- polar_xThe x component of the polarization vector
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The x component of the polarization vector
- polar_yThe y component of the polarization vector
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The y component of the polarization vector
CubicParentElasticEnergy
buildconstruction:Undocumented Class
The CubicParentElasticEnergy 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 volume integral over the electrostrictive coupling energy density.
Overview
Example Input File Syntax
Input Parameters
- base_nameMaterial property base name
C++ Type:std::string
Controllable:No
Description:Material property base name
- 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
- energy_scale1the energy scale, useful for transition between eV and J
Default:1
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:the energy scale, useful for transition between eV and J
- polar_zThe z component of the polarization vector
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The z component of the polarization vector
Optional Parameters
- allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
- execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, LINEAR_CONVERGENCE, NONLINEAR, NONLINEAR_CONVERGENCE, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, MULTIAPP_FIXED_POINT_CONVERGENCE, MULTISYSTEM_FIXED_POINT_ITERATION_END, FINAL, CUSTOM, TRANSFER
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
- execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
- force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
- force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
- force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
Execution Scheduling Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- 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
- outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object
- 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
- 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
Unit:(no unit assumed)
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.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
- (test/tests/polar-elastic-electric/PTO_3D_E_full.i)
- (test/tests/polar-elastic-electric/PTO_2D_E_multi_mech.i)
- (test/tests/electrooptics/BTO_monodomain_T298K_REFnoEO.i)
- (test/tests/film/PTO_film_substrate_full.i)
- (test/tests/polar-elastic/PTO_2D_multi_mech.i)
- (test/tests/film/PTO_film_clamped_full.i)
- (test/tests/auxkernels/surface_charge.i)
- (test/tests/domain_wall/test_BTO_domain_wall.i)
- (test/tests/userobjects/terminator_multi_mech.i)
- (test/tests/film/PTO_film_substrate_multi_mech.i)
- (test/tests/polar-elastic/PTO_2D_full.i)
- (test/tests/polar-elastic/PTO_3D_multi_mech.i)
- (test/tests/dispersion/perturbBTO_PzEz.i)
- (test/tests/dispersion/perturbBTO_PyEz.i)
- (test/tests/pertsev/PTO_pertsev_mech.i)
- (test/tests/bulk/BTO_bulk_relax.i)
- (test/tests/electrostatics/PTO_STO_2D_E_full.i)
- (test/tests/pertsev/BTO_pertsev_mech.i)
- (test/tests/userobjects/terminator_full.i)
- (test/tests/ics/PTO_3D_fluct.i)
- (test/tests/polar-elastic-electric/PTO_2D_E_full.i)
- (test/tests/polar-elastic-electric/PTO_3D_E_multi_mech.i)
- (tutorial/ferroelectric_domain_wall.i)
- (test/tests/polar-elastic/PTO_3D_full.i)
- (test/tests/film/PTO_film_clamped_multi_mech.i)
(test/tests/polar-elastic-electric/PTO_3D_E_full.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
eps_r = 10.0
eps0 = 0.0088542
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 1
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 2
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 3
[]
[]
[potential_E_int]
order = FIRST
family = LAGRANGE
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[permittivity]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '${fparse eps_r*eps0}'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[poisson]
type = Electrostatics
variable = potential_E_int
[]
[divP]
type = PolarElectricEStrong
variable = potential_E_int
[]
[Ephi_x]
type = PolarElectricPStrong
variable = polar_x
component = 0
[]
[Ephi_y]
type = PolarElectricPStrong
variable = polar_y
component = 1
[]
[Ephi_z]
type = PolarElectricPStrong
variable = polar_z
component = 2
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y u_z'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y u_z'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y u_z'
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'polar_x polar_y polar_z potential_E_int u_x u_y u_z'
[]
[]
[phi_pin]
type = DirichletBC
variable = potential_E_int
boundary = 'pin_node'
value = 0
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = '1 1 1 1'
execute_on = 'timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 5.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/polar-elastic-electric/PTO_2D_E_multi_mech.i)
TC = 25.0
um = -0.01
l0 = 1.0
Lx = 8.0
tf = 2.0
nx = 40
ny = 10
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = ${nx}
ny = ${ny}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${tf}
elem_type = QUAD4
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_yy]
type = RankTwoAux
variable = strain_yy
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 0 0 0 0 ${um}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y'
component = 1
[]
[]
[BCs]
[Periodic]
[x]
auto_direction = 'x'
variable = 'u_x u_y'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'bottom'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'bottom'
value = 0
[]
[]
[Postprocessors]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-6 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/electrooptics/BTO_monodomain_T298K_REFnoEO.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
[]
[Functions]
[./stripe1]
type = ParsedFunction
expression = 0.01*cos(0.08975979010256552*(x))
[../]
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0.01
max = 0.02
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -0.01e-4
max = 0.01e-4
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_1]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_2]
order = CONSTANT
family = MONOMIAL
[../]
[./dpn_3]
order = CONSTANT
family = MONOMIAL
[../]
[./den_1]
order = CONSTANT
family = MONOMIAL
[../]
[./den_2]
order = CONSTANT
family = MONOMIAL
[../]
[./den_3]
order = CONSTANT
family = MONOMIAL
[../]
[./n_1]
order = CONSTANT
family = MONOMIAL
[../]
[./n_2]
order = CONSTANT
family = MONOMIAL
[../]
[./n_3]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./dn_p1]
type = PolarOpticChangeInRefractiveIndex
component = 0
variable = dpn_1
execute_on = 'timestep_end'
[../]
[./dn_p2]
type = PolarOpticChangeInRefractiveIndex
component = 1
variable = dpn_2
execute_on = 'timestep_end'
[../]
[./dn_p3]
type = PolarOpticChangeInRefractiveIndex
component = 2
variable = dpn_3
execute_on = 'timestep_end'
[../]
[./dn_e1]
type = ElastoChangeInRefractiveIndex
component = 0
variable = den_1
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./dn_e2]
type = ElastoChangeInRefractiveIndex
component = 1
variable = den_2
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./dn_e3]
type = ElastoChangeInRefractiveIndex
component = 2
variable = den_3
u_x = u_x
u_y = u_y
u_z = u_z
execute_on = 'timestep_end'
[../]
[./n_1_c]
type = ReworkedRefractiveIndex
variable = n_1
elasto = false
electro = false
polar = true
component = 0
var1 = dpn_1
execute_on = 'timestep_end'
[../]
[./n_2_c]
type = ReworkedRefractiveIndex
variable = n_2
elasto = false
electro = false
polar = true
component = 1
var1 = dpn_2
execute_on = 'timestep_end'
[../]
[./n_3_c]
type = ReworkedRefractiveIndex
variable = n_3
elasto = false
electro = false
polar = true
component = 2
var1 = dpn_3
execute_on = 'timestep_end'
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -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'
[../]
[./ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
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 = 'ferro'
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./ref_index]
type = GenericConstantMaterial
prop_names = 'n1 n2 n3 n4 n5 n6'
prop_values = '2.4272 2.4272 2.4272 0.0 0.0 0.0'
[../]
[./po_tensor]
type = GenericConstantMaterial
prop_names = 'g1111 g1122 g1212'
prop_values = '0.15 0.038 0.07'
[../]
[./eo_tensor]
type = GenericConstantMaterial
prop_names = 'p1111 p1122 p1212'
prop_values = '0.37 0.11 -0.30'
[../]
[./eps]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
[./SolidMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
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
[../]
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
verbose = true
num_steps = 5
[]
[Outputs]
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = test_bire_no_EO
elemental_as_nodal = true
[../]
[]
(test/tests/film/PTO_film_substrate_full.i)
TC = 25.0
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
h_film = 4.0
h_sub = 2.0
nz = ${fparse int((h_film + h_sub)/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nz}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = ${fparse -h_sub}
zmax = ${h_film}
elem_type = HEX8
[]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = gen
block_id = 1
bottom_left = '0.0 0.0 ${fparse -h_sub}'
top_right = '${L} ${L} 0.0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 'film_interface'
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
displacements = 'u_x u_y u_z'
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
block = 0
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 1
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
block = 0
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 2
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
block = 0
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 3
[]
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
block = 0
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
block = 0
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 0.0 0.0 0.0 0.0'
block = 0
[]
[Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.6 0.0 0.3 0.3'
block = 0
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
block = 0
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
block = 0
[]
[elasticity_tensor_film]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
block = 0
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
block = 0
[]
[strain_film]
type = ComputeSmallStrain
eigenstrain_names = 'ferro'
block = 0
[]
[stress_film]
type = ComputeLinearElasticStress
block = 0
[]
[elasticity_tensor_sub]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '318.0 103.0 103.0 318.0 103.0 318.0 124.0 124.0 124.0'
block = 1
[]
[strain_sub]
type = ComputeSmallStrain
block = 1
[]
[stress_sub]
type = ComputeLinearElasticStress
block = 1
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
component = 2
[]
[time_x]
type = TimeDerivative
variable = polar_x
block = 0
[]
[time_y]
type = TimeDerivative
variable = polar_y
block = 0
[]
[time_z]
type = TimeDerivative
variable = polar_z
block = 0
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = 0
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = 0
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = 0
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = 0
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
block = 0
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
block = 0
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
block = 0
[]
[]
[BCs]
[Periodic]
[xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[]
[]
[sub_fix_x]
type = DirichletBC
variable = u_x
boundary = 'back'
value = 0
[]
[sub_fix_y]
type = DirichletBC
variable = u_y
boundary = 'back'
value = 0
[]
[sub_fix_z]
type = DirichletBC
variable = u_z
boundary = 'back'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
block = 0
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
block = 0
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
block = 0
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic'
pp_coefs = '1 1 1'
execute_on = 'timestep_end'
[]
[exx_film]
type = ElementAverageValue
variable = strain_xx
block = 0
execute_on = 'initial timestep_end'
[]
[ezz_film]
type = ElementAverageValue
variable = strain_zz
block = 0
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
file_base = PTO_film_substrate_full_exo
[]
[]
(test/tests/polar-elastic/PTO_2D_multi_mech.i)
TC = 25.0
um = -0.01
l0 = 1.0
Lx = 8.0
tf = 2.0
nx = 40
ny = 10
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = ${nx}
ny = ${ny}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${tf}
elem_type = QUAD4
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_yy]
type = RankTwoAux
variable = strain_yy
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 0 0 0 0 ${um}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y'
component = 1
[]
[]
[BCs]
[Periodic]
[x]
auto_direction = 'x'
variable = 'u_x u_y'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'bottom'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'bottom'
value = 0
[]
[]
[Postprocessors]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-6 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/film/PTO_film_clamped_full.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 1
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 2
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 3
[]
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y u_z'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y u_z'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y u_z'
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'polar_x polar_y polar_z u_x u_y u_z'
[]
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic'
pp_coefs = '1 1 1'
execute_on = 'timestep_end'
[]
[exx_avg]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz_avg]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
file_base = PTO_film_clamped_full_exo
[]
[]
(test/tests/auxkernels/surface_charge.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 4
ny = 4
nz = 8
xmin = -1.0
xmax = 1.0
ymin = -1.0
ymax = 1.0
zmin = -2.0
zmax = 2.0
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '-1.0 -1.0 -2.0'
new_boundary = 100
[../]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = cnode
bottom_left = '-1.0 -1.0 -2.0'
block_id = 1
top_right = '1.0 1.0 0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 52
[]
[film_surface]
type = SideSetsFromNormalsGenerator
input = film_interface
normals = '0 0 1'
fixed_normal = true
new_boundary = '107'
[]
[substrate_bottom]
type = SideSetsFromNormalsGenerator
input = film_surface
normals = '0 0 -1'
fixed_normal = true
new_boundary = '108'
[]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-2
max = 1e-2
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_x]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_y]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[./u_z]
order = FIRST
family = LAGRANGE
block = '0 1'
[../]
[]
[AuxVariables]
[./disp_x]
block = '0 1'
[../]
[./disp_y]
block = '0 1'
[../]
[./disp_z]
block = '0 1'
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./s12]
order = CONSTANT
family = MONOMIAL
[../]
[./s22]
order = CONSTANT
family = MONOMIAL
[../]
[./divP]
order = CONSTANT
family = MONOMIAL
block = '0'
[../]
[./surfP]
order = CONSTANT
family = MONOMIAL
[../]
## P.n on the film/substrate interface (52), the remaining piece of
## the closed surface of block 0. It needs its OWN variable: a face
## value is written into the element dof, so two boundaries sharing
## an element cannot share a CONSTANT MONOMIAL variable.
[./surfP_52]
order = CONSTANT
family = MONOMIAL
block = '0'
## This variable exists only to feed the divergence-theorem assertion
## in [UserObjects], so keep it out of the Exodus file. That makes the
## whole check strictly additive and leaves the gold untouched.
outputs = none
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s12]
type = RankTwoAux
variable = s12
rank_two_tensor = stress
index_i = 1
index_j = 2
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./s22]
type = RankTwoAux
variable = s22
rank_two_tensor = stress
index_i = 2
index_j = 2
[../]
[./divP]
type = DivP
variable = divP
[../]
[./surfP]
type = SurfaceChargeP
variable = surfP
boundary = '107'
[../]
[./surfP_52]
type = SurfaceChargeP
variable = surfP_52
boundary = '52'
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./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'
[../]
[./mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
block = '0 1'
[../]
[./ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
block = '0'
[../]
[./eigen_strain]
type = ComputeEigenstrain
eigen_base = '1.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0'
eigenstrain_name = eigenstrain
prefactor = 0.0
block = '1'
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '175.0 79.4 79.4 175.0 79.4 175.0 111.1 111.1 111.1'
[../]
[./strain_film]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = 'ferro'
block = '0'
[../]
[./strain_substrate]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = 'eigenstrain'
block = '1'
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
[./div_x]
type = StressDivergenceTensors
variable = u_x
component = 0
use_displaced_mesh = false
[../]
[./div_y]
type = StressDivergenceTensors
variable = u_y
component = 1
use_displaced_mesh = false
[../]
[./div_z]
type = StressDivergenceTensors
variable = u_z
component = 2
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
block = '0'
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
block = '0'
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
block = '0'
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
block = '0'
[../]
[./electrostr_polar_coupled_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y u_z'
block = '0'
[../]
[./electrostr_polar_coupled_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y u_z'
block = '0'
[../]
[./electrostr_polar_coupled_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y u_z'
block = '0'
[../]
[./polar_x_electric_E]
type = PolarElectricEStrong
variable = potential_E_int
block = '0'
[../]
[./FE_E_int]
type = Electrostatics
variable = potential_E_int
block = '0 1'
[../]
[./polar_electric_px]
type = PolarElectricPStrong
variable = polar_x
component = 0
block = '0'
[../]
[./polar_electric_py]
type = PolarElectricPStrong
variable = polar_y
component = 1
block = '0'
[../]
[./polar_electric_pz]
type = PolarElectricPStrong
variable = polar_z
component = 2
block = '0'
[../]
[./polar_x_time]
type = TimeDerivativeScaled
variable=polar_x
time_scale = 1.0
block = '0'
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable=polar_y
time_scale = 1.0
block = '0'
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1.0
block = '0'
[../]
[./u_x_time]
type = TimeDerivativeScaled
variable = u_x
time_scale = 1.0
[../]
[./u_y_time]
type = TimeDerivativeScaled
variable = u_y
time_scale = 1.0
[../]
[./u_z_time]
type = TimeDerivativeScaled
variable = u_z
time_scale = 1.0
[../]
[]
[BCs]
[./Periodic]
[./xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z polar_x polar_y polar_z potential_E_int'
[../]
[../]
[./boundary_interface_grounding]
type = DirichletBC
boundary = '52'
variable = potential_E_int
value = 0.0
[../]
[./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]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felastic]
type = CubicParentElasticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = '0.160218 0.160218 0.160218 0.160218'
execute_on = 'timestep_end'
[../]
###############################################
##
## Gold-independent correctness check on the bound-charge
## capability: the divergence theorem
##
## int_V div(P) dV == oint_dV P.n dS
##
## over the FILM (block 0, z in [0,2]). The closed boundary of
## block 0 is the free surface 107 (z=+2), the film/substrate
## interface 52 (z=0), and the four lateral faces, which cancel
## pairwise under the x/y periodic BCs.
##
## NOTE: boundary 108 is the SUBSTRATE bottom (z=-2) and lies on
## block 1, where P is not defined. It is NOT part of this
## surface -- adding it is an error, not a refinement.
##
## Sign convention: DivP returns div(P) and SurfaceChargeP returns
## P.n, so the identity carries no minus sign. (The bound charges
## themselves are rho_b = -div(P) and sigma_b = +P.n.)
##
## Verified 2026-09-22 on the full closed surface: residual ~1e-18,
## i.e. ~1e-17 relative to the sum of the absolute face contributions.
## The 1e-6 tolerance below is loose because the lateral faces are
## omitted here; they cancel only to solver tolerance (~1e-8), not to
## round-off. Restricting sidesets to block 0 so they could be
## included would break Periodic/auto_direction, which is not worth it.
##
## outputs = none on purpose: this check must not perturb the Exodus
## gold file, so it adds no global variables to the output.
##
###############################################
[./volDivP]
type = ElementIntegralVariablePostprocessor
variable = divP
block = '0'
execute_on = 'timestep_end'
outputs = none
[../]
[./surfInt_107]
type = SideIntegralVariablePostprocessor
variable = surfP
boundary = '107'
execute_on = 'timestep_end'
outputs = none
[../]
[./surfInt_52]
type = SideIntegralVariablePostprocessor
variable = surfP_52
boundary = '52'
execute_on = 'timestep_end'
outputs = none
[../]
[./closedSurfP]
type = LinearCombinationPostprocessor
pp_names = 'surfInt_107 surfInt_52'
pp_coefs = '1 1'
execute_on = 'timestep_end'
outputs = none
[../]
[./divThmResidual]
type = LinearCombinationPostprocessor
pp_names = 'closedSurfP volDivP'
pp_coefs = '1 -1'
execute_on = 'timestep_end'
outputs = none
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalATiO3MaterialRVEUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
block = '0'
[../]
###############################################
##
## Assert the divergence theorem every step. Unlike the Exodiff
## this does not care what the solution IS, only that DivP and
## SurfaceChargeP are consistent, so it survives a regold.
## error_level = ERROR is required: fail_mode = HARD on its own
## stops the run but still exits 0, which a test would not catch.
##
###############################################
[./divthm_assert]
type = Terminator
expression = 'abs(divThmResidual) > 1.0e-6'
fail_mode = HARD
error_level = ERROR
execute_on = 'TIMESTEP_END'
message = 'Divergence theorem violated: oint P.n dS != int div(P) dV over block 0. DivP/SurfaceChargeP are inconsistent.'
[../]
[]
[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 = ' 80 1e-8 1e-5 1e-5 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'bdf2'
dtmin = 1e-13
dtmax = 0.6
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 6
growth_factor = 1.2
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.6
[../]
verbose = true
nl_max_its = 20
num_steps = 6
[]
[Outputs]
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_surface_charge
elemental_as_nodal = true
time_step_interval = 1
[../]
[]
(test/tests/domain_wall/test_BTO_domain_wall.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '-0.5 -0.5 -0.5'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
[]
[Functions]
[./stripe1]
type = ParsedFunction
expression = 0.01*cos(0.08975979010256552*(x))
[../]
[]
[Variables]
[./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]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -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'
[../]
[./ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
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 = 'ferro'
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
[./SolidMechanics]
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_polar_coupled_x]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
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
[../]
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-8 1e-8 1e-8 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
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]
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = test
elemental_as_nodal = true
[../]
[]
(test/tests/userobjects/terminator_multi_mech.i)
TC = 25.0
um = -0.002
C11 = 175.549
C12 = 84.639
C44 = 108.225
umzz = ${fparse -2.0*C12/C11*um}
alpha1 = ${fparse 3.3e-4*(TC - 110.0)}
alpha11 = ${fparse 3.6e-3*(TC - 175.0)}
alpha123 = ${fparse 7.6e-2*(TC - 120.0) + 44.0}
G110 = 1.0
Lx = 2.0
Ly = 2.0
tf = 2.0
nx = 2
ny = 2
nz = 8
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${ny}
nz = ${nz}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${Ly}
zmin = 0.0
zmax = ${tf}
elem_type = HEX8
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[f_el]
order = CONSTANT
family = MONOMIAL
[]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[strain_xz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[f_el]
type = ElasticEnergyAux
variable = f_el
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[strain_xz]
type = RankTwoAux
variable = strain_xz
rank_two_tensor = total_strain
index_i = 0
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} ${alpha11} 0.49 6.6 2.9 ${alpha123} 0.0 0.0 0.0 0.0'
[]
[Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.51 -0.02 0.02 0.0'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '${C11} ${C12} ${C44}'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.11 -0.043 0.0295'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 ${umzz}'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '${C11} ${C12} ${C12} ${C11} ${C12} ${C11} ${C44} ${C44} ${C44}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[]
[BCs]
[Periodic]
[xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'back'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'back'
value = 0
[]
[clamp_z]
type = DirichletBC
variable = u_z
boundary = 'back'
value = 0
[]
[]
[Postprocessors]
[Felastic_true]
type = ElementIntegralVariablePostprocessor
variable = f_el
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[exz]
type = ElementAverageValue
variable = strain_xz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-8 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-12
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/film/PTO_film_substrate_multi_mech.i)
TC = 25.0
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
h_film = 4.0
h_sub = 2.0
nz = ${fparse int((h_film + h_sub)/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nz}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = ${fparse -h_sub}
zmax = ${h_film}
elem_type = HEX8
[]
[subdomains]
type = SubdomainBoundingBoxGenerator
input = gen
block_id = 1
bottom_left = '0.0 0.0 ${fparse -h_sub}'
top_right = '${L} ${L} 0.0'
location = INSIDE
[]
[film_interface]
type = SideSetsBetweenSubdomainsGenerator
input = subdomains
primary_block = 0
paired_block = 1
new_boundary = 'film_interface'
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
displacements = 'u_x u_y u_z'
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[polar_x]
order = FIRST
family = LAGRANGE
block = 0
[]
[polar_y]
order = FIRST
family = LAGRANGE
block = 0
[]
[polar_z]
order = FIRST
family = LAGRANGE
block = 0
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 0.0 0.0 0.0 0.0'
block = 0
[]
[Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.6 0.0 0.3 0.3'
block = 0
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
block = 0
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
block = 0
[]
[elasticity_tensor_film]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
block = 0
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
block = 0
[]
[strain_film]
type = ComputeSmallStrain
eigenstrain_names = 'ferro'
block = 0
[]
[stress_film]
type = ComputeLinearElasticStress
block = 0
[]
[elasticity_tensor_sub]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '318.0 103.0 103.0 318.0 103.0 318.0 124.0 124.0 124.0'
block = 1
[]
[strain_sub]
type = ComputeSmallStrain
block = 1
[]
[stress_sub]
type = ComputeLinearElasticStress
block = 1
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
component = 2
[]
[]
[BCs]
[Periodic]
[xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z'
[]
[]
[sub_fix_x]
type = DirichletBC
variable = u_x
boundary = 'back'
value = 0
[]
[sub_fix_y]
type = DirichletBC
variable = u_y
boundary = 'back'
value = 0
[]
[sub_fix_z]
type = DirichletBC
variable = u_z
boundary = 'back'
value = 0
[]
[]
[Postprocessors]
[Felastic]
type = CubicParentElasticEnergy
block = 0
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
block = 0
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
block = 0
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-6 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/polar-elastic/PTO_2D_full.i)
TC = 25.0
um = -0.01
l0 = 1.0
Lx = 8.0
tf = 2.0
dx = 0.2
nx = ${fparse int(Lx/dx + 0.5)}
ny = ${fparse int(tf/dx + 0.5)}
lam = 8.0
P_seed = 0.3
Px_seed = 0.01
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = ${nx}
ny = ${ny}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${tf}
elem_type = QUAD4
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Functions]
[ic_Py]
type = ParsedFunction
expression = '${P_seed}*cos(2*pi*x/${lam})'
[]
[ic_Px]
type = ParsedFunction
expression = '${Px_seed}*sin(2*pi*x/${lam})'
[]
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Px
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Py
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = ConstantIC
value = 0.0
[]
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_yy]
type = RankTwoAux
variable = strain_yy
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 0 0 0 0 ${um}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y'
component = 1
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y'
[]
[]
[BCs]
[Periodic]
[x]
auto_direction = 'x'
variable = 'polar_x polar_y polar_z u_x u_y'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'bottom'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'bottom'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic'
pp_coefs = '1 1 1'
execute_on = 'timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 5.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/polar-elastic/PTO_3D_multi_mech.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z'
[]
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-6 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/dispersion/perturbBTO_PzEz.i)
freq = 1778279410.0389228
amplitude = 0.001
[Mesh]
file = out_PzEz.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
[]
[Functions]
[./bc_func_1]
type = ParsedFunction
expression = 'amplitude*sin(freq*t)'
symbol_names = 'freq amplitude'
symbol_values = '${freq} ${amplitude}'
[../]
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_x
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_y
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_z
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./Ez]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./cEy]
type = QuasistaticFieldAux
component = 2
potential_int = potential_E_int
variable = Ez
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -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'
[../]
[./ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
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 = 'ferro'
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
[./SolidMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
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 = 1e-12
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1e-12
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1e-12
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./front_pot]
type = FunctionDirichletBC
variable = potential_E_int
boundary = 'front'
function = bc_func_1
[../]
[./boundary_grounding]
type = DirichletBC
boundary = 'back'
variable = potential_E_int
value = 0.0
[../]
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'initial timestep_end'
[../]
[./Ea]
type = ElementAverageValue
variable = Ez
execute_on = 'initial timestep_end'
[../]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = ChangeOverTimePostprocessor
compute_relative_change = true
take_absolute_value = true
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options = '-snes_ksp_ew'
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-8 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-16
dt = 3.5332947520558994e-11
dtmax = 1e-10
verbose = true
num_steps = 5
[]
[Outputs]
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_perturbBTO_PzEz0
elemental_as_nodal = true
[../]
[./outCSV]
type = CSV
new_row_tolerance = 1e-16
file_base = out_perturbBTO_PzEz0
[../]
[]
(test/tests/dispersion/perturbBTO_PyEz.i)
freq = 177827941.00389227
amplitude = 1e-3
[Mesh]
file = out_PyEz.e
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
[]
[Functions]
[./bc_func_1]
type = ParsedFunction
expression = 'amplitude*sin(freq*t)'
symbol_names = 'freq amplitude'
symbol_values = '${freq} ${amplitude}'
[../]
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_x
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_y
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
initial_from_file_var = polar_z
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./stress_xx_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xy_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_xz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_zz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./stress_yz_elastic]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./Ez]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e12]
type = RankTwoAux
variable = e12
rank_two_tensor = total_strain
index_i = 1
index_j = 2
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
[../]
[./cEy]
type = QuasistaticFieldAux
component = 2
potential_int = potential_E_int
variable = Ez
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[Materials]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.027721 -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'
[../]
[./ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
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 = 'ferro'
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_1]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.08854187'
[../]
[]
[Kernels]
[./SolidMechanics]
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_x
component = 0
[../]
[./electrostr_polar_coupled_y]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
variable = polar_y
component = 1
[../]
[./electrostr_polar_coupled_z]
type = CubicParentElasticPDerivative
displacements = 'u_x u_y u_z'
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 = 1e-12
[../]
[./polar_y_time]
type = TimeDerivativeScaled
variable = polar_y
time_scale = 1e-12
[../]
[./polar_z_time]
type = TimeDerivativeScaled
variable = polar_z
time_scale = 1e-12
[../]
[]
[BCs]
[./Periodic]
[./xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z polar_x polar_y polar_z'
[../]
[../]
[./front_pot]
type = FunctionDirichletBC
variable = potential_E_int
boundary = 'front'
function = bc_func_1
[../]
[./boundary_grounding]
type = DirichletBC
boundary = 'left right top bottom back'
variable = potential_E_int
value = 0.0
[../]
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = u_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = u_y
value = 0
[../]
[./centerfix_z]
type = DirichletBC
boundary = 100
variable = u_z
value = 0
[../]
[]
[Postprocessors]
[./avePz]
type = ElementAverageValue
variable = polar_z
execute_on = 'initial timestep_end'
[../]
[./Ea]
type = ElementAverageValue
variable = Ez
execute_on = 'initial timestep_end'
[../]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./perc_change]
type = ChangeOverTimePostprocessor
compute_relative_change = true
take_absolute_value = true
postprocessor = Ftotal
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
applied_stress_tensor = '0.0 0.0 0.0 0.0 0.0 0.0'
[../]
[]
[Preconditioning]
[./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]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-16
dt = 3.5332947520558995e-10
dtmax = 1e-10
verbose = true
num_steps = 5
[]
[Outputs]
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = out_perturbBTO_PyEz0
elemental_as_nodal = true
[../]
[./outCSV]
type = CSV
new_row_tolerance = 1e-16
file_base = out_perturbBTO_PyEz0
[../]
[]
(test/tests/pertsev/PTO_pertsev_mech.i)
TC = 25.0
um = -0.002
C11 = 174.6032
C12 = 79.3651
C44 = 111.1111
umzz = ${fparse -2.0*C12/C11*um}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
alpha11 = -0.073
alpha123 = -3.7
G110 = 1.0
Lx = 2.0
Ly = 2.0
tf = 2.0
nx = 2
ny = 2
nz = 8
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${ny}
nz = ${nz}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${Ly}
zmin = 0.0
zmax = ${tf}
elem_type = HEX8
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[f_el]
order = CONSTANT
family = MONOMIAL
[]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[strain_xz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[f_el]
type = ElasticEnergyAux
variable = f_el
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[strain_xz]
type = RankTwoAux
variable = strain_xz
rank_two_tensor = total_strain
index_i = 0
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} ${alpha11} 0.75 0.26 0.61 ${alpha123} 0.0 0.0 0.0 0.0'
[]
[Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.51 -0.02 0.02 0.0'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '${C11} ${C12} ${C44}'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 ${umzz}'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '${C11} ${C12} ${C12} ${C11} ${C12} ${C11} ${C44} ${C44} ${C44}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[]
[BCs]
[Periodic]
[xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'back'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'back'
value = 0
[]
[clamp_z]
type = DirichletBC
variable = u_z
boundary = 'back'
value = 0
[]
[]
[Postprocessors]
[Felastic_true]
type = ElementIntegralVariablePostprocessor
variable = f_el
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[exz]
type = ElementAverageValue
variable = strain_xz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-8 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-12
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/bulk/BTO_bulk_relax.i)
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 2
ny = 2
nz = 2
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[GlobalParams]
len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
displacements = 'u_x u_y u_z'
[]
[Variables]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = ConstantIC
value = 0.0
[../]
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = ConstantIC
value = 0.0
[../]
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = ConstantIC
value = 0.05
[../]
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = ConstantIC
value = 0.0
[../]
[../]
[./u_x]
order = FIRST
family = LAGRANGE
[../]
[./u_y]
order = FIRST
family = LAGRANGE
[../]
[./u_z]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[./disp_z]
order = FIRST
family = LAGRANGE
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Kernels]
[./SolidMechanics]
displacements = 'u_x u_y u_z'
use_displaced_mesh = false
[../]
[./bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[../]
[./bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[../]
[./bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[../]
[./walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[../]
[./walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[../]
[./walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[../]
[./electrostr_polar_coupled_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
use_displaced_mesh = false
[../]
[./electrostr_polar_coupled_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
use_displaced_mesh = false
[../]
[./electrostr_polar_coupled_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
use_displaced_mesh = false
[../]
[./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
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
use_displaced_mesh = false
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
use_displaced_mesh = false
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
use_displaced_mesh = false
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
use_displaced_mesh = false
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'timestep_end'
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'timestep_end'
[../]
[./e22]
type = RankTwoAux
variable = e22
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'timestep_end'
[../]
[]
[Materials]
[./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'
[../]
[./ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
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 = 'ferro'
[../]
[./stress_1]
type = ComputeLinearElasticStress
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./permitivitty_bulk]
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'
[../]
[../]
[./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
[../]
[./centerfix_phi]
type = DirichletBC
boundary = 100
variable = potential_E_int
value = 0
[../]
[]
[Postprocessors]
[./Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[../]
[./Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[../]
[./Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
use_displaced_mesh = false
[../]
[./Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[../]
[./Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = ' 1 1 1 1'
execute_on = 'initial timestep_end'
[../]
[./e00_avg]
type = ElementAverageValue
variable = e00
execute_on = 'initial timestep_end'
[../]
[./e11_avg]
type = ElementAverageValue
variable = e11
execute_on = 'initial timestep_end'
[../]
[./e22_avg]
type = ElementAverageValue
variable = e22
execute_on = 'initial timestep_end'
[../]
[./Pz_avg]
type = ElementAverageValue
variable = polar_z
execute_on = 'initial timestep_end'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
applied_stress_tensor = '0 0 0 0 0 0'
use_displaced_mesh = false
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
petsc_options_iname = '-ksp_gmres_restart -snes_atol -snes_rtol -ksp_rtol -pc_type -build_twosided'
petsc_options_value = ' 160 1e-10 1e-8 1e-6 bjacobi allreduce'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
scheme = 'implicit-euler'
dtmin = 1e-13
dtmax = 3.0
l_max_its = 200
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
cutback_factor = 0.75
linear_iteration_ratio = 1000
dt = 0.3
[../]
num_steps = 40
[]
[Outputs]
print_linear_residuals = false
perf_graph = false
[./out]
type = Exodus
file_base = BTO_bulk_relax_out
elemental_as_nodal = true
[../]
[./csv]
type = CSV
file_base = BTO_bulk_relax_out
[../]
[]
(test/tests/electrostatics/PTO_STO_2D_E_full.i)
TC = 25.0
Lx = 6.0
t_pto = 2.0
t_sto = 2.0
Ly = ${fparse 2.0*t_pto + t_sto}
dx = 0.25
nx = ${fparse int(Lx/dx + 0.5)}
ny = ${fparse int(Ly/dx + 0.5)}
y0 = ${t_pto}
y1 = ${fparse t_pto + t_sto}
lam = 6.0
P_seed = 0.3
Px_seed = 0.01
eps0 = 0.0088542
eps_r = 10.0
eps_sto = 300.0
a_pto = 3.957
a_sto = 3.905
a_sub = 3.944
um_pto = ${fparse (a_sub - a_pto)/a_pto}
um_sto = ${fparse (a_sub - a_sto)/a_sto}
l0 = 1.0
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
alpha1_sto = ${fparse 1.0/(2.0*(eps_sto - eps_r)*eps0)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = ${nx}
ny = ${ny}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${Ly}
elem_type = QUAD4
[]
[sto_layer]
type = SubdomainBoundingBoxGenerator
input = gen
bottom_left = '0.0 ${y0} 0.0'
top_right = '${Lx} ${y1} 0.0'
block_id = 1
[]
[pin]
type = ExtraNodesetGenerator
input = sto_layer
new_boundary = 'pin_node'
coord = '${fparse 0.5*Lx} 0.0 0.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
[]
[Functions]
[ic_Py]
type = ParsedFunction
expression = '${P_seed}*cos(2*pi*x/${lam})'
[]
[ic_Px]
type = ParsedFunction
expression = '${Px_seed}*sin(2*pi*x/${lam})'
[]
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Px
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Py
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = ConstantIC
value = 0.0
[]
[]
[potential_E_int]
order = FIRST
family = LAGRANGE
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_yy]
type = RankTwoAux
variable = strain_yy
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P_pto]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 0.0 0.0 0.0 0.0'
block = '0'
[]
[Landau_G_pto]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.6 0.0 0.3 0.3'
block = '0'
[]
[mat_Q_pto]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
block = '0'
[]
[mat_C_pto]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
block = '0'
[]
[elasticity_tensor_pto]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
block = '0'
[]
[misfit_pto]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um_pto} 0 0 0 0 0 0 0 ${um_pto}'
block = '0'
[]
[ferro_pto]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
block = '0'
[]
[Landau_P_sto]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1_sto} 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0'
block = '1'
[]
[Landau_G_sto]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.6 0.0 0.3 0.3'
block = '1'
[]
[mat_Q_sto]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.04575 -0.01350 0.00957'
block = '1'
[]
[mat_C_sto]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '318.1 102.5 123.5'
block = '1'
[]
[elasticity_tensor_sto]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '318.1 102.5 102.5 318.1 102.5 318.1 123.5 123.5 123.5'
block = '1'
[]
[misfit_sto]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um_sto} 0 0 0 0 0 0 0 ${um_sto}'
block = '1'
[]
[ferro_sto]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
block = '1'
[]
[permittivity]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '${fparse eps_r*eps0}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[poisson]
type = Electrostatics
variable = potential_E_int
[]
[divP]
type = PolarElectricEStrong
variable = potential_E_int
[]
[Ephi_x]
type = PolarElectricPStrong
variable = polar_x
component = 0
[]
[Ephi_y]
type = PolarElectricPStrong
variable = polar_y
component = 1
[]
[Ephi_z]
type = PolarElectricPStrong
variable = polar_z
component = 2
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y'
component = 1
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y'
[]
[]
[BCs]
[Periodic]
[x]
auto_direction = 'x'
variable = 'polar_x polar_y polar_z potential_E_int u_x u_y'
[]
[]
[phi_pin]
type = DirichletBC
variable = potential_E_int
boundary = 'pin_node'
value = 0
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'bottom'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'bottom'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = '1 1 1 1'
execute_on = 'timestep_end'
[]
[Pmag_pto]
type = ElementAverageValue
variable = Pmag
block = '0'
execute_on = 'initial timestep_end'
[]
[Pmag_sto]
type = ElementAverageValue
variable = Pmag
block = '1'
execute_on = 'initial timestep_end'
[]
[exx_pto]
type = ElementAverageValue
variable = strain_xx
block = '0'
execute_on = 'initial timestep_end'
[]
[exx_sto]
type = ElementAverageValue
variable = strain_xx
block = '1'
execute_on = 'initial timestep_end'
[]
[phi_max]
type = NodalExtremeValue
variable = potential_E_int
value_type = max
execute_on = 'initial timestep_end'
[]
[phi_min]
type = NodalExtremeValue
variable = potential_E_int
value_type = min
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 5.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 4
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/pertsev/BTO_pertsev_mech.i)
TC = 25.0
um = -0.002
C11 = 175.549
C12 = 84.639
C44 = 108.225
umzz = ${fparse -2.0*C12/C11*um}
alpha1 = ${fparse 3.3e-4*(TC - 110.0)}
alpha11 = ${fparse 3.6e-3*(TC - 175.0)}
alpha123 = ${fparse 7.6e-2*(TC - 120.0) + 44.0}
G110 = 1.0
Lx = 2.0
Ly = 2.0
tf = 2.0
nx = 2
ny = 2
nz = 8
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${ny}
nz = ${nz}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${Ly}
zmin = 0.0
zmax = ${tf}
elem_type = HEX8
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[f_el]
order = CONSTANT
family = MONOMIAL
[]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[strain_xz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[f_el]
type = ElasticEnergyAux
variable = f_el
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[strain_xz]
type = RankTwoAux
variable = strain_xz
rank_two_tensor = total_strain
index_i = 0
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} ${alpha11} 0.49 6.6 2.9 ${alpha123} 0.0 0.0 0.0 0.0'
[]
[Landau_G]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} 0.51 -0.02 0.02 0.0'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '${C11} ${C12} ${C44}'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.11 -0.043 0.0295'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 ${umzz}'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '${C11} ${C12} ${C12} ${C11} ${C12} ${C11} ${C44} ${C44} ${C44}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[]
[BCs]
[Periodic]
[xy]
auto_direction = 'x y'
variable = 'u_x u_y u_z'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'back'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'back'
value = 0
[]
[clamp_z]
type = DirichletBC
variable = u_z
boundary = 'back'
value = 0
[]
[]
[Postprocessors]
[Felastic_true]
type = ElementIntegralVariablePostprocessor
variable = f_el
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[exz]
type = ElementAverageValue
variable = strain_xz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-8 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-12
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(test/tests/userobjects/terminator_full.i)
TC = 25.0
um = -0.01
l0 = 1.0
Lx = 8.0
tf = 2.0
dx = 0.2
nx = ${fparse int(Lx/dx + 0.5)}
ny = ${fparse int(tf/dx + 0.5)}
lam = 8.0
ftol = 1.0e-2
tmin = 1.0
P_seed = 0.3
Px_seed = 0.01
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = ${nx}
ny = ${ny}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${tf}
elem_type = QUAD4
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Functions]
[ic_Py]
type = ParsedFunction
expression = '${P_seed}*cos(2*pi*x/${lam})'
[]
[ic_Px]
type = ParsedFunction
expression = '${Px_seed}*sin(2*pi*x/${lam})'
[]
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Px
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Py
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = ConstantIC
value = 0.0
[]
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_yy]
type = RankTwoAux
variable = strain_yy
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 0 0 0 0 ${um}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y'
component = 1
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y'
[]
[]
[BCs]
[Periodic]
[x]
auto_direction = 'x'
variable = 'polar_x polar_y polar_z u_x u_y'
[]
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'bottom'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'bottom'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic'
pp_coefs = '1 1 1'
execute_on = 'timestep_end'
[]
[t]
type = TimePostprocessor
execute_on = 'timestep_end'
[]
[perc_change]
type = ChangeOverTimePostprocessor
postprocessor = Ftotal
compute_relative_change = true
take_absolute_value = true
execute_on = 'timestep_end'
[]
[]
[UserObjects]
[kill]
type = Terminator
expression = 'perc_change <= ${ftol} & t >= ${tmin}'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 100.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 10
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/ics/PTO_3D_fluct.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
nx = 4
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FluctuationsIC
epsilon = 1.0e-5
q1 = '354 1005 645'
q2 = '715 1065 1132'
q3 = '391 305 1106'
q4 = '1053 1116 627'
h = 0.22
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FluctuationsIC
epsilon = 1.0e-5
q1 = '354 850 10'
q2 = '715 28 5'
q3 = '391 305 1106'
q4 = '653 1116 627'
h = 0.15
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FluctuationsIC
epsilon = 1.0e-5
q1 = '860 165 645'
q2 = '715 665 1332'
q3 = '361 15 706'
q4 = '253 1116 627'
h = 0.05
[]
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y u_z'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y u_z'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y u_z'
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'polar_x polar_y polar_z u_x u_y u_z'
[]
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic'
pp_coefs = '1 1 1'
execute_on = 'timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 5.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/polar-elastic-electric/PTO_2D_E_full.i)
TC = 25.0
um = -0.01
l0 = 1.0
Lx = 8.0
tf = 2.0
dx = 0.2
nx = ${fparse int(Lx/dx + 0.5)}
ny = ${fparse int(tf/dx + 0.5)}
lam = 8.0
P_seed = 0.3
Px_seed = 0.01
eps_r = 10.0
eps0 = 0.0088542
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = ${nx}
ny = ${ny}
xmin = 0.0
xmax = ${Lx}
ymin = 0.0
ymax = ${tf}
elem_type = QUAD4
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '8.0 0.0 0.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
potential_E_int = potential_E_int
[]
[Functions]
[ic_Py]
type = ParsedFunction
expression = '${P_seed}*cos(2*pi*x/${lam})'
[]
[ic_Px]
type = ParsedFunction
expression = '${Px_seed}*sin(2*pi*x/${lam})'
[]
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Px
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = ic_Py
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = ConstantIC
value = 0.0
[]
[]
[potential_E_int]
order = FIRST
family = LAGRANGE
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_yy]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_yy]
type = RankTwoAux
variable = strain_yy
rank_two_tensor = total_strain
index_i = 1
index_j = 1
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[permittivity]
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '${fparse eps_r*eps0}'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 0 0 0 0 ${um}'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[poisson]
type = Electrostatics
variable = potential_E_int
[]
[divP]
type = PolarElectricEStrong
variable = potential_E_int
[]
[Ephi_x]
type = PolarElectricPStrong
variable = polar_x
component = 0
[]
[Ephi_y]
type = PolarElectricPStrong
variable = polar_y
component = 1
[]
[Ephi_z]
type = PolarElectricPStrong
variable = polar_z
component = 2
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y'
component = 1
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y'
[]
[]
[BCs]
[Periodic]
[x]
auto_direction = 'x'
variable = 'polar_x polar_y polar_z potential_E_int u_x u_y'
[]
[]
[phi_pin]
type = DirichletBC
variable = potential_E_int
boundary = 'pin_node'
value = 0
[]
[clamp_x]
type = DirichletBC
variable = u_x
boundary = 'bottom'
value = 0
[]
[clamp_y]
type = DirichletBC
variable = u_y
boundary = 'bottom'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felec]
type = ElectrostaticEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic Felec'
pp_coefs = '1 1 1 1'
execute_on = 'timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 5.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/polar-elastic-electric/PTO_3D_E_multi_mech.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z'
[]
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-6 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]
(tutorial/ferroelectric_domain_wall.i)
###############################################################
##
## Ferroelectric 180-degree domain wall in BaTiO3.
##
## This input is the NON-FLEXOELECTRIC, UNROTATED reduction of the
## flexoelectric domain-wall model. Two systematic changes were made
## relative to that model:
##
## 1. RotatedCubicParentNVFlexoelectricFullPDerivative ->
## CubicParentElasticPDerivative. The "Full" kernel carried BOTH the
## electrostrictive and the flexoelectric parts of dF/dP (which is why
## there was no separate elastic P-derivative Kernel). Every gradient-
## test term in it carries a flexocoupling factor mu, so as mu -> 0 it
## reduces exactly to the elastic P-derivative. Verified numerically:
## running the flexo input with mu11 = mu12 = mu44 = 0 reproduces this
## input's elastic energy to 4e-8 relative and total energy to 1.2e-8.
##
## 2. All Rotated* objects -> their unrotated counterparts, and the twist
## angle / euler angles removed. Nothing here is rotated, so the crystal
## axes and the simulation axes coincide.
##
## The flexoelectric eigenstrain, the flexocoupling constants mu_ij and the
## elastic compliances s_ij are gone with them. NOTE that the flexo
## eigenstrain entered the CompositeEigenstrain with weight -1, so dropping
## it is not a no-op.
##
## GRADIENT COEFFICIENT CONVENTION -- read before editing the G block.
## The unrotated WallEnergyDerivative/WallEnergy take G110 together with the
## RATIOS G11/G110 etc. The Rotated variants took bare G11/G12/G44. Matching
## the two residuals term-by-term at twist = 0 gives
## G110 = G11, G11_G110 = 1, G12_G110 = G12/G11, G44_G110 = G44/G11
## and, crucially, G44P_G110 = 0: the Rotated kernel carries NO antisymmetric
## G44' term. Other unrotated Ferret inputs ship a nonzero G44P_G110
## (surface_charge.i uses 0.3), so copying a G block from one of those would
## silently add physics this model never had.
##
## Units in Ferret are nm, kg, seconds and attocoulombs.
##
## CAVEAT: the Terminator below stops on the ENERGY RATE, which is blind to
## small polarization components -- it can fire while a component orders of
## magnitude below the dominant one is still evolving. If you care about such
## a component, disable it and use a fixed end_time instead.
##
###############################################################
## Gradient (wall) energy coefficients.
## The unrotated WallEnergyDerivative/WallEnergy take G110 together with the
## ratios G11/G110 etc., NOT the bare G11/G12/G44 that the Rotated variants use.
## Matching the two residuals term-by-term at twist = 0 gives
## G110 = G11, G11_G110 = 1, G12_G110 = G12/G11, G44_G110 = G44/G11
## and, crucially, G44P_G110 = 0: the Rotated kernel carries NO antisymmetric
## G44' term, so copying a G-block from another unrotated input (surface_charge.i
## ships G44P_G110 = 0.3) would silently add physics this model never had.
## Here G11 = 0.5, G12 = -0.02, G44 = 0.02.
G110 = 0.5
G11_G110 = 1.0
G12_G110 = -0.04
G44_G110 = 0.04
G44P_G110 = 0.0
L = 0.25
n_xy = 1
Z = 110.0
n_z = 440.0
period = 0.028559933214452663
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${n_z}
ny = ${n_xy}
nz = ${n_xy}
xmin = -${Z}
xmax = ${Z}
ymin = -${L}
ymax = ${L}
zmin = -${L}
zmax = ${L}
elem_type = HEX8
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '-${Z} -${L} -${L}'
new_boundary = 100
[../]
[]
[GlobalParams]
#len_scale = 1.0
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
displacements = 'u_x u_y u_z'
potential_E_int = potential_E_int
[]
[Functions]
[./DW_func]
type = ParsedFunction
symbol_names = 'A p'
symbol_values = '0.2 ${period}'
expression = 'A*cos(p*x)'
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./polar_x]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-5
max = 1e-5
seed = 1
[../]
block = '0'
[../]
[./polar_y]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = -1e-5
max = 1e-5
seed = 2
[../]
block = '0'
[../]
[./polar_z]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = DW_func
[../]
block = '0'
[../]
[./potential_E_int]
order = FIRST
family = LAGRANGE
block = '0'
[../]
[]
[Physics]
[SolidMechanics]
[QuasiStatic]
[./all_FE]
strain = SMALL
add_variables = true
incremental = false
eigenstrain_names = 'total_eigenstrain'
global_strain = global_strain
generate_output = 'strain_xx strain_yy strain_zz strain_yz strain_xz strain_xy'
block = '0'
[../]
[]
# GlobalStrain action for generating the objects associated with the global
# strain calculation and associated displacement visualization
[./GlobalStrain]
[./global_strain]
scalar_global_strain = global_strain
displacements = 'u_x u_y u_z'
auxiliary_displacements = 'disp_x disp_y disp_z'
global_displacements = 'ug_x ug_y ug_z'
[../]
[../]
[]
[]
[Kernels]
### Operators for the polar field: ###
[./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'
[../]
[./elastic_polar_coupled_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
block = '0'
[../]
[./elastic_polar_coupled_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
block = '0'
[../]
[./elastic_polar_coupled_z]
type = CubicParentElasticPDerivative
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'
[../]
[./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'
[../]
[]
[Materials]
[./eigen_strain]
type = ComputeEigenstrain
#xx yy zz (xy yz xz)
eigen_base = '0.0 0.0 0.0 0.0 0.0 0.0'
eigenstrain_name = 'epitaxy'
block = '0'
[../]
[./Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '-0.03635 -0.2097 0.7974 1.294 -1.95 -2.5 38.63 25.29 16.37 13.67'
block = '0'
[../]
[./Landau0_G_FE]
type = GenericConstantMaterial
prop_names = 'G110 G11_G110 G12_G110 G44_G110 G44P_G110'
prop_values = '${G110} ${G11_G110} ${G12_G110} ${G44_G110} ${G44P_G110}'
block = '0'
[../]
[./mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '178.0 96.4 122.0'
block = '0'
[../]
[./mat_Q] #this is slightly different from Phys Rev B 89, 174111 (2014) ?
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.10 -0.045 0.029' #0.059/4?
block = '0'
[../]
[./elasticity_tensor_1]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '178.0 96.4 96.4 178.0 96.4 178.0 122.0 122.0 122.0'
block = '0'
[../]
[./film_eigenstrain]
type = CompositeEigenstrain
## NOTE: 'flexo' carried weight2 = -1, so dropping it is not a no-op.
tensors = 'ferro epitaxy'
weights = 'weight1 weight3'
eigenstrain_name = total_eigenstrain
coupled_variables = 'polar_x polar_y polar_z'
block = '0'
[../]
[./weight1]
type = DerivativeParsedMaterial
block = '0'
expression = '1'
property_name = weight1
coupled_variables = 'polar_x polar_y polar_z'
[../]
[./weight3]
type = DerivativeParsedMaterial
block = '0'
expression = '1'
property_name = weight3
[../]
[./stress_1]
type = ComputeLinearElasticStress
block = '0'
[../]
[./electrostrictive_eigenstrain]
type = ComputeCubicParentElectrostrictiveStrain
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
eigenstrain_name = 'ferro'
block = '0'
[../]
[./permitivitty]
###############################################
##
## BTO background permittivity 45 (used in flexo paper)
##
###############################################
type = GenericConstantMaterial
prop_names = 'permittivity'
prop_values = '0.39'
block = '0'
[../]
[]
[Postprocessors]
[./dt]
type = TimestepSize
[../]
[./FbP]
type = BulkEnergyEighth
execute_on = 'timestep_end'
block = '0'
[../]
[./FgP]
type = WallEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Fele]
type = ElectrostaticEnergy
execute_on = 'timestep_end'
block = '0'
[../]
[./Fela]
type = CubicParentElasticEnergy
execute_on = 'timestep_end'
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
block = '0'
[../]
[./Ftot]
type = LinearCombinationPostprocessor
pp_names = 'FbP FgP Fela Fele'
pp_coefs = ' 1 1 1 1'
execute_on = 'timestep_end'
##########################################
#
# NOTE: Ferret output is in attojoules
#
##########################################
[../]
[./maxPy]
type = NodalExtremeValue
variable = polar_y
[../]
[./maxPx]
type = NodalExtremeValue
variable = polar_x
[../]
[./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 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]
[./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'
petsc_options_value = ' 121 1e-8 1e-6 1e-5 bjacobi'
[../]
[]
[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 = 0.1
growth_factor = 1.1
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph_live = false
[./out]
type = Exodus
execute_on = 'INITIAL FINAL'
file_base = out_ferroelectric_domain_wall
elemental_as_nodal = true
[../]
[./csv]
type = CSV
file_base = out_ferroelectric_domain_wall
[../]
[]
(test/tests/polar-elastic/PTO_3D_full.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[polar_x]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 1
[]
[]
[polar_y]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 2
[]
[]
[polar_z]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = RandomIC
min = -0.5
max = 0.5
seed = 3
[]
[]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[wE]
order = CONSTANT
family = MONOMIAL
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[wE]
type = WallEnergyDensity
variable = wE
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[time_x]
type = TimeDerivative
variable = polar_x
[]
[time_y]
type = TimeDerivative
variable = polar_y
[]
[time_z]
type = TimeDerivative
variable = polar_z
[]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[bed_x]
type = BulkEnergyDerivativeEighth
variable = polar_x
component = 0
[]
[bed_y]
type = BulkEnergyDerivativeEighth
variable = polar_y
component = 1
[]
[bed_z]
type = BulkEnergyDerivativeEighth
variable = polar_z
component = 2
[]
[walled_x]
type = WallEnergyDerivative
variable = polar_x
component = 0
[]
[walled_y]
type = WallEnergyDerivative
variable = polar_y
component = 1
[]
[walled_z]
type = WallEnergyDerivative
variable = polar_z
component = 2
[]
[electrostr_x]
type = CubicParentElasticPDerivative
variable = polar_x
component = 0
displacements = 'u_x u_y u_z'
[]
[electrostr_y]
type = CubicParentElasticPDerivative
variable = polar_y
component = 1
displacements = 'u_x u_y u_z'
[]
[electrostr_z]
type = CubicParentElasticPDerivative
variable = polar_z
component = 2
displacements = 'u_x u_y u_z'
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'polar_x polar_y polar_z u_x u_y u_z'
[]
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Fbulk]
type = BulkEnergyEighth
execute_on = 'initial timestep_end'
[]
[Fwall]
type = WallEnergy
execute_on = 'initial timestep_end'
[]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[Ftotal]
type = LinearCombinationPostprocessor
pp_names = 'Fbulk Fwall Felastic'
pp_coefs = '1 1 1'
execute_on = 'timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -ksp_gmres_restart'
petsc_options_value = 'bjacobi ilu gmres 1e-6 100'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = PJFNK
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 200
end_time = 5.0
[TimeStepper]
type = IterationAdaptiveDT
dt = 0.5
growth_factor = 1.3
cutback_factor = 0.8
optimal_iterations = 8
linear_iteration_ratio = 1000
[]
dtmax = 5.0
num_steps = 3
[]
[Outputs]
print_linear_residuals = false
[exo]
type = Exodus
[]
[]
(test/tests/film/PTO_film_clamped_multi_mech.i)
TC = 25.0
um = -0.01
l0 = 1.0
L = 4.0
dx = 1.0
nx = ${fparse int(L/dx + 0.5)}
alpha1 = ${fparse 3.8e-4*(TC - 479.0)}
G110 = ${fparse l0*l0*abs(alpha1)}
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = ${nx}
ny = ${nx}
nz = ${nx}
xmin = 0.0
xmax = ${L}
ymin = 0.0
ymax = ${L}
zmin = 0.0
zmax = ${L}
elem_type = HEX8
[]
[pin]
type = ExtraNodesetGenerator
input = gen
new_boundary = 'pin_node'
coord = '2.0 2.0 2.0'
use_closest_node = true
[]
[]
[GlobalParams]
polar_x = polar_x
polar_y = polar_y
polar_z = polar_z
[]
[Variables]
[u_x]
order = FIRST
family = LAGRANGE
[]
[u_y]
order = FIRST
family = LAGRANGE
[]
[u_z]
order = FIRST
family = LAGRANGE
[]
[]
[AuxVariables]
[polar_x]
order = FIRST
family = LAGRANGE
[]
[polar_y]
order = FIRST
family = LAGRANGE
[]
[polar_z]
order = FIRST
family = LAGRANGE
[]
[Pmag]
order = FIRST
family = LAGRANGE
[]
[strain_xx]
order = CONSTANT
family = MONOMIAL
[]
[strain_zz]
order = CONSTANT
family = MONOMIAL
[]
[]
[AuxKernels]
[Pmag]
type = ParsedAux
variable = Pmag
coupled_variables = 'polar_x polar_y polar_z'
expression = 'sqrt(polar_x^2 + polar_y^2 + polar_z^2)'
execute_on = 'initial timestep_end'
[]
[strain_xx]
type = RankTwoAux
variable = strain_xx
rank_two_tensor = total_strain
index_i = 0
index_j = 0
execute_on = 'initial timestep_end'
[]
[strain_zz]
type = RankTwoAux
variable = strain_zz
rank_two_tensor = total_strain
index_i = 2
index_j = 2
execute_on = 'initial timestep_end'
[]
[]
[Materials]
[Landau_P]
type = GenericConstantMaterial
prop_names = 'alpha1 alpha11 alpha12 alpha111 alpha112 alpha123 alpha1111 alpha1112 alpha1122 alpha1123'
prop_values = '${alpha1} -0.073 0.75 0.26 0.61 -3.7 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 = '${G110} 0.6 0.0 0.3 0.3'
[]
[mat_C]
type = GenericConstantMaterial
prop_names = 'C11 C12 C44'
prop_values = '174.269 79.029 47.62'
[]
[mat_Q]
type = GenericConstantMaterial
prop_names = 'Q11 Q12 Q44'
prop_values = '0.089 -0.026 0.03375'
[]
[elasticity_tensor]
type = ComputeElasticityTensor
fill_method = symmetric9
C_ijkl = '174.269 79.029 79.029 174.269 79.029 174.269 47.62 47.62 47.62'
[]
[misfit]
type = GenericConstantRankTwoTensor
tensor_name = global_strain
tensor_values = '${um} 0 0 0 ${um} 0 0 0 0'
[]
[strain]
type = ComputeSmallStrain
displacements = 'u_x u_y u_z'
eigenstrain_names = 'ferro'
global_strain = global_strain
[]
[ferro]
type = ComputeCubicParentElectrostrictiveStrain
eigenstrain_name = ferro
[]
[stress]
type = ComputeLinearElasticStress
[]
[]
[Kernels]
[div_x]
type = StressDivergenceTensors
variable = u_x
displacements = 'u_x u_y u_z'
component = 0
[]
[div_y]
type = StressDivergenceTensors
variable = u_y
displacements = 'u_x u_y u_z'
component = 1
[]
[div_z]
type = StressDivergenceTensors
variable = u_z
displacements = 'u_x u_y u_z'
component = 2
[]
[]
[BCs]
[Periodic]
[xyz]
auto_direction = 'x y z'
variable = 'u_x u_y u_z'
[]
[]
[pin_ux]
type = DirichletBC
variable = u_x
boundary = 'pin_node'
value = 0
[]
[pin_uy]
type = DirichletBC
variable = u_y
boundary = 'pin_node'
value = 0
[]
[pin_uz]
type = DirichletBC
variable = u_z
boundary = 'pin_node'
value = 0
[]
[]
[Postprocessors]
[Felastic]
type = CubicParentElasticEnergy
execute_on = 'initial timestep_end'
[]
[exx]
type = ElementAverageValue
variable = strain_xx
execute_on = 'initial timestep_end'
[]
[ezz]
type = ElementAverageValue
variable = strain_zz
execute_on = 'initial timestep_end'
[]
[]
[Preconditioning]
[smp]
type = SMP
full = true
petsc_options_iname = '-pc_type -sub_pc_type -ksp_type -ksp_rtol -snes_type'
petsc_options_value = 'bjacobi ilu cg 1e-6 ksponly'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
nl_rel_tol = 1e-8
nl_abs_tol = 1e-10
l_max_its = 500
dt = 1.0
end_time = 1e9
[]
[Outputs]
print_linear_residuals = false
[]