- componentAn integer corresponding to the direction the variable this auxkernel acts in. (0 for x, 1 for y, 2 for z)
C++ Type:unsigned int
Controllable:No
Description:An integer corresponding to the direction the variable this auxkernel acts in. (0 for x, 1 for y, 2 for z)
- variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Controllable:No
Description:The name of the variable that this object applies to
ElecFieldAux
Converts electrostatic potential to the vector electric field.
Overview
Computes a user-defined component of .
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
- boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
- check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
- execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE.
- potential_E_extThe external electrostatic potential variable (disabled for now)
C++ Type:std::vector<VariableName>
Controllable:No
Description:The external electrostatic potential variable (disabled for now)
- potential_E_intThe internal electrostatic potential variable
C++ Type:std::vector<VariableName>
Controllable:No
Description:The internal electrostatic potential variable
- 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
- 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.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- 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
(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/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
[../]
[]
(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
[../]
[]