- componentAn integer corresponding changes in the refractive index's index (0, 1, 2, 3, 4, 5)
C++ Type:unsigned int
Controllable:No
Description:An integer corresponding changes in the refractive index's index (0, 1, 2, 3, 4, 5)
- 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 object applies to
C++ Type:AuxVariableName
Controllable:No
Description:The name of the variable that this object applies to
PolarOpticChangeInRefractiveIndex
buildconstruction:Undocumented Class
The PolarOpticChangeInRefractiveIndex 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 the changes to local refractive index due to the polar-optic effect.
Overview
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.
- 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
- 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
(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/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
[../]
[]