- variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Description:The name of the variable that this object applies to
TotalFreeEnergy
under construction:Undocumented Class
The TotalFreeEnergy 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.
# TotalFreeEnergy
!syntax description /AuxKernels/TotalFreeEnergy
## Overview
!! Replace these lines with information regarding the TotalFreeEnergy object.
## Example Input File Syntax
!! Describe and include an example of how to use the TotalFreeEnergy object.
!syntax parameters /AuxKernels/TotalFreeEnergy
!syntax inputs /AuxKernels/TotalFreeEnergy
!syntax children /AuxKernels/TotalFreeEnergy
Total free energy (both the bulk and gradient parts), where the bulk free energy has been defined in a material
Input Parameters
- additional_free_energyCoupled variable holding additional free energy contributions to be summed up
C++ Type:std::vector
Options:
Description:Coupled variable holding additional free energy contributions to be summed up
- blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
- boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
- execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM PRE_DISPLACE
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
- f_nameF Base name of the free energy function
Default:F
C++ Type:MaterialPropertyName
Options:
Description: Base name of the free energy function
- interfacial_varsVariable names that contribute to interfacial energy
C++ Type:std::vector
Options:
Description:Variable names that contribute to interfacial energy
- kappa_namesVector of kappa names corresponding to each variable name in interfacial_vars in the same order.
C++ Type:std::vector
Options:
Description:Vector of kappa names corresponding to each variable name in interfacial_vars in the same order.
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
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
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
Input Files
- modules/combined/examples/mortar/eigenstrain_action.i
- modules/combined/examples/phase_field-mechanics/Pattern1.i
- modules/combined/examples/periodic_strain/global_strain_pfm_3D.i
- modules/phase_field/test/tests/SplitCH/forward_split_math_test.i
- modules/combined/examples/periodic_strain/global_strain_pfm.i
- modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_test.i
- modules/phase_field/examples/measure_interface_energy/1Dinterface_energy.i
- modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_2var_test.i
- modules/phase_field/examples/cahn-hilliard/Parsed_CH.i
- modules/phase_field/examples/cahn-hilliard/Parsed_SplitCH.i
- modules/combined/examples/mortar/eigenstrain.i
- modules/phase_field/examples/multiphase/DerivativeMultiPhaseMaterial.i
- modules/phase_field/tutorials/spinodal_decomposition/s5_energycurve.i
- modules/phase_field/test/tests/actions/conserved_forward_split_1var.i
- modules/phase_field/examples/rigidbodymotion/AC_CH_Multigrain.i
- modules/phase_field/test/tests/MultiPhase/crosstermfreeenergy.i
modules/combined/examples/mortar/eigenstrain_action.i
#
# Eigenstrain with Mortar gradient periodicity
#
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 50
ny = 50
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0'
new_boundary = 100
[../]
[./anode]
input = cnode
type = ExtraNodesetGenerator
coord = '0.0 0.5'
new_boundary = 101
[../]
[]
[Modules/PhaseField/MortarPeriodicity]
[./strain]
variable = 'disp_x disp_y'
periodicity = gradient
periodic_directions = 'x y'
[../]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
block = 0
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = RandomIC
min = 0.49
max = 0.51
[../]
block = 0
[../]
[./w]
block = 0
[../]
# Mesh displacement
[./disp_x]
block = 0
[../]
[./disp_y]
block = 0
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
block = '0'
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '1 1 0 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
block = 0
function = '0.3*c^2'
f_name = weight1
args = c
[../]
[./weight2]
type = DerivativeParsedMaterial
block = 0
function = '0.3*(1-c)^2'
f_name = weight2
args = c
[../]
[./weight3]
type = DerivativeParsedMaterial
block = 0
function = '4*(0.5-c)^2'
f_name = weight3
args = c
[../]
# matrix phase
[./elasticity_tensor]
type = ComputeElasticityTensor
block = 0
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
block = 0
displacements = 'disp_x disp_y'
[../]
[./eigenstrain]
type = CompositeEigenstrain
block = 0
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
args = c
eigenstrain_name = eigenstrain
[../]
[./stress]
type = ComputeLinearElasticStress
block = 0
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
block = 0
f_name = Fc
function = '4*c^2*(1-c)^2'
args = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
block = 0
args = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
f_name = F
sum_materials = 'Fc Fe'
args = 'c'
[../]
[]
[BCs]
[./Periodic]
[./up_down]
primary = top
secondary = bottom
translation = '0 -1 0'
variable = 'c w'
[../]
[./left_right]
primary = left
secondary = right
translation = '1 0 0'
variable = 'c w'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = disp_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = disp_y
value = 0
[../]
# fix side point x coordinate to inhibit rotation
[./angularfix]
type = DirichletBC
boundary = 101
variable = disp_x
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
# mortar currently does not support MPI parallelization
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = ' lu NONZERO 1e-10'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.01
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
modules/combined/examples/phase_field-mechanics/Pattern1.i
#
# Pattern example 1
#
# Phase changes driven by a combination mechanical (elastic) and chemical
# driving forces. In this three phase system a matrix phase, an oversized and
# an undersized precipitate phase compete. The chemical free energy favors a
# phase separation into either precipitate phase. A mix of both precipitate
# emerges to balance lattice expansion and contraction.
#
# This example demonstrates the use of
# * ACMultiInterface
# * SwitchingFunctionConstraintEta and SwitchingFunctionConstraintLagrange
# * DerivativeParsedMaterial
# * ElasticEnergyMaterial
# * DerivativeMultiPhaseMaterial
# * MultiPhaseStressMaterial
# which are the components to se up a phase field model with an arbitrary number
# of phases
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 80
ny = 80
nz = 0
xmin = -20
xmax = 20
ymin = -20
ymax = 20
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[GlobalParams]
# CahnHilliard needs the third derivatives
derivative_order = 3
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0
max = 0.8
seed = 1235
[../]
[../]
# Order parameter for the Matrix
[./eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
# Order parameters for the 2 different inclusion orientations
[./eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
[./eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# Mesh displacement
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
# Lagrange-multiplier
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_res]
type = CahnHilliard
variable = c
f_name = F
args = 'eta1 eta2 eta3'
[../]
[./time]
type = TimeDerivative
variable = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
args = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
args = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
args = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
# Lagrange-multiplier constraint kernel for lambda
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-6
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0 1 1 1 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 '
[../]
# We use this to output the level of constraint enforcement
# ideally it should be 0 everywhere, if the constraint is fully enforced
[./etasummat]
type = ParsedMaterial
f_name = etasum
args = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
function = 'h1+h2+h3-1'
outputs = exodus
[../]
# This parsed material creates a single property for visualization purposes.
# It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
[./phasemap]
type = ParsedMaterial
f_name = phase
args = 'eta2 eta3'
function = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
outputs = exodus
[../]
# matrix phase
[./elasticity_tensor_1]
type = ComputeElasticityTensor
base_name = phase1
C_ijkl = '3 3'
fill_method = symmetric_isotropic
[../]
[./strain_1]
type = ComputeSmallStrain
base_name = phase1
displacements = 'disp_x disp_y'
[../]
[./stress_1]
type = ComputeLinearElasticStress
base_name = phase1
[../]
# oversized phase
[./elasticity_tensor_2]
type = ComputeElasticityTensor
base_name = phase2
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_2]
type = ComputeSmallStrain
base_name = phase2
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./stress_2]
type = ComputeLinearElasticStress
base_name = phase2
[../]
[./eigenstrain_2]
type = ComputeEigenstrain
base_name = phase2
eigen_base = '0.02'
eigenstrain_name = eigenstrain
[../]
# undersized phase
[./elasticity_tensor_3]
type = ComputeElasticityTensor
base_name = phase3
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_3]
type = ComputeSmallStrain
base_name = phase3
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./stress_3]
type = ComputeLinearElasticStress
base_name = phase3
[../]
[./eigenstrain_3]
type = ComputeEigenstrain
base_name = phase3
eigen_base = '-0.05'
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
f_name = Fc1
function = '4*c^2'
args = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
f_name = Fc2
function = '(c-0.9)^2-0.4'
args = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_3]
type = DerivativeParsedMaterial
f_name = Fc3
function = '(c-0.9)^2-0.5'
args = 'c'
derivative_order = 2
[../]
# elastic free energies
[./elastic_free_energy_1]
type = ElasticEnergyMaterial
base_name = phase1
f_name = Fe1
derivative_order = 2
args = 'c' # should be empty
[../]
[./elastic_free_energy_2]
type = ElasticEnergyMaterial
base_name = phase2
f_name = Fe2
derivative_order = 2
args = 'c' # should be empty
[../]
[./elastic_free_energy_3]
type = ElasticEnergyMaterial
base_name = phase3
f_name = Fe3
derivative_order = 2
args = 'c' # should be empty
[../]
# phase free energies (chemical + elastic)
[./phase_free_energy_1]
type = DerivativeSumMaterial
f_name = F1
sum_materials = 'Fc1 Fe1'
args = 'c'
derivative_order = 2
[../]
[./phase_free_energy_2]
type = DerivativeSumMaterial
f_name = F2
sum_materials = 'Fc2 Fe2'
args = 'c'
derivative_order = 2
[../]
[./phase_free_energy_3]
type = DerivativeSumMaterial
f_name = F3
sum_materials = 'Fc3 Fe3'
args = 'c'
derivative_order = 2
[../]
# global free energy
[./free_energy]
type = DerivativeMultiPhaseMaterial
f_name = F
fi_names = 'F1 F2 F3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
args = 'c'
W = 3
[../]
# Generate the global stress from the phase stresses
[./global_stress]
type = MultiPhaseStressMaterial
phase_base = 'phase1 phase2 phase3'
h = 'h1 h2 h3'
[../]
[]
[BCs]
# the boundary conditions on the displacement enforce periodicity
# at zero total shear and constant volume
[./bottom_y]
type = DirichletBC
variable = disp_y
boundary = 'bottom'
value = 0
[../]
[./top_y]
type = DirichletBC
variable = disp_y
boundary = 'top'
value = 0
[../]
[./left_x]
type = DirichletBC
variable = disp_x
boundary = 'left'
value = 0
[../]
[./right_x]
type = DirichletBC
variable = disp_x
boundary = 'right'
value = 0
[../]
[./Periodic]
[./disp_x]
auto_direction = 'y'
[../]
[./disp_y]
auto_direction = 'x'
[../]
# all other phase field variables are fully periodic
[./c]
auto_direction = 'x y'
[../]
[./eta1]
auto_direction = 'x y'
[../]
[./eta2]
auto_direction = 'x y'
[../]
[./eta3]
auto_direction = 'x y'
[../]
[./lambda]
auto_direction = 'x y'
[../]
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm ilu'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.1
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
modules/combined/examples/periodic_strain/global_strain_pfm_3D.i
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 3
nx = 20
ny = 20
nz = 20
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = -0.5
zmax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0 0.0'
new_boundary = 100
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./u_z]
[../]
[./global_strain]
order = SIXTH
family = SCALAR
[../]
[./c]
[./InitialCondition]
type = FunctionIC
function = 'sin(2*x*pi)*sin(2*y*pi)*sin(2*z*pi)*0.05+0.6'
[../]
[../]
[./w]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./disp_x]
[../]
[./disp_y]
[../]
[./disp_z]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./disp_z]
type = GlobalDisplacementAux
variable = disp_z
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 2
[../]
[./local_free_energy]
type = TotalFreeEnergy
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'u_x u_y u_z'
block = 0
[]
[Kernels]
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
block = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
block = 0
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
block = 0
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y z'
variable = 'c w u_x u_y u_z'
[../]
[../]
# 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
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 0.5 0.5 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 -0.5 -0.5 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
tensor_values = '1 1 1 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
function = '0.3*c^2'
f_name = weight1
args = c
[../]
[./weight2]
type = DerivativeParsedMaterial
function = '0.3*(1-c)^2'
f_name = weight2
args = c
[../]
[./weight3]
type = DerivativeParsedMaterial
function = '4*(0.5-c)^2'
f_name = weight3
args = c
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./eigenstrain]
type = CompositeEigenstrain
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
args = c
eigenstrain_name = eigenstrain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
f_name = Fc
function = '4*c^2*(1-c)^2'
args = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
args = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
f_name = F
sum_materials = 'Fc Fe'
args = 'c'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly lu 1'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
end_time = 2.0
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.01
growth_factor = 1.5
cutback_factor = 0.8
optimal_iterations = 9
iteration_window = 2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
modules/phase_field/test/tests/SplitCH/forward_split_math_test.i
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
xmax = 25.0
ymax = 25.0
elem_type = QUAD
[]
[Variables]
[./c]
[../]
[./w]
[../]
[]
[ICs]
[./c_IC]
type = CrossIC
variable = c
x1 = 0
x2 = 25
y1 = 0
y2 = 25
[../]
[]
[Kernels]
[./cdot]
type = TimeDerivative
variable = c
[../]
[./grad_w]
type = MatDiffusion
variable = c
v = w
diffusivity = 1.0
[../]
[./grad_c]
type = MatDiffusion
variable = w
v = c
diffusivity = 2.0
[../]
[./w2]
type = CoupledMaterialDerivative
variable = w
v = c
f_name = F
[../]
[./w3]
type = CoefReaction
variable = w
coefficient = -1.0
[../]
[]
[AuxVariables]
[./local_energy]
family = MONOMIAL
order = CONSTANT
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = F
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Materials]
[./kappa_c]
type = GenericConstantMaterial
prop_names = kappa_c
prop_values = 2.0
[../]
[./free_energy]
type = DerivativeParsedMaterial
args = c
function = '(1 - c)^2 * (1 + c)^2'
f_name = F
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_c]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'initial TIMESTEP_END'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
l_max_its = 30
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 5
dt = 0.7
[]
[Outputs]
exodus = true
[]
modules/combined/examples/periodic_strain/global_strain_pfm.i
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 50
ny = 50
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0'
new_boundary = 100
[../]
[]
[Variables]
[./u_x]
[../]
[./u_y]
[../]
[./global_strain]
order = THIRD
family = SCALAR
[../]
[./c]
[./InitialCondition]
type = FunctionIC
function = 'sin(2*x*pi)*sin(2*y*pi)*0.05+0.6'
[../]
[../]
[./w]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./disp_x]
[../]
[./disp_y]
[../]
[./s00]
order = CONSTANT
family = MONOMIAL
[../]
[./s01]
order = CONSTANT
family = MONOMIAL
[../]
[./s10]
order = CONSTANT
family = MONOMIAL
[../]
[./s11]
order = CONSTANT
family = MONOMIAL
[../]
[./e00]
order = CONSTANT
family = MONOMIAL
[../]
[./e01]
order = CONSTANT
family = MONOMIAL
[../]
[./e10]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./disp_x]
type = GlobalDisplacementAux
variable = disp_x
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 0
[../]
[./disp_y]
type = GlobalDisplacementAux
variable = disp_y
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
component = 1
[../]
[./local_free_energy]
type = TotalFreeEnergy
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[./s00]
type = RankTwoAux
variable = s00
rank_two_tensor = stress
index_i = 0
index_j = 0
[../]
[./s01]
type = RankTwoAux
variable = s01
rank_two_tensor = stress
index_i = 0
index_j = 1
[../]
[./s10]
type = RankTwoAux
variable = s10
rank_two_tensor = stress
index_i = 1
index_j = 0
[../]
[./s11]
type = RankTwoAux
variable = s11
rank_two_tensor = stress
index_i = 1
index_j = 1
[../]
[./e00]
type = RankTwoAux
variable = e00
rank_two_tensor = total_strain
index_i = 0
index_j = 0
[../]
[./e01]
type = RankTwoAux
variable = e01
rank_two_tensor = total_strain
index_i = 0
index_j = 1
[../]
[./e10]
type = RankTwoAux
variable = e10
rank_two_tensor = total_strain
index_i = 1
index_j = 0
[../]
[./e11]
type = RankTwoAux
variable = e11
rank_two_tensor = total_strain
index_i = 1
index_j = 1
[../]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'u_x u_y'
block = 0
[]
[Kernels]
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
block = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
block = 0
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
block = 0
[../]
[]
[ScalarKernels]
[./global_strain]
type = GlobalStrain
variable = global_strain
global_strain_uo = global_strain_uo
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
variable = 'c w u_x u_y'
[../]
[../]
# 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
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 0 0 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
tensor_values = '0 0 0 0 0 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
tensor_values = '1 1 0 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
function = '0.3*c^2'
f_name = weight1
args = c
[../]
[./weight2]
type = DerivativeParsedMaterial
function = '0.3*(1-c)^2'
f_name = weight2
args = c
[../]
[./weight3]
type = DerivativeParsedMaterial
function = '4*(0.5-c)^2'
f_name = weight3
args = c
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
global_strain = global_strain
eigenstrain_names = eigenstrain
[../]
[./eigenstrain]
type = CompositeEigenstrain
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
args = c
eigenstrain_name = eigenstrain
[../]
[./global_strain]
type = ComputeGlobalStrain
scalar_global_strain = global_strain
global_strain_uo = global_strain_uo
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
f_name = Fc
function = '4*c^2*(1-c)^2'
args = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
args = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
f_name = F
sum_materials = 'Fc Fe'
args = 'c'
[../]
[]
[UserObjects]
[./global_strain_uo]
type = GlobalStrainUserObject
execute_on = 'Initial Linear Nonlinear'
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly lu 1'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
end_time = 2.0
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.01
growth_factor = 1.5
cutback_factor = 0.8
optimal_iterations = 9
iteration_window = 2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_test.i
#
# Test the TotalFreeEnergy auxkernel, which outputs both the sum of the bulk and interfacial free energies. This test has only one variable.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
nz = 0
xmin = 0
xmax = 250
ymin = 0
ymax = 250
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./c]
[../]
[./w]
[../]
[]
[AuxVariables]
[./local_free_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./cIC]
type = SmoothCircleIC
variable = c
x1 = 125.0
y1 = 125.0
radius = 60.0
invalue = 1.0
outvalue = 0.1
int_width = 30.0
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_free_energy
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1e-3 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
args = c
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
function = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2
derivative_order = 2
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_free_energy
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = -pc_type
petsc_options_value = lu
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 6
dt = 200
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
modules/phase_field/examples/measure_interface_energy/1Dinterface_energy.i
[Mesh]
type = GeneratedMesh
dim = 1
nx = 100
xmax = 100
xmin = 0
elem_type = EDGE
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
scaling = 1e1
[./InitialCondition]
type = RampIC
variable = c
value_left = 0
value_right = 1
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[Functions]
[./Int_energy]
type = ParsedFunction
vals = 'total_solute Cleft Cright Fleft Fright volume'
value = '((total_solute-Cleft*volume)/(Cright-Cleft))*Fright+(volume-(total_solute-Cleft*volume)/(Cright-Cleft))*Fleft'
vars = 'total_solute Cleft Cright Fleft Fright volume'
[../]
[./Diff]
type = ParsedFunction
vals = 'total_free_energy total_no_int'
vars = 'total_free_energy total_no_int'
value = total_free_energy-total_no_int
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'kappa_c M'
prop_values = '25 150'
[../]
[./Free_energy]
type = DerivativeParsedMaterial
f_name = F
function = 'c^2*(c-1)^2'
args = c
derivative_order = 2
[../]
[]
[Postprocessors]
# The total free energy of the simulation cell to observe the energy reduction.
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
# for testing we also monitor the total solute amount, which should be conserved,
# gives Cavg in % for this problem.
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
# Get simulation cell size (1D volume) from postprocessor
[./volume]
type = ElementIntegralMaterialProperty
mat_prop = 1
[../]
# Find concentration in each phase using SideAverageValue
[./Cleft]
type = SideAverageValue
boundary = left
variable = c
[../]
[./Cright]
type = SideAverageValue
boundary = right
variable = c
[../]
# Find local energy in each phase by checking boundaries
[./Fleft]
type = SideAverageValue
boundary = left
variable = local_energy
[../]
[./Fright]
type = SideAverageValue
boundary = right
variable = local_energy
[../]
# Use concentrations and energies to find total free energy without any interface,
# only applies once equilibrium is reached!!
# Difference between energy with and without interface
# gives interface energy per unit area.
[./total_no_int]
type = FunctionValuePostprocessor
function = Int_energy
[../]
[./Energy_of_Interface]
type = FunctionValuePostprocessor
function = Diff
[../]
[]
[Preconditioning]
# This preconditioner makes sure the Jacobian Matrix is fully populated. Our
# kernels compute all Jacobian matrix entries.
# This allows us to use the Newton solver below.
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
# Automatic differentiation provides a _full_ Jacobian in this example
# so we can safely use NEWTON for a fast solve
solve_type = 'NEWTON'
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 15
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-4
start_time = 0.0
# make sure that the result obtained for the interfacial free energy is fully converged
end_time = 40
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.5
[../]
[]
[Outputs]
gnuplot = true
csv = true
[./exodus]
type = Exodus
show = 'c local_energy'
execute_on = 'failed initial nonlinear timestep_end final'
[../]
[./console]
type = Console
execute_on = 'FAILED INITIAL NONLINEAR TIMESTEP_END final'
[../]
perf_graph = true
[]
modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_2var_test.i
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
nz = 0
xmin = 0
xmax = 1000
ymin = 0
ymax = 1000
zmin = 0
zmax = 0
elem_type = QUAD4
uniform_refine = 2
[]
[GlobalParams]
op_num = 2
var_name_base = gr
[]
[Variables]
[./PolycrystalVariables]
[../]
[]
[ICs]
[./PolycrystalICs]
[./BicrystalCircleGrainIC]
radius = 333.333
x = 500
y = 500
int_width = 60
[../]
[../]
[]
[AuxVariables]
[./bnds]
order = FIRST
family = LAGRANGE
[../]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Kernels]
[./gr0dot]
type = TimeDerivative
variable = gr0
[../]
[./gr0bulk]
type = AllenCahn
variable = gr0
f_name = F
args = gr1
[../]
[./gr0int]
type = ACInterface
variable = gr0
kappa_name = kappa_op
[../]
[./gr1dot]
type = TimeDerivative
variable = gr1
[../]
[./gr1bulk]
type = AllenCahn
variable = gr1
f_name = F
args = gr0
[../]
[./gr1int]
type = ACInterface
variable = gr1
kappa_name = kappa_op
[../]
[]
[AuxKernels]
[./BndsCalc]
type = BndsCalcAux
variable = bnds
[../]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
kappa_names = 'kappa_op kappa_op'
interfacial_vars = 'gr0 gr1'
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./Copper]
type = GBEvolution
T = 500 # K
wGB = 60 # nm
GBmob0 = 2.5e-6 # m^4/(Js) from Schoenfelder 1997
Q = 0.23 # Migration energy in eV
GBenergy = 0.708 # GB energy in J/m^2
[../]
[./free_energy]
type = DerivativeParsedMaterial
args = 'gr0 gr1'
material_property_names = 'mu gamma_asymm'
function = 'mu*( gr0^4/4.0 - gr0^2/2.0 + gr1^4/4.0 - gr1^2/2.0 + gamma_asymm*gr0^2*gr1^2) + 1.0/4.0'
derivative_order = 2
enable_jit = true
[../]
[]
[Postprocessors]
[./total_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
petsc_options_value = 'hypre boomeramg 31'
l_tol = 1.0e-4
l_max_its = 30
nl_max_its = 30
nl_rel_tol = 1.0e-9
start_time = 0.0
num_steps = 7
dt = 80.0
[./Adaptivity]
initial_adaptivity = 2
refine_fraction = 0.8
coarsen_fraction = 0.05
max_h_level = 2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
csv = true
exodus = true
[]
modules/phase_field/examples/cahn-hilliard/Parsed_CH.i
#
# Example problem showing how to use the DerivativeParsedMaterial with CahnHilliard.
# The free energy is identical to that from CHMath, f_bulk = 1/4*(1-c)^2*(1+c)^2.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 100
ny = 100
xmax = 60
ymax = 60
[]
[Modules]
[./PhaseField]
[./Conserved]
[./c]
free_energy = fbulk
mobility = M
kappa = kappa_c
solve_type = DIRECT
[../]
[../]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./cIC]
type = RandomIC
variable = c
min = -0.1
max = 0.1
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = fbulk
interfacial_vars = c
kappa_names = kappa_c
execute_on = timestep_end
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./mat]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1.0 0.5'
[../]
[./free_energy]
type = DerivativeParsedMaterial
f_name = fbulk
args = c
constant_names = W
constant_expressions = 1.0/2^2
function = W*(1-c)^2*(1+c)^2
enable_jit = true
[../]
[]
[Postprocessors]
[./top]
type = SideIntegralVariablePostprocessor
variable = c
boundary = top
[../]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
scheme = bdf2
# Alternative preconditioning using the additive Schwartz method and LU decomposition
#petsc_options_iname = '-pc_type -sub_ksp_type -sub_pc_type'
#petsc_options_value = 'asm preonly lu '
# Preconditioning options using Hypre (algebraic multi-grid)
petsc_options_iname = '-pc_type -pc_hypre_type'
petsc_options_value = 'hypre boomeramg'
l_max_its = 30
l_tol = 1e-4
nl_max_its = 20
nl_rel_tol = 1e-9
dt = 2.0
end_time = 20.0
[]
[Outputs]
exodus = true
perf_graph = true
[]
modules/phase_field/examples/cahn-hilliard/Parsed_SplitCH.i
#
# Example problem showing how to use the DerivativeParsedMaterial with SplitCHParsed.
# The free energy is identical to that from SplitCHMath, f_bulk = 1/4*(1-c)^2*(1+c)^2.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 150
ny = 150
xmax = 60
ymax = 60
[]
[Modules]
[./PhaseField]
[./Conserved]
[./c]
free_energy = fbulk
mobility = M
kappa = kappa_c
solve_type = REVERSE_SPLIT
[../]
[../]
[../]
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./cIC]
type = RandomIC
variable = c
min = -0.1
max = 0.1
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = fbulk
interfacial_vars = c
kappa_names = kappa_c
execute_on = timestep_end
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./mat]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1.0 0.5'
[../]
[./free_energy]
type = DerivativeParsedMaterial
f_name = fbulk
args = c
constant_names = W
constant_expressions = 1.0/2^2
function = W*(1-c)^2*(1+c)^2
enable_jit = true
outputs = exodus
[../]
[]
[Postprocessors]
[./top]
type = SideIntegralVariablePostprocessor
variable = c
boundary = top
[../]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[]
[Preconditioning]
[./cw_coupling]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
scheme = bdf2
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu '
l_max_its = 30
l_tol = 1e-4
nl_max_its = 20
nl_rel_tol = 1e-9
dt = 2.0
end_time = 20.0
[]
[Outputs]
exodus = true
perf_graph = true
[]
modules/combined/examples/mortar/eigenstrain.i
#
# Eigenstrain with Mortar gradient periodicity
#
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 50
ny = 50
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
[]
[./cnode]
input = gen
type = ExtraNodesetGenerator
coord = '0.0 0.0'
new_boundary = 100
[../]
[./anode]
input = cnode
type = ExtraNodesetGenerator
coord = '0.0 0.5'
new_boundary = 101
[../]
[slave_x]
input = anode
type = LowerDBlockFromSidesetGenerator
sidesets = '3'
new_block_id = 10
new_block_name = "slave_x"
[]
[master_x]
input = slave_x
type = LowerDBlockFromSidesetGenerator
sidesets = '1'
new_block_id = 12
new_block_name = "master_x"
[]
[slave_y]
input = master_x
type = LowerDBlockFromSidesetGenerator
sidesets = '0'
new_block_id = 11
new_block_name = "slave_y"
[]
[master_y]
input = slave_y
type = LowerDBlockFromSidesetGenerator
sidesets = '2'
new_block_id = 13
new_block_name = "master_y"
[]
[]
[GlobalParams]
derivative_order = 2
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
block = 0
execute_on = 'initial LINEAR'
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = RandomIC
min = 0.49
max = 0.51
[../]
block = 0
[../]
[./w]
block = 0
[../]
# Mesh displacement
[./disp_x]
block = 0
[../]
[./disp_y]
block = 0
[../]
# Lagrange multipliers for gradient component periodicity
[./lm_left_right_xx]
order = FIRST
family = LAGRANGE
block = slave_x
[../]
[./lm_left_right_xy]
order = FIRST
family = LAGRANGE
block = slave_x
[../]
[./lm_left_right_yx]
order = FIRST
family = LAGRANGE
block = slave_x
[../]
[./lm_left_right_yy]
order = FIRST
family = LAGRANGE
block = slave_x
[../]
[./lm_up_down_xx]
order = FIRST
family = LAGRANGE
block = slave_y
[../]
[./lm_up_down_xy]
order = FIRST
family = LAGRANGE
block = slave_y
[../]
[./lm_up_down_yx]
order = FIRST
family = LAGRANGE
block = slave_y
[../]
[./lm_up_down_yy]
order = FIRST
family = LAGRANGE
block = slave_y
[../]
[]
[Constraints]
[./ud_disp_x_grad_x]
type = EqualGradientConstraint
variable = lm_up_down_xx
component = 0
slave_variable = disp_x
slave_boundary = bottom
master_boundary = top
slave_subdomain = slave_y
master_subdomain = master_y
periodic = true
[../]
[./ud_disp_x_grad_y]
type = EqualGradientConstraint
variable = lm_up_down_xy
component = 1
slave_variable = disp_x
slave_boundary = bottom
master_boundary = top
slave_subdomain = slave_y
master_subdomain = master_y
periodic = true
[../]
[./ud_disp_y_grad_x]
type = EqualGradientConstraint
variable = lm_up_down_yx
component = 0
slave_variable = disp_y
slave_boundary = bottom
master_boundary = top
slave_subdomain = slave_y
master_subdomain = master_y
periodic = true
[../]
[./ud_disp_y_grad_y]
type = EqualGradientConstraint
variable = lm_up_down_yy
component = 1
slave_variable = disp_y
slave_boundary = bottom
master_boundary = top
slave_subdomain = slave_y
master_subdomain = master_y
periodic = true
[../]
[./lr_disp_x_grad_x]
type = EqualGradientConstraint
variable = lm_left_right_xx
component = 0
slave_variable = disp_x
slave_boundary = left
master_boundary = right
slave_subdomain = slave_x
master_subdomain = master_x
periodic = true
[../]
[./lr_disp_x_grad_y]
type = EqualGradientConstraint
variable = lm_left_right_xy
component = 1
slave_variable = disp_x
slave_boundary = left
master_boundary = right
slave_subdomain = slave_x
master_subdomain = master_x
periodic = true
[../]
[./lr_disp_y_grad_x]
type = EqualGradientConstraint
variable = lm_left_right_yx
component = 0
slave_variable = disp_y
slave_boundary = left
master_boundary = right
slave_subdomain = slave_x
master_subdomain = master_x
periodic = true
[../]
[./lr_disp_y_grad_y]
type = EqualGradientConstraint
variable = lm_left_right_yy
component = 1
slave_variable = disp_y
slave_boundary = left
master_boundary = right
slave_subdomain = slave_x
master_subdomain = master_x
periodic = true
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
block = 0
[../]
# Cahn-Hilliard kernels
[./c_dot]
type = CoupledTimeDerivative
variable = w
v = c
block = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
block = 0
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
block = 0
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
block = '0 10 11'
prop_names = 'M kappa_c'
prop_values = '0.2 0.01 '
[../]
[./shear1]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 0.5'
tensor_name = shear1
[../]
[./shear2]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '0 0 0 0 0 -0.5'
tensor_name = shear2
[../]
[./expand3]
type = GenericConstantRankTwoTensor
block = 0
tensor_values = '1 1 0 0 0 0'
tensor_name = expand3
[../]
[./weight1]
type = DerivativeParsedMaterial
block = 0
function = '0.3*c^2'
f_name = weight1
args = c
[../]
[./weight2]
type = DerivativeParsedMaterial
block = 0
function = '0.3*(1-c)^2'
f_name = weight2
args = c
[../]
[./weight3]
type = DerivativeParsedMaterial
block = 0
function = '4*(0.5-c)^2'
f_name = weight3
args = c
[../]
# matrix phase
[./elasticity_tensor]
type = ComputeElasticityTensor
block = 0
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./strain]
type = ComputeSmallStrain
block = 0
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./eigenstrain]
type = CompositeEigenstrain
block = 0
tensors = 'shear1 shear2 expand3'
weights = 'weight1 weight2 weight3'
args = c
eigenstrain_name = eigenstrain
[../]
[./stress]
type = ComputeLinearElasticStress
block = 0
[../]
# chemical free energies
[./chemical_free_energy]
type = DerivativeParsedMaterial
block = 0
f_name = Fc
function = '4*c^2*(1-c)^2'
args = 'c'
outputs = exodus
output_properties = Fc
[../]
# elastic free energies
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
block = 0
args = 'c'
outputs = exodus
output_properties = Fe
[../]
# free energy (chemical + elastic)
[./free_energy]
type = DerivativeSumMaterial
block = 0
f_name = F
sum_materials = 'Fc Fe'
args = 'c'
[../]
[]
[BCs]
[./Periodic]
[./up_down]
primary = top
secondary = bottom
translation = '0 -1 0'
variable = 'c w'
[../]
[./left_right]
primary = left
secondary = right
translation = '1 0 0'
variable = 'c w'
[../]
[../]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = disp_x
value = 0
[../]
[./centerfix_y]
type = DirichletBC
boundary = 100
variable = disp_y
value = 0
[../]
# fix side point x coordinate to inhibit rotation
[./angularfix]
type = DirichletBC
boundary = 101
variable = disp_x
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
block = 0
execute_on = 'initial TIMESTEP_END'
variable = c
[../]
[./min]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = min
variable = c
[../]
[./max]
type = ElementExtremeValue
block = 0
execute_on = 'initial TIMESTEP_END'
value_type = max
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
line_search = basic
# mortar currently does not support MPI parallelization
petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
petsc_options_value = ' lu NONZERO 1e-10'
l_max_its = 30
nl_max_its = 12
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.01
[../]
[]
[Outputs]
execute_on = 'timestep_end'
print_linear_residuals = false
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
modules/phase_field/examples/multiphase/DerivativeMultiPhaseMaterial.i
[Mesh]
type = GeneratedMesh
dim = 2
nx = 40
ny = 40
nz = 0
xmin = -12
xmax = 12
ymin = -12
ymax = 12
elem_type = QUAD4
[]
[GlobalParams]
# let's output all material properties for demonstration purposes
outputs = exodus
# prefactor on the penalty function kernels. The higher this value is, the
# more rigorously the constraint is enforced
penalty = 1e3
[]
#
# These AuxVariables hold the directly calculated free energy density in the
# simulation cell. They are provided for visualization purposes.
#
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
[../]
#
# Helper kernel to cpompute the gradient contribution from interfaces of order
# parameters evolved using the ACMultiInterface kernel
#
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
#
# The interface coefficient matrix. This should be symmetrical!
#
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
#
# We set up a smooth cradial concentrtaion gradient
# The concentration will quickly change to adapt to the preset order
# parameters eta1, eta2, and eta3
#
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 5.0
invalue = 1.0
outvalue = 0.01
int_width = 10.0
[../]
[../]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
#
# Note: this initial conditions sets up a _sharp_ interface. Ideally
# we should start with a smooth interface with a width consistent
# with the kappa parameter supplied for the given interface.
#
function = 'r:=sqrt(x^2+y^2);if(r<=4,1,0)'
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'r:=sqrt(x^2+y^2);if(r>4&r<=7,1,0)'
[../]
[../]
[./eta3]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = FunctionIC
function = 'r:=sqrt(x^2+y^2);if(r>7,1,0)'
[../]
[../]
[]
[Kernels]
#
# Cahn-Hilliard kernel for the concentration variable.
# Note that we are not using an interfcae kernel on this variable, but rather
# rely on the interface width enforced on the order parameters. This allows us
# to use a direct solve using the CahnHilliard kernel _despite_ only using first
# order elements.
#
[./c_res]
type = CahnHilliard
variable = c
f_name = F
args = 'eta1 eta2 eta3'
[../]
[./time]
type = TimeDerivative
variable = c
[../]
#
# Order parameter eta1
# Each order parameter is acted on by 4 kernels:
# 1. The stock time derivative deta_i/dt kernel
# 2. The Allen-Cahn kernel that takes a Dervative Material for the free energy
# 3. A gradient interface kernel that includes cross terms
# see http://mooseframework.org/wiki/PhysicsModules/PhaseField/DevelopingModels/MultiPhaseModels/ACMultiInterface/
# 4. A penalty contribution that forces the interface contributions h(eta)
# to sum up to unity
#
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
args = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./penalty1]
type = SwitchingFunctionPenalty
variable = eta1
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
[../]
#
# Order parameter eta2
#
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
args = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./penalty2]
type = SwitchingFunctionPenalty
variable = eta2
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
[../]
#
# Order parameter eta3
#
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
args = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./penalty3]
type = SwitchingFunctionPenalty
variable = eta3
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
# here we declare some of the model parameters: the mobilities and interface
# gradient prefactors. For this example we use arbitrary numbers. In an actual simulation
# physical mobilities would be used, and the interface gradient prefactors would
# be readjusted to the free energy magnitudes.
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0.75 1 1 1 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 '
[../]
# This material sums up the individual phase contributions. It is written to the output file
# (see GlobalParams section above) and can be used to check the constraint enforcement.
[./etasummat]
type = ParsedMaterial
f_name = etasum
args = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
function = 'h1+h2+h3'
[../]
# The phase contribution factors for each material point are computed using the
# SwitchingFunctionMaterials. Each phase with an order parameter eta contributes h(eta)
# to the global free energy density. h is a function that switches smoothly from 0 to 1
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
# The barrier function adds a phase transformation energy barrier. It also
# Drives order parameters toward the [0:1] interval to avoid negative or larger than 1
# order parameters (these are set to 0 and 1 contribution by the switching functions
# above)
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# We use DerivativeParsedMaterials to specify three (very) simple free energy
# expressions for the three phases. All necessary derivatives are built automatically.
# In a real problem these expressions can be arbitrarily complex (or even provided
# by custom kernels).
[./phase_free_energy_1]
type = DerivativeParsedMaterial
f_name = F1
function = '(c-1)^2'
args = 'c'
[../]
[./phase_free_energy_2]
type = DerivativeParsedMaterial
f_name = F2
function = '(c-0.5)^2'
args = 'c'
[../]
[./phase_free_energy_3]
type = DerivativeParsedMaterial
f_name = F3
function = 'c^2'
args = 'c'
[../]
# The DerivativeMultiPhaseMaterial ties the phase free energies together into a global free energy.
# http://mooseframework.org/wiki/PhysicsModules/PhaseField/DevelopingModels/MultiPhaseModels/
[./free_energy]
type = DerivativeMultiPhaseMaterial
f_name = F
# we use a constant free energy (GeneriConstantmaterial property Fx)
fi_names = 'F1 F2 F3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
args = 'c'
W = 1
[../]
[]
[Postprocessors]
# The total free energy of the simulation cell to observe the energy reduction.
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
# for testing we also monitor the total solute amount, which should be conserved.
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
[]
[Preconditioning]
# This preconditioner makes sure the Jacobian Matrix is fully populated. Our
# kernels compute all Jacobian matrix entries.
# This allows us to use the Newton solver below.
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
# Automatic differentiation provedes a _full_ Jacobian in this example
# so we can safely use NEWTON for a fast solve
solve_type = 'NEWTON'
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-6
nl_abs_tol = 1.0e-6
start_time = 0.0
end_time = 150.0
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.1
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
modules/phase_field/tutorials/spinodal_decomposition/s5_energycurve.i
#
# Example simulation of an iron-chromium alloy at 500 C. Equilibrium
# concentrations are at 23.6 and 82.3 mol% Cr. Kappa value, free energy equation,
# and mobility equation were provided by Lars Hoglund. Solved using the split
# form of the Cahn-Hilliard equation.
[Mesh]
type = GeneratedMesh
dim = 2
elem_type = QUAD4
nx = 25
ny = 25
nz = 0
xmin = 0
xmax = 25
ymin = 0
ymax = 25
zmin = 0
zmax = 0
uniform_refine = 2
[]
[Variables]
[./c] # Mole fraction of Cr (unitless)
order = FIRST
family = LAGRANGE
scaling = 1e+04
[../]
[./w] # Chemical potential (eV/mol)
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./f_density] # Local energy density (eV/mol)
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./concentrationIC] # 46.774 mol% Cr with variations
type = RandomIC
min = 0.44774
max = 0.48774
seed = 210
variable = c
[../]
[]
[BCs]
[./Periodic]
[./c_bcs]
auto_direction = 'x y'
[../]
[../]
[]
[Kernels]
[./w_dot]
variable = w
v = c
type = CoupledTimeDerivative
[../]
[./coupled_res]
variable = w
type = SplitCHWRes
mob_name = M
[../]
[./coupled_parsed]
variable = c
type = SplitCHParsed
f_name = f_loc
kappa_name = kappa_c
w = w
[../]
[]
[AuxKernels]
# Calculates the energy density by combining the local and gradient energies
[./f_density] # (eV/mol/nm^2)
type = TotalFreeEnergy
variable = f_density
f_name = 'f_loc'
kappa_names = 'kappa_c'
interfacial_vars = c
[../]
[]
[Materials]
# d is a scaling factor that makes it easier for the solution to converge
# without changing the results. It is defined in each of the first three
# materials and must have the same value in each one.
[./kappa] # Gradient energy coefficient (eV nm^2/mol)
type = GenericFunctionMaterial
prop_names = 'kappa_c'
prop_values = '8.125e-16*6.24150934e+18*1e+09^2*1e-27'
# kappa_c *eV_J*nm_m^2* d
[../]
[./mobility] # Mobility (nm^2 mol/eV/s)
# NOTE: This is a fitted equation, so only 'Conv' has units
type = DerivativeParsedMaterial
f_name = M
args = c
constant_names = 'Acr Bcr Ccr Dcr
Ecr Fcr Gcr
Afe Bfe Cfe Dfe
Efe Ffe Gfe
nm_m eV_J d'
constant_expressions = '-32.770969 -25.8186669 -3.29612744 17.669757
37.6197853 20.6941796 10.8095813
-31.687117 -26.0291774 0.2286581 24.3633544
44.3334237 8.72990497 20.956768
1e+09 6.24150934e+18 1e-27'
function = 'nm_m^2/eV_J/d*((1-c)^2*c*10^
(Acr*c+Bcr*(1-c)+Ccr*c*log(c)+Dcr*(1-c)*log(1-c)+
Ecr*c*(1-c)+Fcr*c*(1-c)*(2*c-1)+Gcr*c*(1-c)*(2*c-1)^2)
+c^2*(1-c)*10^
(Afe*c+Bfe*(1-c)+Cfe*c*log(c)+Dfe*(1-c)*log(1-c)+
Efe*c*(1-c)+Ffe*c*(1-c)*(2*c-1)+Gfe*c*(1-c)*(2*c-1)^2))'
derivative_order = 1
outputs = exodus
[../]
[./local_energy] # Local free energy function (eV/mol)
type = DerivativeParsedMaterial
f_name = f_loc
args = c
constant_names = 'A B C D E F G eV_J d'
constant_expressions = '-2.446831e+04 -2.827533e+04 4.167994e+03 7.052907e+03
1.208993e+04 2.568625e+03 -2.354293e+03
6.24150934e+18 1e-27'
function = 'eV_J*d*(A*c+B*(1-c)+C*c*log(c)+D*(1-c)*log(1-c)+
E*c*(1-c)+F*c*(1-c)*(2*c-1)+G*c*(1-c)*(2*c-1)^2)'
derivative_order = 2
[../]
[./precipitate_indicator] # Returns 1/625 if precipitate
type = ParsedMaterial
f_name = prec_indic
args = c
function = if(c>0.6,0.0016,0)
[../]
[]
[Postprocessors]
[./step_size] # Size of the time step
type = TimestepSize
[../]
[./iterations] # Number of iterations needed to converge timestep
type = NumNonlinearIterations
[../]
[./nodes] # Number of nodes in mesh
type = NumNodes
[../]
[./evaluations] # Cumulative residual calculations for simulation
type = NumResidualEvaluations
[../]
[./total_energy] # Total free energy at each timestep
type = ElementIntegralVariablePostprocessor
variable = f_density
execute_on = 'initial timestep_end'
[../]
[./num_features] # Number of precipitates formed
type = FeatureFloodCount
variable = c
threshold = 0.6
[../]
[./precipitate_area] # Fraction of surface devoted to precipitates
type = ElementIntegralMaterialProperty
mat_prop = prec_indic
[../]
[./active_time] # Time computer spent on simulation
type = PerfGraphData
section_name = "Root"
data_type = total
[../]
[]
[Preconditioning]
[./coupled]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = NEWTON
l_max_its = 30
l_tol = 1e-6
nl_max_its = 50
nl_abs_tol = 1e-9
end_time = 604800 # 7 days
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type
-sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly
ilu 1'
[./TimeStepper]
type = IterationAdaptiveDT
dt = 10
cutback_factor = 0.8
growth_factor = 1.5
optimal_iterations = 7
[../]
[./Adaptivity]
coarsen_fraction = 0.1
refine_fraction = 0.7
max_h_level = 2
[../]
[]
[Outputs]
exodus = true
console = true
csv = true
[./console]
type = Console
max_rows = 10
[../]
[]
modules/phase_field/test/tests/actions/conserved_forward_split_1var.i
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
xmax = 25.0
ymax = 25.0
elem_type = QUAD
[]
[Debug]
show_actions = true
[]
[Modules]
[./PhaseField]
[./Conserved]
[./c]
solve_type = FORWARD_SPLIT
mobility = 1.0
kappa = kappa_c
free_energy = F
[../]
[../]
[../]
[]
[ICs]
[./c_IC]
type = CrossIC
variable = c
x1 = 0.0
x2 = 25.0
y1 = 0.0
y2 = 25.0
[../]
[]
[AuxVariables]
[./local_energy]
family = MONOMIAL
order = CONSTANT
[../]
[]
[AuxKernels]
[./local_energy]
type = TotalFreeEnergy
variable = local_energy
f_name = F
kappa_names = kappa_c
interfacial_vars = c
[../]
[]
[Materials]
[./kappa_c]
type = GenericConstantMaterial
prop_names = kappa_c
prop_values = 2.0
[../]
[./free_energy]
type = DerivativeParsedMaterial
args = c
function = '(1 - c)^2 * (1 + c)^2'
f_name = F
[../]
[]
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_c]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'initial TIMESTEP_END'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
l_max_its = 30
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 5
dt = 0.7
[]
[Outputs]
perf_graph = true
exodus = true
[]
modules/phase_field/examples/rigidbodymotion/AC_CH_Multigrain.i
# Tests the rigid body motion due to applied force of multiple particles.
# ***COPY AND PASTE THESE AS NEEDED***
# 'gr0 gr1 gr2 gr3 gr4 gr5 gr6 gr7 gr8 gr9 gr10 gr11 gr12 gr13 gr14 gr15 gr16 gr17 gr18 gr19'
# (gr0^2+gr1^2+gr2^2+gr3^2+gr4^2+gr5^2+gr6^2+gr7^2+gr8^2+gr9^2+gr10^2+gr11^2+gr12^2+gr13^2+gr14^2+gr15^2+gr16^2+gr17^2+gr18^2+gr19^2)
# (gr0^3+gr1^3+gr2^3+gr3^3+gr4^3+gr5^3+gr6^3+gr7^3+gr8^3+gr9^3+gr10^3+gr11^3+gr12^3+gr13^3+gr14^3+gr15^3+gr16^3+gr17^3+gr18^3+gr19^3)
[GlobalParams]
op_num = 4
var_name_base = gr
[]
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
xmin = 0
xmax = 600
ymin = 0
ymax = 600
elem_type = QUAD4
uniform_refine = 1
[]
[Variables]
[./c]
[../]
[./w]
[../]
[./PolycrystalVariables] # Automatically creates order parameter variables
[../]
[]
[AuxVariables]
[./bnds]
[../]
[./force]
order = CONSTANT
family = MONOMIAL
[../]
[./free_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./var_indices]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Functions]
[./load_x]
# Defines the force on the grains in the x-direction
type = ParsedFunction
value = 0.005*cos(x*pi/600)
[../]
[./load_y]
# Defines the force on the grains in the y-direction
type = ConstantFunction
value = 0.002
[../]
[]
[Kernels]
[./RigidBodyMultiKernel]
# Creates all of the necessary Allen Cahn kernels automatically
c = c
f_name = f_loc
mob_name = L
kappa_name = kappa_gr
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
[../]
# Cahn Hilliard kernels
[./dt_w]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./CH_wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./CH_Parsed]
type = SplitCHParsed
variable = c
f_name = f_loc
w = w
kappa_name = kappa_c
args = 'gr0 gr1 gr2 gr3' # Must be changed as op_num changes. Copy/paste from line 4
[../]
[./CH_RBM]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = 'gr0 gr1 gr2 gr3'
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
[../]
[]
[AuxKernels]
[./force_x]
type = FunctionAux
variable = force
function = load_x
[../]
[./force_y]
type = FunctionAux
variable = force
function = load_y
[../]
[./energy_density]
type = TotalFreeEnergy
variable = free_energy
f_name = f_loc
kappa_names = kappa_c
interfacial_vars = c
[../]
[./bnds]
type = BndsCalcAux
variable = bnds
[../]
[]
[BCs]
[./bcs]
#zero flux BC
type = NeumannBC
value = 0
variable = c
boundary = '0 1 2 3'
[../]
[]
[Materials]
[./constants]
type = GenericConstantMaterial
prop_names = 'kappa_gr kappa_c M L'
prop_values = '250 4000 4.5 60'
[../]
[./free_energy]
type = DerivativeParsedMaterial
f_name = f_loc
constant_names = 'A B'
constant_expressions = '450 1.5'
args = 'c gr0 gr1 gr2 gr3' #Must be changed as op_num changes. Copy/paste from line 4
function = 'A*c^2*(1-c)^2+B*(c^2+6*(1-c)*(gr0^2+gr1^2+gr2^2+gr3^2)
-4*(2-c)*(gr0^3+gr1^3+gr2^3+gr3^3)
+3*(gr0^2+gr1^2+gr2^2+gr3^2)^2)'
#Copy/paste from lines 5-6
derivative_order = 2
[../]
[./force_density]
type = ExternalForceDensityMaterial
c = c
k = 10.0
force_x = load_x
force_y = load_y
[../]
[]
[Postprocessors]
[./total_energy]
type = ElementIntegralVariablePostprocessor
variable = free_energy
execute_on = 'initial timestep_end'
[../]
[]
[VectorPostprocessors]
[./forces]
type = GrainForcesPostprocessor
grain_force = grain_force
[../]
[./grain_volumes]
type = FeatureVolumeVectorPostprocessor
flood_counter = grain_center
execute_on = 'initial timestep_begin'
[../]
[]
[UserObjects]
[./grain_center]
type = GrainTracker
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ComputeExternalGrainForceAndTorque
grain_data = grain_center
c = c
etas = 'gr0 gr1 gr2 gr3'
force_density = force_density_ext
execute_on = 'linear nonlinear'
[../]
[]
[Preconditioning]
[./coupled]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type
-sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 preonly
ilu 2'
l_tol = 1e-05
nl_max_its = 30
l_max_its = 30
nl_rel_tol = 1e-07
nl_abs_tol = 1e-09
start_time = 0.0
end_time = 4
dt = 0.05
[]
[Outputs]
exodus = true
perf_graph = true
[./display]
type = Console
max_rows = 12
[../]
[]
[ICs]
[./concentration_IC]
type = SpecifiedSmoothCircleIC
x_positions = '150 450 150 450'
y_positions = '150 150 450 450'
z_positions = '0 0 0 0'
radii = '120 120 120 120'
variable = c
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr0_IC]
type = SmoothCircleIC
variable = gr0
x1 = 150
y1 = 150
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr1_IC]
type = SmoothCircleIC
variable = gr1
x1 = 450
y1 = 150
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr2_IC]
type = SmoothCircleIC
variable = gr2
x1 = 150
y1 = 450
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[./gr3_IC]
type = SmoothCircleIC
variable = gr3
x1 = 450
y1 = 450
radius = 120
invalue = 1.0
outvalue = 0.0
int_width = 25
[../]
[]
modules/phase_field/test/tests/MultiPhase/crosstermfreeenergy.i
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = -8
xmax = 8
ymin = -8
ymax = 8
elem_type = QUAD4
[]
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
f_name = F0
variable = local_energy
additional_free_energy = cross_energy
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 5.0
radius = 5.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = -4.0
y1 = -2.0
radius = 5.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[./eta3]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 4.0
y1 = -2.0
radius = 5.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[]
[Kernels]
[./dummy_diff1]
type = Diffusion
variable = eta1
[../]
[./dummy_time1]
type = TimeDerivative
variable = eta1
[../]
[./dummy_diff2]
type = Diffusion
variable = eta2
[../]
[./dummy_time2]
type = TimeDerivative
variable = eta2
[../]
[./dummy_diff3]
type = Diffusion
variable = eta3
[../]
[./dummy_tim3]
type = TimeDerivative
variable = eta3
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'F0 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0 11 12 13 12 22 23 13 23 33 '
[../]
[]
[Executioner]
type = Transient
dt = 0.001
num_steps = 1
[]
[Outputs]
execute_on = 'timestep_end'
[./out]
type = Exodus
hide = 'eta1 eta2 eta3 local_energy'
[../]
[]