- componentAn integer corresponding to the direction in OP 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 OP 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
Wall2EnergyDerivative
buildconstruction:Undocumented Class
The Wall2EnergyDerivative 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 WallEnergyDerivative!
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
- 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/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
[../]
[]
(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
[../]
[]
(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
[../]
[]
(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'
[../]
[]
(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
[../]
[]
(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
[../]
[]