Materials]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.5843763'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -pc_factor_zeropivot'
petsc_options_value = ' 121 1e-10 1e-8 1e-6 bjacobi 1e-50 '
[../]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON' #"PJFNK, JFNK, NEWTON"
scheme = 'implicit-euler' #"implicit-euler, explicit-euler, crank-nicolson, bdf2, rk-2"
dtmin = 1e-13
dtmax = 0.5
num_steps = 10
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
file_base = out_thermal_test
elemental_as_nodal = true
[../]
[]
(test/tests/dispersion/genDomain_PzEz.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 2
ny = 2
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.01
max = 0.02
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs00]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs11]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./eigs00]
type = LocalABO3EigenstressAux
variable = eigs00
index_i = 0
index_j = 0
[../]
[./eigs11]
type = LocalABO3EigenstressAux
variable = eigs11
index_i = 1
index_j = 1
[../]
[./eigs22]
type = LocalABO3EigenstressAux
variable = eigs22
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0.0 0.0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_name = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_PzEz
elemental_as_nodal = true
[../]
[]
(test/tests/dispersion/genDomain_PyEz.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 2
ny = 2
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.01
max = 0.02
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs00]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs11]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./eigs00]
type = LocalABO3EigenstressAux
variable = eigs00
index_i = 0
index_j = 0
[../]
[./eigs11]
type = LocalABO3EigenstressAux
variable = eigs11
index_i = 1
index_j = 1
[../]
[./eigs22]
type = LocalABO3EigenstressAux
variable = eigs22
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0.0 0.0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_name = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_PyEz
elemental_as_nodal = true
[../]
[]
(test/tests/film/PTO_film3_T298K.i)
[Mesh]
[gen]
############################################
##=
## Type and dimension of the mesh
##=
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##=
#############################################
nx = 4
ny = 4
nz = 18 #need approximately 90 processors for this since dof is 953133 and we want 10k dof/proc
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -2.0
xmax = 2.0
ymin = -2.0
ymax = 2.0
zmin = -10.0
zmax = 8.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##=
############################################
type = ExtraNodesetGenerator
coord = '-2.0 -2.0 -10.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-2.0 -2.0 -10.0'
block_id = 1
top_right = '2.0 2.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
vol = vol
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
block = '0 1'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
block = '0 1'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
block = '0 1'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## add comments
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##=
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_substr]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[../]
############################################
##
## add comments
##
############################################
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '0'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '220.0 34.4 161.1'
block = '1'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
block = '0 1'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0 1'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0 1'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0 1'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '0 1'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '0 1'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '0 1'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '0 1'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '0 1'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '0 1'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0 1'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0 1'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0 1'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0 1'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 'back'
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 'back'
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 'back'
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '0'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = u_x
u_y = u_y
u_z = u_z
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
block = '0'
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
block = '0'
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
block = '0'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##=
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '4.375 4.375 3.97 0.0 0.0 0.0'
block = '0 1'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##=
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-8 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
num_steps = 5
[]
[Outputs]
###############################################
##===============
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_pto_film_test
elemental_as_nodal = true
interval = 1
[../]
[]
(examples/films/PZTfilm_e12_T298K_E0.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 32
ny = 32
nz = 30
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -16.0
xmax = 16.0
ymin = -16.0
ymax = 16.0
zmin = -10.0
zmax = 20.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-16.0 -16.0 -10.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-16.0 -16.0 -10.0'
block_id = 1
top_right = '16.0 16.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[film_surface]
type = SideSetsFromNormalsGenerator
input = film_interface
normals = '0 0 1'
fixed_normal = true
new_boundary = '107'
[]
[substrate_bottom]
type = SideSetsFromNormalsGenerator
input = film_surface
normals = '0 0 -1'
fixed_normal = true
new_boundary = '108'
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
vol = vol
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_x]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_y]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_z]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./ex]
type = ElecFieldAux
variable = E_x
component = 0
[../]
[./ey]
type = ElecFieldAux
variable = E_y
component = 1
[../]
[./ez]
type = ElecFieldAux
variable = E_z
component = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Landau, electrostrictive, elastic coefficients
## M. Mtebwa, A. K. Tagantsev, and N. Setter
## AIP Adv. 4, 127150 (2014).
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.048889 0.04764 0.1336 0.1735 0.6128 -2.894 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_substr]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '179.073 66.71 82.6446'
block = '0'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '220.0 34.4 161.1'
block = '1'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.0966 0.046 -0.0819'
block = '0 1'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.1608 4.86165 -6.76859'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '179.073 66.71 66.71 179.073 66.71 179.073 82.6446 82.6446 82.6446'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '0'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '0'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '0'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
[./boundary_interface_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = '108'
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = '108'
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = '108'
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total
## energy decomposed into linear combinations of
## the different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '0'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = '0.160218 0.160218 0.160218 0.160218' #converted to eV
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
block = '0'
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
block = '0'
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
block = '0'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[./elapsed]
type = PerfGraphData
section_name = "Root" # for profiling the problem [on]
data_type = total
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '2.1 2.1 1.9056 0.0 0.0 0.0'
block = '0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-4'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 80 1e-8 1e-6 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integ=ration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
[]
[Outputs]
###############################################
##==
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_PTOfilm_e12_T298K_E0_E0
elemental_as_nodal = true
interval = 1
[../]
[]
(test/tests/auxkernels/surface_charge.i)
[Mesh]
[gen]
############################################
##=
## Type and dimension of the mesh
##=
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##=
#############################################
nx = 4
ny = 4
nz = 8
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -1.0
xmax = 1.0
ymin = -1.0
ymax = 1.0
zmin = -2.0
zmax = 2.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-1.0 -1.0 -2.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-1.0 -1.0 -2.0'
block_id = 1
top_right = '1.0 1.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[film_surface]
type = SideSetsFromNormalsGenerator
input = film_interface
normals = '0 0 1'
fixed_normal = true
new_boundary = '107'
[]
[substrate_bottom]
type = SideSetsFromNormalsGenerator
input = film_surface
normals = '0 0 -1'
fixed_normal = true
new_boundary = '108'
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
######################################
##
## divP and surf charge
##
######################################
[./divP]
order = CONSTANT
family = MONOMIAL
block = '0'
[../]
[./surfP]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./divP]
type = DivP
variable = divP
[../]
[./surfP]
type = SurfaceChargeP
variable = surfP
boundary = '107'
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## add comments
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##=
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_substr]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[../]
############################################
##
## add comments
##
############################################
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '0'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '220.0 34.4 161.1'
block = '1'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
block = '0 1'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '0'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '0'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '0'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
[./boundary_interface_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = '108'
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = '108'
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = '108'
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '0'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = '0.160218 0.160218 0.160218 0.160218' #convert to eV
execute_on = 'timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##=
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
block = '0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-4'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##=
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 80 1e-8 1e-5 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integ=ration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
num_steps = 6
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_surface_charge
elemental_as_nodal = true
interval = 1
[../]
[]
(test/tests/dispersion/perturbBTO_PyEz.i)
freq = 177827941.00389227
amplitude = 1e-3
[Mesh]
file = out_PyEz.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
##############################
##
## Define the electric field
## expression to be used below
##
##############################
[./bc_func_1]
type = ParsedFunction
value = 'amplitude*sin(freq*t)'
vars = 'freq amplitude'
vals = '${freq} ${amplitude}'
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_x
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_y
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_z
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./Ez]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./cEy]
type = QuasistaticFieldAux
component = 2
potential_int = potential_E_int
variable = Ez
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0.0 0.0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable = polar_x
# Time scale estimate for BTO, from Hlinka (2007)
# We use seconds here
time_scale = 1e-12
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1e-12
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1e-12
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./front_pot]
type = FunctionDirichletBC
variable = potential_E_int
boundary = 'front'
function = bc_func_1
[../]
[./boundary_grounding]
type = DirichletBC
boundary = 'left right top bottom back'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'initial timestep_end'
[../]
[./Ea]
type = ElementAverageValue
variable = Ez
execute_on = 'initial timestep_end'
[../]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-16
dt = 3.5332947520558995e-10
dtmax = 1e-10
verbose = true
num_steps = 5
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_perturbBTO_PyEz0
elemental_as_nodal = true
[../]
[./outCSV]
type = CSV
new_row_tolerance = 1e-16
file_base = out_perturbBTO_PyEz0
[../]
[]
(examples/monodomain/PZT_monodomain_Tdef.i)
a1temp = a1def
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 8
ny = 8
nz = 8
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -2.0
xmax = 2.0
ymin = -2.0
ymax = 2.0
zmin = -2.0
zmax = 2.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
vol = vol
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-6
max = 0.1e-6
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-6
max = 0.1e-6
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.05
max = 0.1
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs00]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs11]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./eigs00]
type = LocalABO3EigenstressAux
variable = eigs00
index_i = 0
index_j = 0
[../]
[./eigs11]
type = LocalABO3EigenstressAux
variable = eigs11
index_i = 1
index_j = 1
[../]
[./eigs22]
type = LocalABO3EigenstressAux
variable = eigs22
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Landau, electrostrictive, elastic coefficients
## M. Mtebwa, A. K. Tagantsev, and N. Setter
## AIP Adv. 4, 127150 (2014).
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${a1temp} 0.04764 0.1336 0.1735 0.6128 -2.894 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '179.073 66.71 82.6446'
block = '0'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.0966 0.046 -0.0819'
block = '0'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.1608 4.86165 -6.76859'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '179.073 66.71 66.71 179.073 66.71 179.073 82.6446 82.6446 82.6446'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrains_name = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./avePx]
type = ElementAverageValue
variable = polar_x
execute_on = 'timestep_end'
[../]
[./avePy]
type = ElementAverageValue
variable = polar_y
execute_on = 'timestep_end'
[../]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'timestep_end'
[../]
[./ave_e00]
type = ElementAverageValue
variable = e00
execute_on = 'timestep_end'
[../]
[./ave_e11]
type = ElementAverageValue
variable = e11
execute_on = 'timestep_end'
[../]
[./ave_e22]
type = ElementAverageValue
variable = e22
execute_on = 'timestep_end'
[../]
[./Fb]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is smallhotkey for tilde
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-6 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
##
###########################################
dtmax = 1.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./outCSV]
type = CSV
file_base = out_pzt_monodomain_Tdef
[../]
[]
(examples/other/PTO_E0.i)
[Mesh]
file = 2sphere.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi
## and their initial conditions
##
#################################
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-2
max = 0.1e-2
seed = 1
[../]
block = '1 2'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-2
max = 0.1e-2
seed = 2
[../]
block = '1 2'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-2
max = 0.1e-2
seed = 3
[../]
block = '1 2'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[Materials]
#################################################
##
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0' #corresponds to T = 298K
block = '1 2'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '1 2'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '1 2'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '121.0 42.0 37.0'
block = '3'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
block = '1 2'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
block = '1 2'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
block = '1 2'
[../]
[./elasticity_tensor_2]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '121.0 0.0 0.0 121.0 0.0 121.0 0.0 0.0 0.0'
block = '3'
[../]
[./strain_12]
type = ComputeSmallStrain
eigenstrain_names = eigenstrain
[../]
[./stress_12]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
block = '1 2'
[../]
[./permitivitty_2]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '2.6562561'
block = '3'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '1 2'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '1 2'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '1 2'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '1 2'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '1 2'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '1 2'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '1 2'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '1 2'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '1 2'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '1 2'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '1 2'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '1 2'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '1 2'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '1 2 3'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '1 2'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '1 2'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '1 2'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable=u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable=u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./boundary_grounding]
type = DirichletBC
boundary = '1 2 3 4 5 6'
variable = potential_E_int
value = 0.0
[../]
[./elastic_grounding_ux]
type = DirichletBC
boundary = '1 2 3 4 5 6'
variable = u_x
value = 0.0
[../]
[./elastic_grounding_uy]
type = DirichletBC
boundary = '1 2 3 4 5 6'
variable = u_y
value = 0.0
[../]
[./elastic_grounding_uz]
type = DirichletBC
boundary = '1 2 3 4 5 6'
variable = u_z
value = 0.0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '1 2'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 1e-5
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-5'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##=
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-6 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 1.5
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
[./out]
type = Exodus
file_base = out_PTOsphere0_inSTO_2_2
elemental_as_nodal = true
interval = 1
[../]
[./outCSV]
type = CSV
file_base = out_PTOsphere0_inSTO_2_2
[../]
[]
(test/tests/pbc/pbc.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 6
ny = 6
nz = 2
xmin = -6.0
xmax = 6.0
ymin = -6.0
ymax = 6.0
zmin = -2.0
zmax = 2.0
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '-6.0 -6.0 -2.0'
new_boundary = 100
[../]
# additional boundary sideset (one node) to zero one of the elastic displacement vectors - eliminates rigid body translations from the degrees of freedom
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 6
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 6
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 6
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 0.42 0.735 0.26 0.61 -3.67 0 0 0 0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175 79.4 111.1'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.089 0.026 0.026 -0.089 0.026 -0.089 -0.03375 -0.03375 -0.03375'
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
#note below we use a strain-renormalized functional for lead titanate (this is different than the stress-free functionals typically used)
# they are related by a Legendre transformation
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
#[./elapsed]
# type = PerfGraphData
# section_name = "Root"
# data_type = total
#[../]
#[./nodes]
# type = NumNodes
#[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-8 1e-8 bjacobi allreduce'
[../]
[]
#[Debug]
# show_var_residual_norms = true
#[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 0.8
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
num_steps = 10
#[./Adaptivity]
# coarsen_fraction = 0.1
# refine_fraction = 0.7
# max_h_level = 1
#[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
[./out]
type = Exodus
file_base = out_pbc
elemental_as_nodal = true
interval = 5
[../]
[./outCSV]
type = CSV
file_base = out_pbc
[../]
[]
(test/tests/electrostatics/Ferro_para_superlattice.i)
#############################################################
# TEMPORARILY DEACTIVATED
############################################################
#alpha1 alpha3
alpha1 = '-0.0827836 -0.250056'
#alpha11 alpha33
alpha11 = '0.42229 0.04990909090909092'
#alpha12 alpha13
alpha12 = '0.734181277056277 0.4521818181818182'
alpha111 = 0.0#0.26
alpha112 = 0.0#0.61
alpha123 = 0.0#-3.7
alpha1_para = '0.1854662 0.1854662'
alpha11_para = '0.0 0.0'
alpha12_para = '0.0 0.0'
alpha111_para = 0.0
alpha112_para = 0.0
alpha123_para = 0.0
G110 = 0.173
G11_G110 = 1.6
G12_G110 = 0
G44_G110 = 1.6
G44P_G110 = 1.6
G110_para = 0.173
G11_G110_para = 1.6
G12_G110_para = 0
G44_G110_para = 1.6
G44P_G110_para = 1.6
permittivity_electrostatic = 0.0885
permittivity_electrostatic_para = 0.0885
permitivitty_depol = 0.00885
permitivitty_depol_para = 0.00885
[Mesh]
type = FileMesh
file = template_mesh.msh
[]
[GlobalParams]
len_scale = 1.0
[]
[Variables]
[./FE_polar_x]
order = FIRST
family = LAGRANGE
block = 'ferro_volume'
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./FE_polar_y]
order = FIRST
family = LAGRANGE
block = 'ferro_volume'
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./FE_polar_z]
order = FIRST
family = LAGRANGE
block = 'ferro_volume'
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./PE_polar_x]
order = FIRST
family = LAGRANGE
block = 'para_bottom_volume para_top_volume'
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./PE_polar_y]
order = FIRST
family = LAGRANGE
block = 'para_bottom_volume para_top_volume'
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./PE_polar_z]
order = FIRST
family = LAGRANGE
block = 'para_bottom_volume para_top_volume'
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-5
max = 0.01e-5
seed = 5
legacy_generator = true
[../]
[../]
[]
[Kernels]
#FERROELECTRIC BLOCK
[./bed_x_ferro]
type = BulkEnergyDerivativeSixth
block = 'ferro_volume'
variable = FE_polar_x
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
alpha1 = ${alpha1}
alpha11 = ${alpha11}
alpha12 = ${alpha12}
alpha111 = ${alpha111}
alpha112 = ${alpha112}
alpha123 = ${alpha123}
component = 0
[../]
[./bed_y_ferro]
type = BulkEnergyDerivativeSixth
block = 'ferro_volume'
variable = FE_polar_y
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
alpha1 = ${alpha1}
alpha11 = ${alpha11}
alpha12 = ${alpha12}
alpha111 = ${alpha111}
alpha112 = ${alpha112}
alpha123 = ${alpha123}
component = 1
[../]
[./bed_z_ferro]
type = BulkEnergyDerivativeSixth
block = 'ferro_volume'
variable = FE_polar_z
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
alpha1 = ${alpha1}
alpha11 = ${alpha11}
alpha12 = ${alpha12}
alpha111 = ${alpha111}
alpha112 = ${alpha112}
alpha123 = ${alpha123}
component = 2
[../]
[./polar_x_electric_E_ferro]
type = PolarElectricEStrong
block = 'ferro_volume'
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
variable = potential_E_int
[../]
[./FE_E_int_ferro]
type = Electrostatics
block = 'ferro_volume'
variable = potential_E_int
permittivity = ${permittivity_electrostatic}
[../]
[./polar_electric_px_ferro]
type = PolarElectricPStrong
block = 'ferro_volume'
variable = FE_polar_x
potential_E_int = potential_E_int
component = 0
[../]
[./polar_electric_py_ferro]
type = PolarElectricPStrong
block = 'ferro_volume'
variable = FE_polar_y
potential_E_int = potential_E_int
component = 1
[../]
[./polar_electric_pz_ferro]
type = PolarElectricPStrong
block = 'ferro_volume'
variable = FE_polar_z
potential_E_int = potential_E_int
component = 2
[../]
G110 = 0.173
G11_G110 = 1.6
G12_G110 = 0
G44_G110 = 1.6
G44P_G110 = 1.6
G110_para = 0.173
G11_G110_para = 1.6
G12_G110_para = 0
G44_G110_para = 1.6
G44P_G110_para = 1.6
[./walled_x_ferro]
type = WallEnergyDerivative
block = 'ferro_volume'
variable = FE_polar_x
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
component = 0
[../]
[./walled_y_ferro]
type = WallEnergyDerivative
block = 'ferro_volume'
variable = FE_polar_y
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
component = 1
[../]
[./walled_z_ferro]
type = WallEnergyDerivative
block = 'ferro_volume'
variable = FE_polar_z
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
component = 2
[../]
[./polar_x_time_ferro]
type = TimeDerivativeScaled
block = 'ferro_volume'
variable = FE_polar_x
[../]
[./polar_y_time_ferro]
type = TimeDerivativeScaled
block = 'ferro_volume'
variable = FE_polar_y
[../]
[./polar_z_time_ferro]
type = TimeDerivativeScaled
block = 'ferro_volume'
variable = FE_polar_z
[../]
#PARAELECTRIC BLOCK
[./bed_xp_para]
alpha1111 = 0
alpha1112 = 0
alpha1122 = 0
alpha1123 = 0
type = BulkEnergyDerivativeSixth
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_x
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
alpha1 = ${alpha1_para}
alpha11 = ${alpha11_para}
alpha12 = ${alpha12_para}
alpha111 = ${alpha111_para}
alpha112 = ${alpha112_para}
alpha123 = ${alpha123_para}
component = 0
[../]
[./bed_yp_para]
alpha1111 = 0
alpha1112 = 0
alpha1122 = 0
alpha1123 = 0
type = BulkEnergyDerivativeSixth
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_y
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
alpha1 = ${alpha1_para}
alpha11 = ${alpha11_para}
alpha12 = ${alpha12_para}
alpha111 = ${alpha111_para}
alpha112 = ${alpha112_para}
alpha123 = ${alpha123_para}
component = 1
[../]
[./bed_zp_para]
alpha1111 = 0
alpha1112 = 0
alpha1122 = 0
alpha1123 = 0
type = BulkEnergyDerivativeSixth
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_z
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
alpha1 = ${alpha1_para}
alpha11 = ${alpha11_para}
alpha12 = ${alpha12_para}
alpha111 = ${alpha111_para}
alpha112 = ${alpha112_para}
alpha123 = ${alpha123_para}
component = 2
[../]
[./polar_x_electric_Ep_para]
type = PolarElectricEStrong
block = 'para_bottom_volume para_top_volume'
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
variable = potential_E_int
[../]
[./FE_E_intp_para]
type = Electrostatics
block = 'para_bottom_volume para_top_volume'
variable = potential_E_int
permittivity = ${permittivity_electrostatic_para}
[../]
[./polar_electric_pxp_para]
type = PolarElectricPStrong
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_x
potential_E_int = potential_E_int
component = 0
[../]
[./polar_electric_pyp_para]
type = PolarElectricPStrong
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_y
potential_E_int = potential_E_int
component = 1
[../]
[./polar_electric_pzp_para]
type = PolarElectricPStrong
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_z
potential_E_int = potential_E_int
component = 2
[../]
[./walled_xp_para]
type = WallEnergyDerivative
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_x
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
component = 0
[../]
[./walled_yp_para]
type = WallEnergyDerivative
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_y
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
component = 1
[../]
[./walled_zp_para]
type = WallEnergyDerivative
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_z
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
component = 2
[../]
[./polar_x_timep_para]
type = TimeDerivativeScaled
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_x
[../]
[./polar_y_timep_para]
type = TimeDerivativeScaled
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_y
[../]
[./polar_z_timep_para]
type = TimeDerivativeScaled
block = 'para_bottom_volume para_top_volume'
variable = PE_polar_z
[../]
[]
[BCs]
[./top_phi]
type = DirichletBC
variable = potential_E_int
value = 0.0001
boundary = 'para_top_surface_top'
[../]
[./bottom_phi]
type = DirichletBC
variable = potential_E_int
value = 0.0
boundary = 'para_bottom_surface_bottom'
[../]
[./Periodic]
[./per1]
variable = 'PE_polar_x PE_polar_y PE_polar_z potential_E_int'
primary = 'para_top_side_1'
secondary = 'para_top_side_3'
translation = '0 1 0'
[../]
[./per2]
variable = 'PE_polar_x PE_polar_y PE_polar_z potential_E_int'
primary = 'para_bottom_side_1'
secondary = 'para_bottom_side_3'
translation = '0 1 0'
[../]
[./per3]
variable = 'PE_polar_x PE_polar_y PE_polar_z potential_E_int'
primary = 'para_top_side_4'
secondary = 'para_top_side_2'
translation = '1 0 0'
[../]
[./per4]
variable = 'PE_polar_x PE_polar_y PE_polar_z potential_E_int'
primary = 'para_bottom_side_4'
secondary = 'para_bottom_side_2'
translation = '1 0 0'
[../]
[./per5]
variable = 'FE_polar_x FE_polar_y FE_polar_z potential_E_int'
primary = 'ferro_side_4'
secondary = 'ferro_side_2'
translation = '1 0 0'
[../]
[./per6]
variable = 'FE_polar_x FE_polar_y FE_polar_z potential_E_int'
primary = 'ferro_side_1'
secondary = 'ferro_side_3'
translation = '0 1 0'
[../]
[../]
[]
[Postprocessors]
[./aveFEPz]
type = ElementAverageValue
variable = FE_polar_z
execute_on = 'initial timestep_end'
block = 'ferro_volume'
#'initial linear nonlinear timestep_begin timestep_end'
[../]
[./avePEPz]
type = ElementAverageValue
variable = PE_polar_z
execute_on = 'initial timestep_end'
block = 'para_bottom_volume para_top_volume'
#'initial linear nonlinear timestep_begin timestep_end'
[../]
[./Fbulk_ferro]
type = BulkEnergy
block = 'ferro_volume'
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
alpha1 = ${alpha1}
alpha11 = ${alpha11}
alpha12 = ${alpha12}
alpha111 = ${alpha111}
alpha112 = ${alpha112}
alpha123 = ${alpha123}
execute_on = 'initial timestep_end'
[../]
[./Fwall_ferro]
type = WallEnergy
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
G110 = ${G110}
G11_G110 = ${G11_G110}
G12_G110 = ${G12_G110}
G44_G110 = ${G44_G110}
G44P_G110 = ${G44P_G110}
block = 'ferro_volume'
execute_on = 'initial timestep_end'
[../]
[./Felec_ferro]
type = ElectrostaticEnergy
block = 'ferro_volume'
polar_x = FE_polar_x
polar_y = FE_polar_y
polar_z = FE_polar_z
potential_E_int = potential_E_int
execute_on = 'initial timestep_end'
[../]
[./Fbulk_para]
type = BulkEnergy
block = 'para_bottom_volume para_top_volume'
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
alpha1 = ${alpha1_para}
alpha11 = ${alpha11_para}
alpha12 = ${alpha12_para}
alpha111 = ${alpha111_para}
alpha112 = ${alpha112_para}
alpha123 = ${alpha123_para}
execute_on = 'initial timestep_end'
[../]
[./Fwall_para]
type = WallEnergy
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
G110 = ${G110_para}
G11_G110 = ${G11_G110_para}
G12_G110 = ${G12_G110_para}
G44_G110 = ${G44_G110_para}
G44P_G110 = ${G44P_G110_para}
block = 'para_bottom_volume para_top_volume'
execute_on = 'initial timestep_end'
[../]
[./Felec_para]
type = ElectrostaticEnergy
block = 'para_bottom_volume para_top_volume'
polar_x = PE_polar_x
polar_y = PE_polar_y
polar_z = PE_polar_z
potential_E_int = potential_E_int
execute_on = 'initial timestep_end'
[../]
[./perc_change_ferro]
type = PercentChangePostprocessor
postprocessor = Fbulk_ferro
[../]
[]
[UserObjects]
[./kill]
type = Terminator
expression = 'perc_change_ferro <= 2.5e-6'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type '
petsc_options_value = ' 120 1e-10 1e-8 1e-5 bjacobi'
[../]
[]
[Executioner]
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.4
cutback_factor = 0.9
optimal_iterations = 7
[../]
type = Transient
solve_type = 'PJFNK' #"PJFNK, JFNK, NEWTON"
scheme = 'bdf2' #"implicit-euler, explicit-euler, crank-nicolson, bdf2, rk-2"
dtmax = 1.0
num_steps = 25
[]
[Outputs]
print_linear_residuals = false
[./out]
type = Exodus
execute_on = 'timestep_end'
file_base = out_split_polar
elemental_as_nodal = true
interval = 1
[../]
[]
(test/tests/film/PTO_film3_T298K_noP.i)
[Mesh]
[gen]
############################################
##=
## Type and dimension of the mesh
##=
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##=
#############################################
nx = 4
ny = 4
nz = 18 #need approximately 90 processors for this since dof is 953133 and we want 10k dof/proc
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -2.0
xmax = 2.0
ymin = -2.0
ymax = 2.0
zmin = -10.0
zmax = 8.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##=
############################################
type = ExtraNodesetGenerator
coord = '-2.0 -2.0 -10.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-2.0 -2.0 -10.0'
block_id = 1
top_right = '2.0 2.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
vol = vol
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-5
max = 0.1e-5
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## add comments
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##=
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_substr]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[../]
############################################
##
## add comments
##
############################################
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '0'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '220.0 34.4 161.1'
block = '1'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
block = '0 1'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '0'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '0'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '0'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 'back'
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 'back'
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 'back'
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '0'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = u_x
u_y = u_y
u_z = u_z
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
block = '0'
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
block = '0'
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
block = '0'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##=
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '4.375 4.375 3.97 0.0 0.0 0.0'
block = '0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##=
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-8 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
num_steps = 5
[]
[Outputs]
###############################################
##===============
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_pto_film_noP_test
elemental_as_nodal = true
interval = 1
[../]
[]
(test/tests/electrostatics/FE_8nmFilm_Die_4nmLayer_U0.i)
[Mesh]
[gen]
#######################################################
##
## Type and dimension of the mesh
##
#######################################################
type = GeneratedMeshGenerator
dim = 2
#######################################################
##
## Finite element grid definition. For ferroelectric
## calculations, this should be limited by the
## domain wall width. We suggest ~1.2-2 elements per
## 1 nm of spatial resolution)
##
#######################################################
nx = 150
ny = 20
#######################################################
##
## Actual spatial coordinates of mesh.
## Units are in nanometers. Note the above constraint
##
#######################################################
xmin = -30.0
xmax = 30.0
ymin = -4.0
ymax = 4.0
#######################################################
##
## Finite element type/order (hexahedral, tetrahedral)
##
#######################################################
elem_type = QUAD4
[]
[subdomains1]
#######################################################
##
## One of the many mesh modifiers in MOOSE
## This one splits the computational domain into
## two (and then three) different layers
## These layers are where we change the physics to
## reflect the different materials
##
#######################################################
type = SubdomainBoundingBoxGenerator
input = gen
bottom_left = '-30.0 3.0 0.0'
block_id = 1
top_right = '30.0 4.0 0.0'
[]
[subdomains2]
type = SubdomainBoundingBoxGenerator
input = subdomains1
bottom_left = '-30.0 -4.0 0.0'
block_id = 2
top_right = '30.0 -3.0 0.0'
[]
[]
[GlobalParams]
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
potential_E_int = potential_E_int
[]
[Variables]
#################################
##
## Variable definitions
## Px, Py, \Phi
## and their initial conditions
##
#################################
[./polar_x]
order = FIRST
family = LAGRANGE
block = '0 1 2'
[./InitialCondition]
type = RandomIC
min = -0.01e-6
max = 0.01e-6
seed = 6
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
block = '0 1 2'
[./InitialCondition]
type = RandomIC
min = -0.01e-6
max = 0.01e-6
seed = 6
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1 2'
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and gradient
## coefficients retrieved from
## Park and Hwang
## Adv. Mater. 2019, 31, 1805266
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027722 -0.6381 0.0 7.89 0.0 0.0 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_die_layer]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '8.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0' # arbitrary positive value set
block = '1 2'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.0138 0.0 0.0138 0.0' #note the 0.5 out front is set with G110 instead of in the expression.
[../]
[./in_P_susc]
type = GenericConstantMaterial
prop_names = 'chi'
prop_values = '10.0' # arbitrary positive value set
[../]
###############################################
##
## Background dielectric constant of the
## dielectric layer. It is isotropic e_d = 208
## where e_0 = 0.008854187 in Ferret's units
##
##############################################
[./permitivitty]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '1.84167'
block = '1 2'
[../]
[./eps1]
###############################################
##
## background dielectric constant of the
## ferroelectric layer is anisotropic with two
## components. Note that e_0 is 0.008854187 in
## Ferret's native units
##
##############################################
type = GenericConstantMaterial
prop_names = 'eps1 eps2 eps3'
prop_values = '3.692195979 1.5450556315 0.0'
block = '0'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
[./bed_FE_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_FE_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./ip_FE_x]
type = InPlaneSusceptibilityDerivative
variable = polar_x
block = '0'
[../]
[./bed_die_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '1 2'
[../]
[./bed_die_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '1 2'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0 1 2'
[../]
[./FE_E_int]
type = AnisotropicElectrostatics
variable = potential_E_int
block = '0'
[../]
[./die_E_int]
type = Electrostatics
variable = potential_E_int
block = '1 2'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0 1 2'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0 1 2'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable = polar_x
###############################################
##
## Comments on time_scale:
## time_scale is equal to 1/Gamma
## currently it is set to 1.0
## which means the time scale of the
## problem is "quasi-static". It can be
## turned into real units easily.
##
##############################################
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[]
[BCs]
####################################################
##
## Simple BC: periodicity along x direction in
## the polar field and Dirichlet conditions on the
## electrostatic potential at the electrodes
##
####################################################
[./Periodic]
[./xyz]
auto_direction = 'x'
variable = 'polar_x polar_y'
[../]
[../]
[./boundary_top_grounding]
type = DirichletBC
boundary = 'top'
variable = potential_E_int
value = 0.0
[../]
[./boundary_bottom_grounding]
type = DirichletBC
boundary = 'bottom'
variable = potential_E_int
value = 0.0
[../]
[]
[Postprocessors]
####################################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total
## energy decomposed into linear combinations of
## the different physics. Note that we only track
## the energy of the ferroelectric layer
## The dielectric layer also can be tracked if you
## want.
##
####################################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felec'
pp_coefs = ' 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
####################################################
##
## terminator to end energy evolution when the
## energy difference between subsequent time steps
## is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
####################################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-5'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO/HFO more
## like dt = 3-10
##
###########################################
dtmax = 8.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 12
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.1
[../]
verbose = true
num_steps = 2
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_FE_8nmFilm_Die_4nmLayer_U0
elemental_as_nodal = true
interval = 1
[../]
[./outCSV]
type = CSV
file_base = out_FE_8nmFilm_Die_4nmLayer_U0
[../]
[]
(examples/domain_walls/BTO_90wall_T298K.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
nx = 60
ny = 60
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -30.0
xmax = 30.0
ymin = -30.0
ymax = 30.0
zmin = -1.0
zmax = 1.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
vol = vol
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
[./stripe1]
type = ParsedFunction
value = 0.1*cos(0.10471975511965977*((x+5)+(y+5)))+0.1 # 0.10471975511965977 = pi/(xmax-xmin)
[../]
[./stripe2]
type = ParsedFunction
value = -0.1*cos(0.10471975511965977*((x+5)+(y+5)))+0.1
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'stripe1'
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'stripe2'
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.11 0.045 0.045 -0.11 0.045 -0.11 -0.029 -0.029 -0.029'
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fb]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-6 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_bto_90wall_T298K_2
elemental_as_nodal = true
[../]
[./console]
type = Console
time_precision = 3
[../]
[]
(test/tests/msca/BFO_dwP1A1_100.i)
Nx = 100
Ny = 1
Nz = 1
xMax = 9.42477796076938
yMax = 1.0
zMax = 1.0
freq = 0.2122065907891938
g11 = 12e-3
g12 = -3.0e-3
g44 = 3.0e-3
h11 = 2.0e-4
h12 = -0.2e-3
h44 = 0.8e-3
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${Nx}
ny = ${Ny}
nz = ${Nz}
xmin = 0.0
xmax = ${xMax}
ymin = 0.0
ymax = ${yMax}
zmin = 0.0
zmax = ${zMax}
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
antiphase_A_x = antiphase_A_x
antiphase_A_y = antiphase_A_y
antiphase_A_z = antiphase_A_z
displacements = 'u_x u_y u_z'
potential_E_int = potential_E_int
[]
[Functions]
[./stripeP1]
type = ParsedFunction
value = 0.54*cos(${freq}*(x))
[../]
[./stripeP2]
type = ParsedFunction
value = -0.54*cos(${freq}*(x))
[../]
[./stripeA1]
type = ParsedFunction
value = 7.37*cos(${freq}*(x))
[../]
[./stripeA2]
type = ParsedFunction
value = -7.37*cos(${freq}*(x))
[../]
[./constPm]
type = ParsedFunction
value = -0.54
[../]
[./constPp]
type = ParsedFunction
value = 0.54
[../]
[./constAm]
type = ParsedFunction
value = -7.37
[../]
[./constAp]
type = ParsedFunction
value = 7.37
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = stripeP1
[../]
[../]
[./antiphase_A_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = stripeA1
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e21]
order = CONSTANT
family = MONOMIAL
[../]
[./e02]
order = CONSTANT
family = MONOMIAL
[../]
[./e20]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e21]
type = RankTwoAux
variable = e21
rank_two_tensor = total_strain
index_i = 2
index_j = 1
[../]
[./e20]
type = RankTwoAux
variable = e20
rank_two_tensor = total_strain
index_i = 2
index_j = 0
[../]
[./e02]
type = RankTwoAux
variable = e02
rank_two_tensor = total_strain
index_i = 0
index_j = 2
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[Kernels]
[./TensorMechanics]
[../]
[./rotostr_ux]
type = RotostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./rotostr_uy]
type = RotostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./rotostr_uz]
type = RotostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
### Operators for the polar field: ###
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
[./walled_a_x]
type = AFDWallEnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled_a_y]
type = AFDWallEnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled_a_z]
type = AFDWallEnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./walled2_a_x]
type = AFDWall2EnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled2_a_y]
type = AFDWall2EnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled2_a_z]
type = AFDWall2EnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./roto_polar_coupled_x]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_x
component = 0
[../]
[./roto_polar_coupled_y]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_y
component = 1
[../]
[./roto_polar_coupled_z]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_z
component = 2
[../]
[./roto_dis_coupled_x]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_x
component = 0
[../]
[./roto_dis_coupled_y]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_y
component = 1
[../]
[./roto_dis_coupled_z]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
#Operators for the AFD field
[./rbed_x]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_x
component = 0
[../]
[./rbed_y]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_y
component = 1
[../]
[./rbed_z]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_z
component = 2
[../]
[./rotostr_dis_coupled_x]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_y]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_z]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./a_x_time]
type = TimeDerivativeScaled
variable = antiphase_A_x
time_scale = 0.01
block = '0'
[../]
[./a_y_time]
type = TimeDerivativeScaled
variable = antiphase_A_y
time_scale = 0.01
block = '0'
[../]
[./a_z_time]
type = TimeDerivativeScaled
variable = antiphase_A_z
time_scale = 0.01
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-2.81296 1.72351 2.24147 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_A]
type = GenericConstantMaterial
prop_names = 'beta1 beta11 beta12 beta111 beta112 beta123 beta1111 beta1112 beta1122 beta1123'
prop_values = '-0.0137763 0.0000349266 0.0000498846 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./P_A_couple]
type = GenericConstantMaterial
prop_names = 't1111 t1122 t1212 t42111111 t24111111 t42111122 t24112222 t42112233 t24112233 t42112211 t24111122 t42111212 t42123312 t24121112 t24121233 t6211111111 t2611111111 t6211111122 t2611222222 t4411111111 t4411112222'
prop_values = '0.012516 0.0180504 -0.036155 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '1.0 ${g11} ${g12} ${g44} 0.0'
[../]
[./Landau_H]
type = GenericConstantMaterial
prop_names = 'H110 H11_H110 H12_H110 H44_H110 H44P_H110'
prop_values = '1.0 ${h11} ${h12} ${h44} 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '295.179 117.567 74.0701'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.0603833 0.0111245 -0.0175686'
[../]
[./mat_R]
type = GenericConstantMaterial
prop_names = 'R11 R12 R44'
prop_values = '-0.0000878064 0.0000295306 0.0000627962'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-30.4162 -5.01496 -10.4105'
#the point is the following: use a slightly different definition of Q_ij than Hlinka
[../]
[./mat_r]
type = GenericConstantMaterial
prop_names = 'r11 r12 r44'
prop_values = '-0.0379499 0.00373096 0.0372105'
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '295.179 117.567 117.567 295.179 117.567 295.179 74.0701 74.0701 74.0701'
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Postprocessors]
[./dt]
type = TimestepSize
[../]
[./FbP]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FbA]
type = RotoBulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FcPA]
type = RotoPolarCoupledEnergyEighth
execute_on = 'timestep_end'
[../]
[./FgP]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./FgA]
type = AFDWallEnergy
execute_on = 'timestep_end'
[../]
[./FcPu]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./FcAu]
type = RotostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./Felu]
type = ElasticEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'FbP FbA FgP FgA FcPA FcPu FcAu Felu Fele'
pp_coefs = ' 1 1 1 1 1 1 1 1 1'
execute_on = 'timestep_end'
##########################################
#
# NOTE: Ferret output is in attojoules
#
##########################################
[../]
[./perc_change]
type = EnergyRatePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
dt = dt
[../]
[]
[BCs]
[./Periodic]
[./x]
auto_direction = 'x'
variable = 'u_x u_y u_z polar_x polar_y polar_z antiphase_A_x antiphase_A_y antiphase_A_z'
[../]
[./xyz]
auto_direction = 'x y z'
variable = 'potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalBFOMaterialRVEUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-7'
[../]
[]
#=
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 121 1e-8 1e-7 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 10.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 25 #usually 10
linear_iteration_ratio = 100
dt = 0.08
growth_factor = 1.1
[../]
num_steps = 3
[]
#=
[Outputs]
print_linear_residuals = false
perf_graph_live = false
[./out]
type = Exodus
file_base = BFO_dwP1A1_100
elemental_as_nodal = true
[../]
[]
(test/tests/domain_wall/test_BTO_domain_wall.i)
############################################
##
## to use this file, scale up size and add
## the functionIC to the polar field for the
## appropriate wall
## current Nov 2020 tests benchmark this
## within 10% of FFT calculations using the
## same functional
##
############################################
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 2
ny = 2
nz = 2
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
[./stripe1]
type = ParsedFunction
value = 0.01*cos(0.08975979010256552*(x))
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE1: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
## NOTE2: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.11 0.045 0.045 -0.11 0.045 -0.11 -0.029 -0.029 -0.029'
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./wall2ed_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./wall2ed_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./wall2ed_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-8 1e-8 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
## for PTO is about 0.8 but BTO more like 3-10
##
###########################################
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
num_steps = 4
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = test
elemental_as_nodal = true
[../]
[]
(tutorial/film.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
nx = 32
ny = 32
nz = 30
xmin = -16.0
xmax = 16.0
ymin = -16.0
ymax = 16.0
zmin = -10.0
zmax = 20.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-16.0 -16.0 -10.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-16.0 -16.0 -10.0'
block_id = 1
top_right = '16.0 16.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[film_surface]
type = SideSetsFromNormalsGenerator
input = film_interface
normals = '0 0 1'
fixed_normal = true
new_boundary = '107'
[]
[substrate_bottom]
type = SideSetsFromNormalsGenerator
input = film_surface
normals = '0 0 -1'
fixed_normal = true
new_boundary = '108'
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
vol = vol
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '0'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '0'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '0'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_x]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_y]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_z]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Landau coefficients from Li et al (2001)
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_substr]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '0'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '220.0 34.4 161.1'
block = '1'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
block = '0 1'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
[./boundary_interface_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = '108'
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = '108'
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = '108'
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total
## energy decomposed into linear combinations of
## the different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '0'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = '0.160218 0.160218 0.160218 0.160218' #converted to eV
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
block = '0'
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
block = '0'
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
block = '0'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[./elapsed]
type = PerfGraphData
section_name = "Root" # for profiling the problem [on]
data_type = total
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '2.1 2.1 1.9056 0.0 0.0 0.0'
block = '0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-4'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 80 1e-8 1e-6 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integ=ration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
[]
[Outputs]
###############################################
##==
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_PTOfilm_e12_T298K_E0_E0
elemental_as_nodal = true
interval = 1
[../]
[]
(examples/other/PZT_nanowire_test.i)
[Mesh]
file = exodus_nanowire_rad20_h60.e
[]
[GlobalParams]
len_scale = 1.0
alpha1 = -0.14937
alpha11 = -0.0305
alpha111 = 0.2475
alpha12 = 0.632
alpha112 = 0.9684
alpha123 = -4.901
G110 = 0.173
G11_G110 = 2.0
G12_G110 = 0
G44_G110 = 1.0
G44P_G110 = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_int = potential_int
disp_x = disp_x
disp_y = disp_y
disp_z = disp_z
displacements = 'disp_x disp_y disp_z'
prefactor = 0.00 #negative = tension, positive = compression
[]
[Variables]
[./polar_x]
block = '1'
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.5e-5
max = 0.5e-5
seed = 1
[../]
[../]
[./polar_y]
block = '1'
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.5e-5
max = 0.5e-5
seed = 1
[../]
[../]
[./polar_z]
block = '1'
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.5e-5
max = 0.5e-5
seed = 1
[../]
[../]
[./potential_int]
order = FIRST
family = LAGRANGE
block = '1 2'
[./InitialCondition]
type = RandomIC
min = -0.5e-5
max = 0.5e-5
seed = 1
[../]
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
block = '1 2'
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
block = '1 2'
[../]
[./disp_z]
order = FIRST
family = LAGRANGE
block = '1 2'
[../]
[]
[AuxVariables]
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = stress_xx
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = stress_yy
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = stress_xy
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = stress_xz
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = stress_zz
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = stress_yz
[../]
[./strain_xx_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = strain_xx
[../]
[./strain_yy_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = strain_yy
[../]
[./strain_xy_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = strain_xy
[../]
[./strain_xz_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = strain_xz
[../]
[./strain_zz_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = strain_zz
[../]
[./strain_yz_elastic]
order = CONSTANT
family = MONOMIAL
#initial_from_file_var = strain_yz
[../]
[./chern]
order = CONSTANT
family = MONOMIAL
[../]
[./chernMag]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./cherndens]
type = ChernSimonsDensity
variable = chern
[../]
[./cherndensMag]
type = ChernSimonsDensityMag
block = '1'
variable = chernMag
[../]
[./matl_e11]
type = RankTwoAux
rank_two_tensor = elastic_strain
index_i = 0
index_j = 0
variable = strain_xx_elastic
execute_on = 'timestep_end'
[../]
[./matl_e12]
type = RankTwoAux
rank_two_tensor = elastic_strain
index_i = 0
index_j = 1
variable = strain_xy_elastic
execute_on = 'timestep_end'
[../]
[./matl_e13]
type = RankTwoAux
rank_two_tensor = elastic_strain
index_i = 0
index_j = 2
variable = strain_xz_elastic
execute_on = 'timestep_end'
[../]
[./matl_e22]
type = RankTwoAux
rank_two_tensor = elastic_strain
index_i = 1
index_j = 1
variable = strain_yy_elastic
execute_on = 'timestep_end'
[../]
[./matl_e23]
type = RankTwoAux
rank_two_tensor = elastic_strain
index_i = 1
index_j = 2
variable = strain_yz_elastic
execute_on = 'timestep_end'
[../]
[./matl_e33]
type = RankTwoAux
rank_two_tensor = elastic_strain
index_i = 2
index_j = 2
variable = strain_zz_elastic
execute_on = 'timestep_end'
[../]
[./matl_s11]
type = RankTwoAux
rank_two_tensor = stress
index_i = 0
index_j = 0
variable = stress_xx_elastic
execute_on = 'timestep_end'
[../]
[./matl_s12]
type = RankTwoAux
rank_two_tensor = stress
index_i = 0
index_j = 1
variable = stress_xy_elastic
execute_on = 'timestep_end'
[../]
[./matl_s13]
type = RankTwoAux
rank_two_tensor = stress
index_i = 0
index_j = 2
variable = stress_xz_elastic
execute_on = 'timestep_end'
[../]
[./matl_s22]
type = RankTwoAux
rank_two_tensor = stress
index_i = 1
index_j = 1
variable = stress_yy_elastic
execute_on = 'timestep_end'
[../]
[./matl_s23]
type = RankTwoAux
rank_two_tensor = stress
index_i = 1
index_j = 2
variable = stress_yz_elastic
execute_on = 'timestep_end'
[../]
[./matl_s33]
type = RankTwoAux
rank_two_tensor = stress
index_i = 2
index_j = 2
variable = stress_zz_elastic
execute_on = 'timestep_end'
[../]
[]
[Materials]
[./eigen_strain_zz] #Use for stress-free strain (ie epitaxial)
type = ComputeEigenstrain
block = '1 2'
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1 0 0 0 1 0 0 0 0'
eigenstrain_name = eigenstrain
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
#from MaterialsProject
C_ijkl = '281 115.74 115.74 281 115.74 281 97.18 97.18 97.18'
block = '1'
[../]
[./strain_1]
type = ComputeSmallStrain
block = '1'
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
block = '1'
[../]
[./slab_ferroelectric]
block = '1'
type = ComputeElectrostrictiveTensor
Q_mnkl = '0.0842 -0.02446 -0.02446 0.0842 -0.02446 0.0842 0.06417 0.06417 0.06417'
C_ijkl = '281 115.74 115.74 281 115.74 281 97.18 97.18 97.18'
[../]
[./elasticity_tensor_2]
type = ComputeElasticityTensor
#averaged from BulkMod
C_ijkl = '319 99.6 99.6 319 99.6 319 109.53 109.53 109.53'
fill_method = symmetric9
block = '2'
[../]
[./strain_2]
type = ComputeSmallStrain
block = '2'
eigenstrain_names = eigenstrain
[../]
[./stress_2]
type = ComputeLinearElasticStress
block = '2'
[../]
[]
[Kernels]
#Elastic problem
[./TensorMechanics]
#This is an action block
[../]
#Bulk energy density
[./bed_x]
type = BulkEnergyDerivativeSixth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeSixth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeSixth
variable = polar_z
component = 2
[../]
##Wall energy penalty
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
##Polarization-strain coupling
[./ferroelectriccouplingp_xx]
type = FerroelectricCouplingP
variable = polar_x
component = 0
[../]
[./ferroelectriccouplingp_yy]
type = FerroelectricCouplingP
variable = polar_y
component = 1
[../]
[./ferroelectriccouplingp_zz]
type = FerroelectricCouplingP
variable = polar_z
component = 2
[../]
[./ferroelectriccouplingX_xx]
type = FerroelectricCouplingX
block = '1'
variable = disp_x
component = 0
[../]
[./ferroelectriccouplingX_yy]
type = FerroelectricCouplingX
block = '1'
variable = disp_y
component = 1
[../]
[./ferroelectriccouplingX_zz]
type = FerroelectricCouplingX
block = '1'
variable = disp_z
component = 2
[../]
##Electrostatics
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_int
permittivity = 0.08854187
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_int
block = '1'
permittivity = 0.08854187
[../]
[./DIE_E_int]
type = Electrostatics
variable = potential_int
block = '2'
permittivity = 2.6562561
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
##Time dependence
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./potential_int_1]
type = DirichletBC
variable = potential_int
boundary = '5'
value = -0.00001
[../]
[./potential_int_2]
type = DirichletBC
variable = potential_int
boundary = '6'
value = -0.00001
[../]
[./disp_x]
type = DirichletBC
variable = disp_x
boundary = '1 2 5 6'
value = 0
[../]
[./disp_y]
type = DirichletBC
variable = disp_y
boundary = '1 2 5 6'
value = 0
[../]
[./disp_z]
type = DirichletBC
variable = disp_z
boundary = '1 2 5 6'
value = 0
[../]
[]
[Postprocessors]
[./avgChern]
block = '1'
type = ElementAverageValue
variable = chern
[../]
[./avgchernMag]
block = '1'
type = ElementAverageValue
variable = chernMag
[../]
[./Fbulk]
type = BulkEnergy
block = '1'
execute_on = 'timestep_end'
[../]
[./Fwall]
type = WallEnergy
block = '1'
execute_on = 'timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
block = '1 2'
execute_on = 'timestep_end'
[../]
[./Fcoupled]
block = '1'
type = CoupledEnergy
execute_on = 'timestep_end'
[../]
[./Felec]
block = '1'
type = ElectrostaticEnergy
permittivity = 0.08854187
execute_on = 'timestep_end'
[../]
[./Ftotal]
type = TotalEnergyFlow
Fbulk = Fbulk
Fwall = Fwall
Fcoupled = Fcoupled
Felec = Felec
execute_on = 'timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
[../]
[]
[UserObjects]
[./kill]
type = Terminator
expression = 'perc_change <= 2.0e-3'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_view -snes_linesearch_monitor -snes_converged_reason -ksp_converged_reason'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type'
petsc_options_value = ' 121 1e-10 1e-6 1e-6 bjacobi'
[../]
[]
[Executioner]
type = Transient
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.7
#iteration_window = 3
optimal_iterations = 6 #should be 5 probably
growth_factor = 1.4
linear_iteration_ratio = 1000
cutback_factor = 0.8
[../]
solve_type = 'NEWTON' #"PJFNK, JFNK, NEWTON"
scheme = 'implicit-euler' #"implicit-euler, explicit-euler, crank-nicolson, bdf2, rk-2"
dtmin = 1e-13
dtmax = 0.7
[]
[Outputs]
print_linear_residuals = true
print_perf_log = true
[./out]
type = Exodus
file_base = out_PZT_nanowire_inSTO_test
elemental_as_nodal = true
interval = 8
[../]
[./outcsv]
type = CSV
file_base = out_PZT_nanowire_inSTO_test
[../]
[]
(test/tests/pbc/bcc_pbc.i)
[Mesh]
file = supercell.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi
## and their initial conditions
##
#################################
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-4
max = 0.1e-4
seed = 1
[../]
block = '1 2'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
block = '1 2'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-4
max = 0.1e-4
seed = 2
[../]
block = '1 2'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '1 2 3'
[../]
[]
[ICs]
[./py1]
type = RandomIC
variable = polar_y
min = 0.58
max = 0.6
seed = 3
block = '1'
[../]
[./py2]
type = RandomIC
variable = polar_y
min = -0.6
max = -0.58
seed = 3
block = '2'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '1 2 3'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[]
[Materials]
#################################################
##
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0' #corresponds to T = 298K
block = '1 2'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '1 2'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '1 2'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '121.0 42.0 37.0'
block = '3'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.0084375'
block = '1 2'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
block = '1 2'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
block = '1 2'
[../]
[./elasticity_tensor_2]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '121.0 0.0 0.0 121.0 0.0 121.0 0.0 0.0 0.0'
block = '3'
[../]
[./strain_12]
type = ComputeSmallStrain
eigenstrain_names = eigenstrain
[../]
[./stress_12]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
block = '1 2'
[../]
[./permitivitty_2]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '1.4'
block = '3'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '1 2'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '1 2'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '1 2'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '1 2'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '1 2'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '1 2'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '1 2'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '1 2'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '1 2'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '1 2'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '1 2'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '1 2'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '1 2'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '1 2 3'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '1 2'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '1 2'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '1 2'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable=u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable=u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy1]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[./xy2]
auto_direction = 'x y z'
variable = 'u_x u_y u_z potential_E_int'
[../]
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '1 2'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '1 2'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./perc_change]
type = ChangeOverTimePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
compute_relative_change = true
[../]
[]
[UserObjects]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 1e-5
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-4'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##=
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-6 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'NEWTON'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 1.5
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
num_steps = 1
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
[./out]
type = Exodus
file_base = out_bcc_pbc
elemental_as_nodal = true
interval = 1
[../]
[]
(test/tests/dispersion/perturbBTO_PzEz.i)
freq = 1778279410.0389228
amplitude = 0.001
[Mesh]
file = out_PzEz.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Functions]
##############################
##
## Define the electric field
## expression to be used below
##
##############################
[./bc_func_1]
type = ParsedFunction
value = 'amplitude*sin(freq*t)'
vars = 'freq amplitude'
vals = '${freq} ${amplitude}'
[../]
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_x
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_y
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_z
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./Ez]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./cEy]
type = QuasistaticFieldAux
component = 2
potential_int = potential_E_int
variable = Ez
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -0.64755 0.323 8.004 4.47 4.91 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.5 0.51 -0.02 0.02 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '275.0 179.0 54.3'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.11 0.045 -0.029'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-14.2 0.74 -1.57'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0.0 0.0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '275.0 179.0 179.0 275.0 179.0 275.0 54.3 54.3 54.3'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable = polar_x
# Time scale estimate for BTO, from Hlinka (2007)
# We use seconds here
time_scale = 1e-12
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1e-12
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1e-12
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./front_pot]
type = FunctionDirichletBC
variable = potential_E_int
boundary = 'front'
function = bc_func_1
[../]
[./boundary_grounding]
type = DirichletBC
boundary = 'back'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'initial timestep_end'
[../]
[./Ea]
type = ElementAverageValue
variable = Ez
execute_on = 'initial timestep_end'
[../]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-8 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-16
dt = 3.5332947520558994e-11
dtmax = 1e-10
verbose = true
num_steps = 5
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_perturbBTO_PzEz0
elemental_as_nodal = true
[../]
[./outCSV]
type = CSV
new_row_tolerance = 1e-16
file_base = out_perturbBTO_PzEz0
[../]
[]
(examples/monodomain/PTO_monodomain_Tdef.i)
a1temp = a1def
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 8
ny = 8
nz = 8
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -2.0
xmax = 2.0
ymin = -2.0
ymax = 2.0
zmin = -2.0
zmax = 2.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
vol = vol
displacements = 'u_x u_y u_z'
##############################################
##
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-6
max = 0.1e-6
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.1e-6
max = 0.1e-6
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.05
max = 0.1
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs00]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs11]
order = CONSTANT
family = MONOMIAL
[../]
[./eigs22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./eigs00]
type = LocalABO3EigenstressAux
variable = eigs00
index_i = 0
index_j = 0
[../]
[./eigs11]
type = LocalABO3EigenstressAux
variable = eigs11
index_i = 1
index_j = 1
[../]
[./eigs22]
type = LocalABO3EigenstressAux
variable = eigs22
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Bulk free energy and electrostrictive
## coefficients gleaned from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
## NOTE: there might be some Legendre transforms
## depending on what approach you use
## -i.e. inhomogeneous strain vs
## homogeneous strain [renormalized]
##
##################################################
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${a1temp} -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
[../]
############################################
##
## Gradient coefficients from
## Marton and Hlinka
## Phys. Rev. B. 74, 104014, (2006)
##
############################################
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
[../]
##################################################
##
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrains_name = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./boundary_grounding]
type = DirichletBC
boundary = '0 1 2 3 4 5'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##
## Postprocessors (integrations over the
## computational domain) to calculate the total energy
## decomposed into linear combinations of the
## different physics.
##
###############################################
[./avePx]
type = ElementAverageValue
variable = polar_x
execute_on = 'timestep_end'
[../]
[./avePy]
type = ElementAverageValue
variable = polar_y
execute_on = 'timestep_end'
[../]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'timestep_end'
[../]
[./ave_e00]
type = ElementAverageValue
variable = e00
execute_on = 'timestep_end'
[../]
[./ave_e11]
type = ElementAverageValue
variable = e11
execute_on = 'timestep_end'
[../]
[./ave_e22]
type = ElementAverageValue
variable = e22
execute_on = 'timestep_end'
[../]
[./Fb]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./Fw]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./Fela]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
[../]
[./Fc]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'Fb Fw Fc Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is smallhotkey for tilde
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-6 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
###########################################
##
## dtmax is material dependent!
##
###########################################
dtmax = 1.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
[]
[Outputs]
###############################################
##
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./outCSV]
type = CSV
file_base = out_pto_monodomain_Tdef
[../]
[]
(test/tests/auxkernels/microforce.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 4
ny = 4
nz = 4
xmin = -6.0
xmax = 6.0
ymin = -6.0
ymax = 6.0
zmin = -2.0
zmax = 2.0
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '-6.0 -6.0 -2.0'
new_boundary = 100
[../]
# additional boundary sideset (one node) to zero one of the elastic displacement vectors - eliminates rigid body translations from the degrees of freedom
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 6
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 6
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
seed = 6
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./Fb_x]
order = CONSTANT
family = MONOMIAL
[../]
[./Fb_y]
order = CONSTANT
family = MONOMIAL
[../]
[./Fb_z]
order = CONSTANT
family = MONOMIAL
[../]
[./Felstr_x]
order = CONSTANT
family = MONOMIAL
[../]
[./Felstr_y]
order = CONSTANT
family = MONOMIAL
[../]
[./Felstr_z]
order = CONSTANT
family = MONOMIAL
[../]
[./Felec_x]
order = CONSTANT
family = MONOMIAL
[../]
[./Felec_y]
order = CONSTANT
family = MONOMIAL
[../]
[./Felec_z]
order = CONSTANT
family = MONOMIAL
[../]
[./Fw_x]
order = CONSTANT
family = MONOMIAL
[../]
[./Fw_y]
order = CONSTANT
family = MONOMIAL
[../]
[./Fw_z]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./fbx]
type = MicroforceBulkEnergy
variable = Fb_x
component = 0
[../]
[./fby]
type = MicroforceBulkEnergy
variable = Fb_y
component = 1
[../]
[./fbz]
type = MicroforceBulkEnergy
variable = Fb_z
component = 2
[../]
[./felstrx]
type = MicroforceElectrostrictiveCouplingEnergy
variable = Felstr_x
component = 0
[../]
[./felstry]
type = MicroforceElectrostrictiveCouplingEnergy
variable = Felstr_y
component = 1
[../]
[./felstrz]
type = MicroforceElectrostrictiveCouplingEnergy
variable = Felstr_z
component = 2
[../]
[./felecx]
type = MicroforceElectrostaticEnergy
variable = Felec_x
component = 0
[../]
[./felecy]
type = MicroforceElectrostaticEnergy
variable = Felec_y
component = 1
[../]
[./felecz]
type = MicroforceElectrostaticEnergy
variable = Felec_z
component = 2
[../]
[./fwx]
type = MicroforceWallEnergy
variable = Fw_x
component = 0
[../]
[./fwy]
type = MicroforceWallEnergy
variable = Fw_y
component = 1
[../]
[./fwz]
type = MicroforceWallEnergy
variable = Fw_z
component = 2
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 0.42 0.735 0.26 0.61 -3.67 0 0 0 0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175 79.4 111.1'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '0. 0 0 0 0 0 0 0 0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./slab_ferroelectric]
type = ComputeElectrostrictiveTensor
Q_mnkl = '-0.089 0.026 0.026 -0.089 0.026 -0.089 -0.03375 -0.03375 -0.03375'
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
#note below we use a strain-renormalized functional for lead titanate (this is different than the stress-free functionals typically used)
# they are related by a Legendre transformation
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'initial timestep_end'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
#[./elapsed]
# type = PerfGraphData
# section_name = "Root"
# data_type = total
#[../]
#[./nodes]
# type = NumNodes
#[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
[./kill]
type = Terminator
expression = 'perc_change <= 1.0e-6'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-8 1e-8 bjacobi allreduce'
[../]
[]
#[Debug]
# show_var_residual_norms = true
#[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 0.8
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
num_steps = 10
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
[./out]
type = Exodus
file_base = out_microforce_test
elemental_as_nodal = true
interval = 1
[../]
[./outCSV]
type = CSV
file_base = out_microforce_test
[../]
[]
(examples/films/PTOfilm_e12_T298K_E0.i)
[Mesh]
[gen]
############################################
##
## Type and dimension of the mesh
##
############################################
type = GeneratedMeshGenerator
dim = 3
#############################################
##
## Grid definition. Note that it should be
## nJ = 2*(Jmax-Jmin) for J = x, y, z
##
#############################################
nx = 32
ny = 32
nz = 30
#############################################
##
## Actual spatial coordinates of mesh.
## Jmax - Jmin = nJ/2 for J = x, y, z
## Units are in nanometers
##
#############################################
xmin = -16.0
xmax = 16.0
ymin = -16.0
ymax = 16.0
zmin = -10.0
zmax = 20.0
#############################################
##
## FE type/order (hexahedral, tetrahedral
##
#############################################
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '-16.0 -16.0 -10.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-16.0 -16.0 -10.0'
block_id = 1
top_right = '16.0 16.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[film_surface]
type = SideSetsFromNormalsGenerator
input = film_interface
normals = '0 0 1'
fixed_normal = true
new_boundary = '107'
[]
[substrate_bottom]
type = SideSetsFromNormalsGenerator
input = film_surface
normals = '0 0 -1'
fixed_normal = true
new_boundary = '108'
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
##############################################
##=
## IMPORTANT(!): Units in Ferret are nm, kg,
## seconds, and attocoulombs
##
##############################################
vol = vol
u_x = u_x
u_y = u_y
u_z = u_z
[]
[Variables]
#################################
##
## Variable definitions
## P, u, phi, e^global_ij
## and their initial conditions
##
#################################
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[AuxVariables]
######################################
##
## Auxiarilly variable definitions
## (can be intermediate variables
## or for postprocessed quantities)
##
######################################
######################################
##
## Global displacements
##
######################################
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
######################################
##
## Stress/strain tensor components
##
######################################
[./e00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_x]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_y]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[./E_z]
order = CONSTANT
family = MONOMIAL
block = '0 1'
[../]
[]
[AuxKernels]
######################################
##
## Auxiarilly Kernel definitions
## (can be intermediate "operations"
## or for postprocessed quantities)
##
######################################
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./ex]
type = ElecFieldAux
variable = E_x
component = 0
[../]
[./ey]
type = ElecFieldAux
variable = E_y
component = 1
[../]
[./ez]
type = ElecFieldAux
variable = E_z
component = 2
[../]
[]
[ScalarKernels]
######################################
##
## Necessary for PBC system
##
######################################
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
#################################################
##
## Landau coefficients from Li et al (2001)
##
##################################################
[./Landau_P_FE]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.1722883 -0.073 0.75 0.26 0.61 -3.67 0.0 0.0 0.0 0.0'
block = '0'
[../]
[./Landau_P_substr]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '10.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[../]
[./Landau_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '0.173 0.6 0.0 0.3 0.3'
block = '0'
[../]
[./mat_C_FE]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '175.0 79.4 111.1'
block = '0'
[../]
[./mat_C_sub]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '220.0 34.4 161.1'
block = '1'
[../]
##################################################
##=
## NOTE: Sign convention in Ferret for the
## electrostrictive coeff. is multiplied by
## an overall factor of (-1)
##
##################################################
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.089 0.026 -0.03375'
block = '0 1'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-11.4 -0.01438 -7.5'
[../]
[./eigen_strain]
type = ComputeEigenstrain
# eigen_base = 'exx exy exz eyx eyy eyz ezx ezy ezz'
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
###############################################
##
## symmetric9 fill_method is (default)
## C11 C12 C13 C22 C23 C33 C44 C55 C66
##
###############################################
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_1]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
###############################################
##
## Physical Kernel operators
## to enforce TDLGD evolution
##
###############################################
#Elastic problem
[./TensorMechanics]
use_displaced_mesh = false
eigenstrain_names = eigenstrain
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
block = '0'
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
block = '0'
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
block = '0'
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
[./boundary_interface_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = '108'
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = '108'
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = '108'
variable = u_z
value = 0
[../]
[]
[Postprocessors]
###############################################
##=
## Postprocessors (integrations over the
## computational domain) to calculate the total
## energy decomposed into linear combinations of
## the different physics.
##
###############################################
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = ElasticEnergy
execute_on = 'timestep_end'
use_displaced_mesh = false
block = '0'
[../]
[./Fcoupled]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Fcoupled Felec'
pp_coefs = '0.160218 0.160218 0.160218 0.160218' #converted to eV
execute_on = 'timestep_end'
[../]
[./vol]
type = VolumePostprocessor
execute_on = 'timestep_end'
[../]
[./px]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 0
block = '0'
[../]
[./py]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 1
block = '0'
[../]
[./pz]
type = DomainVariantPopulation
execute_on = 'timestep_end'
component = 2
block = '0'
[../]
[./perc_change]
type = PercentChangePostprocessor
postprocessor = Ftotal
execute_on = 'timestep_end'
[../]
[./elapsed]
type = PerfGraphData
section_name = "Root" # for profiling the problem [on]
data_type = total
[../]
[]
[UserObjects]
###############################################
##
## GlobalStrain system to enforce periodicity
## in the anisotropic strain field
##
###############################################
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '2.1 2.1 1.9056 0.0 0.0 0.0'
block = '0'
[../]
###############################################
##
## terminator to end energy evolution when the energy difference
## between subsequent time steps is lower than 5e-6
##
## NOTE: can fail if the time step is small
##
###############################################
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-4'
[../]
[]
[Preconditioning]
###############################################
##
## Numerical preconditioning/solver options
##
###############################################
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 80 1e-8 1e-6 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
##########################################
##
## Time integ=ration/solver options
##
##########################################
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
[]
[Outputs]
###############################################
##==
## Output options
##
###############################################
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_PTOfilm_e12_T298K_E0_E0
elemental_as_nodal = true
interval = 1
[../]
[]
(tutorial/BFO_homogeneous_PA.i)
Nx = 3
Ny = 3
Nz = 3
xMax = 1.0
yMax = 1.0
zMax = 1.0
g11 = 12e-3
g12 = -3.0e-3
g44 = 3.0e-3
h11 = 2.0e-4
h12 = -0.2e-3
h44 = 0.8e-3
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${Nx}
ny = ${Ny}
nz = ${Nz}
xmin = 0.0
xmax = ${xMax}
ymin = 0.0
ymax = ${yMax}
zmin = 0.0
zmax = ${zMax}
elem_type = HEX8
[]
[./cnode]
input = gen
############################################
##
## additional boundary sideset (one node)
## to zero one of the elastic displacement vectors
## vectors and eliminates rigid body translations
## from the degrees of freedom
##
## NOTE: This must conform with the about
## [Mesh] block settings
##
############################################
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
antiphase_A_x = antiphase_A_x
antiphase_A_y = antiphase_A_y
antiphase_A_z = antiphase_A_z
displacements = 'u_x u_y u_z'
potential_E_int = potential_E_int
[]
[Functions]
[./constPm]
type = ParsedFunction
value = -0.50
[../]
[./constPp]
type = ParsedFunction
value = 0.50
[../]
[./constAm]
type = ParsedFunction
value = -7.1
[../]
[./constAp]
type = ParsedFunction
value = 7.1
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPp
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constPm
[../]
[../]
[./antiphase_A_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAp
[../]
[../]
[./antiphase_A_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = constAm
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./TensorMechanics]
[../]
[./rotostr_ux]
type = RotostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./rotostr_uy]
type = RotostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./rotostr_uz]
type = RotostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
[./electrostr_ux]
type = ElectrostrictiveCouplingDispDerivative
variable = u_x
component = 0
[../]
[./electrostr_uy]
type = ElectrostrictiveCouplingDispDerivative
variable = u_y
component = 1
[../]
[./electrostr_uz]
type = ElectrostrictiveCouplingDispDerivative
variable = u_z
component = 2
[../]
### Operators for the polar field: ###
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./walled2_x]
type = Wall2EnergyDerivative
variable = polar_x
component = 0
[../]
[./walled2_y]
type = Wall2EnergyDerivative
variable = polar_y
component = 1
[../]
[./walled2_z]
type = Wall2EnergyDerivative
variable = polar_z
component = 2
[../]
[./walled_a_x]
type = AFDWallEnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled_a_y]
type = AFDWallEnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled_a_z]
type = AFDWallEnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./walled2_a_x]
type = AFDWall2EnergyDerivative
variable = antiphase_A_x
component = 0
[../]
[./walled2_a_y]
type = AFDWall2EnergyDerivative
variable = antiphase_A_y
component = 1
[../]
[./walled2_a_z]
type = AFDWall2EnergyDerivative
variable = antiphase_A_z
component = 2
[../]
[./roto_polar_coupled_x]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_x
component = 0
[../]
[./roto_polar_coupled_y]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_y
component = 1
[../]
[./roto_polar_coupled_z]
type = RotoPolarCoupledEnergyPolarDerivativeAlt
variable = polar_z
component = 2
[../]
[./roto_dis_coupled_x]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_x
component = 0
[../]
[./roto_dis_coupled_y]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_y
component = 1
[../]
[./roto_dis_coupled_z]
type = RotoPolarCoupledEnergyDistortDerivativeAlt
variable = antiphase_A_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_y]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./electrostr_polar_coupled_z]
type = ElectrostrictiveCouplingPolarDerivative
variable = polar_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
#Operators for the AFD field
[./rbed_x]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_x
component = 0
[../]
[./rbed_y]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_y
component = 1
[../]
[./rbed_z]
type = RotoBulkEnergyDerivativeEighthAlt
variable = antiphase_A_z
component = 2
[../]
[./rotostr_dis_coupled_x]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_x
component = 0
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_y]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_y
component = 1
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./rotostr_dis_coupled_z]
type = RotostrictiveCouplingDistortDerivative
variable = antiphase_A_z
component = 2
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./a_x_time]
type = TimeDerivativeScaled
variable = antiphase_A_x
time_scale = 0.01
block = '0'
[../]
[./a_y_time]
type = TimeDerivativeScaled
variable = antiphase_A_y
time_scale = 0.01
block = '0'
[../]
[./a_z_time]
type = TimeDerivativeScaled
variable = antiphase_A_z
time_scale = 0.01
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e21]
order = CONSTANT
family = MONOMIAL
[../]
[./e02]
order = CONSTANT
family = MONOMIAL
[../]
[./e20]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e21]
type = RankTwoAux
variable = e21
rank_two_tensor = total_strain
index_i = 2
index_j = 1
[../]
[./e20]
type = RankTwoAux
variable = e20
rank_two_tensor = total_strain
index_i = 2
index_j = 0
[../]
[./e02]
type = RankTwoAux
variable = e02
rank_two_tensor = total_strain
index_i = 0
index_j = 2
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-2.81296 1.72351 2.24147 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_A]
type = GenericConstantMaterial
prop_names = 'beta1 beta11 beta12 beta111 beta112 beta123 beta1111 beta1112 beta1122 beta1123'
prop_values = '-0.0137763 0.0000349266 0.0000498846 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./P_A_couple]
type = GenericConstantMaterial
prop_names = 't1111 t1122 t1212 t42111111 t24111111 t42111122 t24112222 t42112233 t24112233 t42112211 t24111122 t42111212 t42123312 t24121112 t24121233 t6211111111 t2611111111 t6211111122 t2611222222 t4411111111 t4411112222'
prop_values = '0.012516 0.0180504 -0.036155 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[./Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '1.0 ${g11} ${g12} ${g44} 0.0'
[../]
[./Landau_H]
type = GenericConstantMaterial
prop_names = 'H110 H11_H110 H12_H110 H44_H110 H44P_H110'
prop_values = '1.0 ${h11} ${h12} ${h44} 0.0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '295.179 117.567 74.0701'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '-0.0603833 0.0111245 -0.0175686'
[../]
[./mat_R]
type = GenericConstantMaterial
prop_names = 'R11 R12 R44'
prop_values = '-0.0000878064 0.0000295306 0.0000627962'
[../]
[./mat_q]
type = GenericConstantMaterial
prop_names = 'q11 q12 q44'
prop_values = '-30.4162 -5.01496 -10.4105'
#the point is the following: use a slightly different definition of Q_ij than Hlinka
[../]
[./mat_r]
type = GenericConstantMaterial
prop_names = 'r11 r12 r44'
prop_values = '-0.0379499 0.00373096 0.0372105'
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '295.179 117.567 117.567 295.179 117.567 295.179 74.0701 74.0701 74.0701'
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./permitivitty_1]
###############################################
##
## so-called background dielectric constant
## (it encapsulates the motion of core electrons
## at high frequency) = e_b*e_0 (here we use
## e_b = 10), see PRB. 74, 104014, (2006)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Postprocessors]
[./dt]
type = TimestepSize
[../]
[./FbP]
type = BulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FbA]
type = RotoBulkEnergyEighth
execute_on = 'timestep_end'
[../]
[./FcPA]
type = RotoPolarCoupledEnergyEighth
execute_on = 'timestep_end'
[../]
[./FgP]
type = WallEnergy
execute_on = 'timestep_end'
[../]
[./FgA]
type = AFDWallEnergy
execute_on = 'timestep_end'
[../]
[./FcPu]
type = ElectrostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./FcAu]
type = RotostrictiveCouplingEnergy
execute_on = 'timestep_end'
u_x = disp_x
u_y = disp_y
u_z = disp_z
[../]
[./Felu]
type = ElasticEnergy
execute_on = 'timestep_end'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'FbP FbA FgP FgA FcPA FcPu FcAu Felu Fele'
pp_coefs = ' 1 1 1 1 1 1 1 1 1'
execute_on = 'timestep_end'
##########################################
#
# NOTE: Ferret output is in attojoules
#
##########################################
[../]
[./perc_change]
type = EnergyRatePostprocessor
postprocessor = Ftot
execute_on = 'timestep_end'
dt = dt
[../]
[]
[BCs]
[./Periodic]
[./x]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z antiphase_A_x antiphase_A_y antiphase_A_z'
[../]
[./xyz]
auto_direction = 'x y z'
variable = 'potential_E_int'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalBFOMaterialRVEUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[./kill]
type = Terminator
expression = 'perc_change <= 5.0e-7'
[../]
[]
#=
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 121 1e-8 1e-7 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 10.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 25 #usually 10
linear_iteration_ratio = 100
dt = 0.001
growth_factor = 1.1
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph_live = false
[./out]
type = Exodus
file_base = BFO_P0A0
elemental_as_nodal = true
[../]
[]