- variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on
ACInterface / ADACInterface
Gradient energy Allen-Cahn Kernel
ACInterface (and its automatic differentiation version, ADACInterface) implements the Allen-Cahn term for the gradient energy contribution for the isotropic mobility case. Its weak form is
where (kappa_name) is the gradient energy coefficient, the non-conserved non-linear order parameter variable the kernel is acting on, (mob_name) is the scalar (isotropic) mobility associated with the order parameter, and is the test function.
Input Parameters
- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- coupled_variablesVector of nonlinear variable arguments this object depends on
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Vector of nonlinear variable arguments this object depends on
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
- kappa_namekappa_opThe kappa used with the kernel
Default:kappa_op
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The kappa used with the kernel
- matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
- mob_nameLThe mobility used with the kernel
Default:L
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:The mobility used with the kernel
- variable_LTrueThe mobility is a function of any MOOSE variable (if this is set to false L must be constant over the entire domain!)
Default:True
C++ Type:bool
Controllable:No
Description:The mobility is a function of any MOOSE variable (if this is set to false L must be constant over the entire domain!)
Optional Parameters
- absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill
Contribution To Tagged Field Data Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
- 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
- (modules/phase_field/test/tests/feature_volume_vpp_test/centroid.i)
- (modules/phase_field/test/tests/KKS_system/nonlinear.i)
- (modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_offset.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_nested_damped.i)
- (modules/phase_field/test/tests/phase_field_kernels/CoupledAllenCahn.i)
- (modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i)
- (modules/combined/test/tests/surface_tension_KKS/surface_tension_VDWgas.i)
- (modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialMultiphase.i)
- (modules/combined/examples/phase_field-mechanics/SimplePhaseTrans.i)
- (modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i)
- (modules/phase_field/test/tests/MultiPhase/lagrangemult.i)
- (modules/phase_field/test/tests/phase_field_kernels/AllenCahn.i)
- (modules/combined/examples/publications/rapid_dev/fig7a.i)
- (modules/phase_field/examples/multiphase/GrandPotential3Phase.i)
- (modules/phase_field/test/tests/phase_field_kernels/AllenCahnVariableL.i)
- (modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialPFM.i)
- (modules/phase_field/test/tests/phase_field_kernels/CoupledCoefAllenCahn.i)
- (modules/phase_field/examples/rigidbodymotion/AC_CH_advection_constforce_rect.i)
- (modules/phase_field/test/tests/mobility_derivative/AC_mobility_derivative_test.i)
- (modules/phase_field/test/tests/phase_field_kernels/MatGradSquareCoupled.i)
- (modules/phase_field/test/tests/rigidbodymotion/update_orientation_verify.i)
- (modules/combined/examples/phase_field-mechanics/LandauPhaseTrans.i)
- (modules/phase_field/test/tests/KKS_system/lagrange_multiplier.i)
- (modules/phase_field/test/tests/rigidbodymotion/grain_motion_fauxGT.i)
- (modules/combined/examples/publications/rapid_dev/fig6.i)
- (modules/combined/examples/publications/rapid_dev/fig7b.i)
- (modules/phase_field/test/tests/rigidbodymotion/grain_forcedensity.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested_damped.i)
- (modules/phase_field/test/tests/KKS_system/two_phase.i)
- (modules/phase_field/test/tests/MultiPhase/penalty.i)
- (modules/phase_field/test/tests/rigidbodymotion/grain_motion2.i)
- (modules/phase_field/test/tests/MultiPhase/barrierfunctionmaterial.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_split.i)
- (modules/phase_field/test/tests/KKS_system/auxkernel.i)
- (modules/phase_field/test/tests/slkks/full_solve.i)
- (modules/phase_field/test/tests/KKS_system/kks_multiphase.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested.i)
- (modules/phase_field/test/tests/mobility_derivative/AC_mobility_derivative_coupled_test.i)
- (modules/phase_field/examples/slkks/CrFe.i)
- (modules/phase_field/test/tests/rigidbodymotion/update_orientation.i)
- (modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i)
- (modules/phase_field/test/tests/KKS_system/kks_example.i)
- (modules/phase_field/examples/multiphase/GrandPotential3Phase_masscons.i)
- (modules/phase_field/test/tests/free_energy_material/CoupledValueFunctionFreeEnergy.i)
- (modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i)
- (modules/phase_field/test/tests/phase_field_kernels/nonuniform_barrier_coefficient.i)
- (modules/phase_field/test/tests/TotalFreeEnergy/TotalFreeEnergy_2var_test.i)
- (modules/phase_field/test/tests/MultiPhase/switchingfunctionmultiphasematerial.i)
- (modules/phase_field/test/tests/MultiPhase/derivativetwophasematerial.i)
- (modules/phase_field/test/tests/rigidbodymotion/grain_motion.i)
- (modules/combined/test/tests/phase_field_fracture/crack2d_iso_wo_time.i)
- (modules/combined/examples/phase_field-mechanics/Nonconserved.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_nested.i)
- (modules/phase_field/test/tests/MultiPhase/mixedswitchingfunctionmaterial.i)
- (modules/combined/test/tests/surface_tension_KKS/surface_tension_KKS.i)
Child Objects
(modules/phase_field/test/tests/feature_volume_vpp_test/centroid.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 25
ny = 15
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
[]
[Variables]
[c]
[]
[w]
[]
[eta]
[]
[]
[ICs]
[rect_c]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = c
x1 = 10.0
type = BoundingBoxIC
[]
[rect_eta]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = eta
x1 = 10.0
type = BoundingBoxIC
[]
[]
[Kernels]
[c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = eta
[]
[w_res]
type = SplitCHWRes
variable = w
mob_name = M
[]
[time]
type = CoupledTimeDerivative
variable = w
v = c
[]
[eta_dot]
type = TimeDerivative
variable = eta
[]
[acint_eta]
type = ACInterface
variable = eta
mob_name = M
coupled_variables = c
kappa_name = kappa_eta
[]
[acbulk_eta]
type = AllenCahn
variable = eta
mob_name = M
f_name = F
coupled_variables = c
[]
[]
[Materials]
[pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '5.0 2.0 0.1'
[]
[free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'c eta'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+(c-eta)^2
derivative_order = 2
[]
[]
[Postprocessors]
[grain_center]
type = GrainTracker
variable = eta
outputs = none
compute_var_to_feature_map = true
execute_on = 'timestep_begin'
[]
[]
[VectorPostprocessors]
[grain_volumes]
type = FeatureVolumeVectorPostprocessor
flood_counter = grain_center
execute_on = 'timestep_begin'
output_centroids = true
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
dt = 0.2
num_steps = 4
[]
[Outputs]
csv = true
[]
(modules/phase_field/test/tests/KKS_system/nonlinear.i)
#
# This test checks if the thwo phase and lagrange multiplier solutions can be replicated
# with a two order parameter approach, where the second order parameter eta2 is a
# nonlinear variable that is set as eta2 := 1 - eta1 (using Reaction, CoupledForce, and BodyForce)
# The solution is reproduced.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 20
xmax = 5
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = x/5
[]
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# phase concentration 1
[c1]
order = FIRST
family = LAGRANGE
initial_condition = 0.9
[]
# phase concentration 2
[c2]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[]
[]
[Materials]
# simple toy free energies
[f1] # = fd
type = DerivativeParsedMaterial
property_name = F1
coupled_variables = 'c1'
expression = '(0.9-c1)^2'
[]
[f2] # = fm
type = DerivativeParsedMaterial
property_name = F2
coupled_variables = 'c2'
expression = '(0.1-c2)^2'
[]
# Switching functions for each phase
[h1_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta1
function_name = h1
[]
[h2_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta2
function_name = h2
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
[]
[Dh2]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2
property_name = Dh2
coupled_variables = eta2
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '0.7 0.7 0.2'
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = c
[]
[diff_c1]
type = MatDiffusion
variable = c
diffusivity = Dh1
v = c1
args = 'eta1'
[]
[diff_c2]
type = MatDiffusion
variable = c
diffusivity = Dh2
v = c2
args = 'eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gi_name = g1
eta_i = eta1
wi = 0.2
coupled_variables = 'c1 c2 eta2'
[]
[ACBulkC1]
type = KKSMultiACBulkC
variable = eta1
Fj_names = 'F1 F2'
hj_names = 'h1 h2'
cj_names = 'c1 c2'
eta_i = eta1
coupled_variables = 'eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
# Phase concentration constraints
[chempot12]
type = KKSPhaseChemicalPotential
variable = c1
cb = c2
fa_name = F1
fb_name = F2
[]
[phaseconcentration]
type = KKSMultiPhaseConcentration
variable = c2
cj = 'c1 c2'
hj_names = 'h1 h2'
etas = 'eta1 eta2'
c = c
[]
# equation for eta2 = 1 - eta1
# 0 = eta2 + eta1 -1
[constraint_eta1] # eta2
type = Reaction
variable = eta2
[]
[constraint_eta2] # + eta1
type = CoupledForce
variable = eta2
coef = -1
v = eta1
[]
[constraint_one] # - 1
type = BodyForce
variable = eta2
[]
[]
[AuxKernels]
[Fglobal_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gj_names = 'g1 g2 '
variable = Fglobal
w = 0.2
interfacial_vars = 'eta1 eta2 '
kappa_names = 'kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'lu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
end_time = 350
dt = 10
[]
[VectorPostprocessors]
[c]
type = LineValueSampler
variable = c
start_point = '0 0 0'
end_point = '5 0 0'
num_points = 21
sort_by = x
[]
[]
[Outputs]
csv = true
execute_on = FINAL
[]
(modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i)
#
# KKS simple example in the split form
#
[Mesh]
type = GeneratedMesh
dim = 2
elem_type = QUAD4
nx = 50
ny = 2
nz = 0
xmin = 0
xmax = 20
ymin = 0
ymax = 0.4
zmin = 0
zmax = 0
[]
[AuxVariables]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# hydrogen concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# Liquid phase solute concentration
[./cl]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# Solid phase solute concentration
[./cs]
order = FIRST
family = LAGRANGE
initial_condition = 0.9
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = 0.5*(1.0-tanh((x)/sqrt(2.0)))
[../]
[./ic_func_c]
type = ParsedFunction
expression = '0.9*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.1*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
[../]
[]
[ICs]
[./eta]
variable = eta
type = FunctionIC
function = ic_func_eta
[../]
[./c]
variable = c
type = FunctionIC
function = ic_func_c
[../]
[]
[BCs]
[./left_c]
type = DirichletBC
variable = 'c'
boundary = 'left'
value = 0.5
[../]
[./left_eta]
type = DirichletBC
variable = 'eta'
boundary = 'left'
value = 0.5
[../]
[]
[Materials]
# Free energy of the liquid
[./fl]
type = DerivativeParsedMaterial
property_name = fl
coupled_variables = 'cl'
expression = '(0.1-cl)^2'
[../]
# Free energy of the solid
[./fs]
type = DerivativeParsedMaterial
property_name = fs
coupled_variables = 'cs'
expression = '(0.9-cs)^2'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L eps_sq'
prop_values = '0.7 0.7 1.0 '
[../]
[]
[Kernels]
# enforce c = (1-h(eta))*cl + h(eta)*cs
[./PhaseConc]
type = KKSPhaseConcentration
ca = cl
variable = cs
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotSolute]
type = KKSPhaseChemicalPotential
variable = cl
cb = cs
fa_name = fl
fb_name = fs
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cl
fa_name = fl
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fl
fb_name = fs
w = 1.0
coupled_variables = 'cl cs'
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cl
cb = cs
fa_name = fl
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = eps_sq
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fl
fb_name = fs
w = 1.0
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 100
nl_max_its = 100
nl_abs_tol = 1e-10
end_time = 800
dt = 4.0
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Postprocessors]
[./dofs]
type = NumDOFs
[../]
[./integral]
type = ElementL2Error
variable = eta
function = ic_func_eta
[../]
[]
[Outputs]
exodus = true
console = true
gnuplot = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_offset.i)
#
# KKS toy problem in the split form
# This has an offset in the minima of the free energies so there will be a shift
# in equilibrium composition
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
nz = 0
xmin = -2.5
xmax = 2.5
ymin = -2.5
ymax = 2.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[AuxVariables]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# hydrogen concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# hydrogen phase concentration (matrix)
[./cm]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[../]
# hydrogen phase concentration (delta phase)
[./cd]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[../]
[]
[ICs]
[./eta]
variable = eta
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.2
outvalue = 0.1
int_width = 0.75
[../]
[./c]
variable = c
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.6
outvalue = 0.4
int_width = 0.75
[../]
[]
[BCs]
[./Periodic]
[./all]
variable = 'eta w c cm cd'
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
# Free energy of the matrix
[./fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '(0.1-cm)^2'
[../]
# Free energy of the delta phase
[./fd]
type = DerivativeParsedMaterial
property_name = fd
coupled_variables = 'cd'
expression = '(0.9-cd)^2+0.5'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L kappa'
prop_values = '0.7 0.7 0.4 '
[../]
[]
[Kernels]
# full transient
active = 'PhaseConc ChemPotVacancies CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'
# enforce c = (1-h(eta))*cm + h(eta)*cd
[./PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cd
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cd
fa_name = fm
fb_name = fd
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cm
fa_name = fm
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fm
fb_name = fd
coupled_variables = 'cm cd'
w = 0.4
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cd
fa_name = fm
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fd
w = 0.4
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 3
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Outputs]
file_base = kks_example_offset
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_nested_damped.i)
#
# Two-phase damped nested KKS with log-free energies
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
nz = 0
xmin = -2.5
xmax = 2.5
ymin = -2.5
ymax = 2.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# order parameter
[eta]
order = FIRST
family = LAGRANGE
[]
# hydrogen concentration
[c]
order = FIRST
family = LAGRANGE
[]
# chemical potential
[w]
order = FIRST
family = LAGRANGE
[]
[]
[ICs]
[eta]
variable = eta
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 1
outvalue = 0.0
int_width = 0.75
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.9
outvalue = 0.1
int_width = 0.75
[]
[]
[BCs]
[Periodic]
[all]
variable = 'eta w c'
auto_direction = 'x y'
[]
[]
[]
[Materials]
# Free energy of the matrix
[fm]
type = DerivativeParsedMaterial
property_name = fm
expression = 'cm*log(cm/1e-4) + (1-cm)*log((1-cm)/(1-1e-4))'
material_property_names = 'cm'
additional_derivative_symbols = 'cm'
compute = false
[]
# Free energy of the delta phase
[fd]
type = DerivativeParsedMaterial
property_name = fd
expression = 'cd*log(cd/0.9999) + (1-cd)*log((1-cd)/(1-0.9999))'
material_property_names = 'cd'
additional_derivative_symbols = 'cd'
compute = false
[]
[C]
type = DerivativeParsedMaterial
property_name = 'C'
material_property_names = 'cm cd'
expression = '(cm>0)&(cm<1)&(cd>0)&(cd<1)'
compute = false
[]
# Compute phase concentrations
[PhaseConcentrationMaterial]
type = KKSPhaseConcentrationMaterial
global_cs = 'c'
ci_names = 'cm cd'
ci_IC = '0.1 0.9'
fa_name = fm
fb_name = fd
h_name = h
min_iterations = 1
max_iterations = 100
absolute_tolerance = 1e-15
relative_tolerance = 1e-8
step_size_tolerance = 1e-05
nested_iterations = iter
outputs = exodus
damped_Newton = true
conditions = C
damping_factor = 0.8
[]
# Compute chain rule terms
[PhaseConcentrationDerivatives]
type = KKSPhaseConcentrationDerivatives
global_cs = 'c'
eta = eta
ci_names = 'cm cd'
fa_name = fm
fb_name = fd
h_name = h
[]
# h(eta)
[h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[]
# g(eta)
[g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'M L kappa'
prop_values = '0.7 0.7 0.4 '
[]
[]
[Kernels]
# full transient
active = 'CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'
#
# Cahn-Hilliard Equation
#
[CHBulk]
type = NestedKKSSplitCHCRes
variable = c
global_cs = 'c'
w = w
all_etas = eta
ca_names = 'cm cd'
fa_name = fm
coupled_variables = 'eta w'
[]
[dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[]
[ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[]
#
# Allen-Cahn Equation
#
[ACBulkF]
type = NestedKKSACBulkF
variable = eta
global_cs = 'c'
ci_names = 'cm cd'
fa_name = fm
fb_name = fd
g_name = g
h_name = h
mob_name = L
w = 0.4
coupled_variables = 'c'
[]
[ACBulkC]
type = NestedKKSACBulkC
variable = eta
global_cs = 'c'
ci_names = 'cm cd'
fa_name = fm
h_name = h
mob_name = L
coupled_variables = 'c'
[]
[ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[]
[detadt]
type = TimeDerivative
variable = eta
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fd
w = 0.4
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 3
dt = 1e-5
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[full]
type = SMP
full = true
[]
[]
[Outputs]
file_base = kks_example_nested_damped
exodus = true
[]
(modules/phase_field/test/tests/phase_field_kernels/CoupledAllenCahn.i)
#
# Test the coupled Allen-Cahn Bulk kernel
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
xmax = 12
ymax = 12
elem_type = QUAD4
[]
[Variables]
[./w]
[../]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[]
[Kernels]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk]
type = CoupledAllenCahn
variable = w
v = eta
f_name = F
[../]
[./W]
type = Reaction
variable = w
[../]
[./CoupledBulk]
type = MatReaction
variable = eta
v = w
reaction_rate = L
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = 1
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L'
prop_values = '1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'eta'
expression = '2 * eta^2 * (1-eta)^2 - 0.2*eta'
derivative_order = 2
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
l_max_its = 15
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-11
start_time = 0.0
num_steps = 2
dt = 0.5
[]
[Debug]
show_var_residual_norms = true
[]
[Outputs]
hide = w
file_base = AllenCahn_out
exodus = true
[]
(modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i)
# KKS phase-field model coupled with elasticity using Khachaturyan's scheme as
# described in L.K. Aagesen et al., Computational Materials Science, 140, 10-21 (2017)
# Original run #170403a
[Mesh]
type = GeneratedMesh
dim = 3
nx = 640
ny = 1
nz = 1
xmin = -10
xmax = 10
ymin = 0
ymax = 0.03125
zmin = 0
zmax = 0.03125
elem_type = HEX8
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# solute concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# solute phase concentration (matrix)
[./cm]
order = FIRST
family = LAGRANGE
[../]
# solute phase concentration (precipitate)
[./cp]
order = FIRST
family = LAGRANGE
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[./disp_z]
order = FIRST
family = LAGRANGE
[../]
[]
[ICs]
[./eta_ic]
variable = eta
type = FunctionIC
function = ic_func_eta
block = 0
[../]
[./c_ic]
variable = c
type = FunctionIC
function = ic_func_c
block = 0
[../]
[./w_ic]
variable = w
type = ConstantIC
value = 0.00991
block = 0
[../]
[./cm_ic]
variable = cm
type = ConstantIC
value = 0.131
block = 0
[../]
[./cp_ic]
variable = cp
type = ConstantIC
value = 0.236
block = 0
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = '0.5*(1.0+tanh((x)/delta_eta/sqrt(2.0)))'
symbol_names = 'delta_eta'
symbol_values = '0.8034'
[../]
[./ic_func_c]
type = ParsedFunction
expression = '0.2389*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10)+0.1339*(1-(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10))'
symbol_names = 'delta'
symbol_values = '0.8034'
[../]
[./psi_eq_int]
type = ParsedFunction
expression = 'volume*psi_alpha'
symbol_names = 'volume psi_alpha'
symbol_values = 'volume psi_alpha'
[../]
[./gamma]
type = ParsedFunction
expression = '(psi_int - psi_eq_int) / dy / dz'
symbol_names = 'psi_int psi_eq_int dy dz'
symbol_values = 'psi_int psi_eq_int 0.03125 0.03125'
[../]
[]
[AuxVariables]
[./sigma11]
order = CONSTANT
family = MONOMIAL
[../]
[./sigma22]
order = CONSTANT
family = MONOMIAL
[../]
[./sigma33]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./e33]
order = CONSTANT
family = MONOMIAL
[../]
[./e_el11]
order = CONSTANT
family = MONOMIAL
[../]
[./e_el12]
order = CONSTANT
family = MONOMIAL
[../]
[./e_el22]
order = CONSTANT
family = MONOMIAL
[../]
[./f_el]
order = CONSTANT
family = MONOMIAL
[../]
[./eigen_strain00]
order = CONSTANT
family = MONOMIAL
[../]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[./psi]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./matl_sigma11]
type = RankTwoAux
rank_two_tensor = stress
index_i = 0
index_j = 0
variable = sigma11
[../]
[./matl_sigma22]
type = RankTwoAux
rank_two_tensor = stress
index_i = 1
index_j = 1
variable = sigma22
[../]
[./matl_sigma33]
type = RankTwoAux
rank_two_tensor = stress
index_i = 2
index_j = 2
variable = sigma33
[../]
[./matl_e11]
type = RankTwoAux
rank_two_tensor = total_strain
index_i = 0
index_j = 0
variable = e11
[../]
[./f_el]
type = MaterialRealAux
variable = f_el
property = f_el_mat
execute_on = timestep_end
[../]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fp
w = 0.0264
kappa_names = kappa
interfacial_vars = eta
[../]
[./psi_potential]
variable = psi
type = ParsedAux
coupled_variables = 'Fglobal w c f_el sigma11 e11'
expression = 'Fglobal - w*c + f_el - sigma11*e11'
[../]
[]
[BCs]
[./left_x]
type = DirichletBC
variable = disp_x
boundary = left
value = 0
[../]
[./right_x]
type = DirichletBC
variable = disp_x
boundary = right
value = 0
[../]
[./front_y]
type = DirichletBC
variable = disp_y
boundary = front
value = 0
[../]
[./back_y]
type = DirichletBC
variable = disp_y
boundary = back
value = 0
[../]
[./top_z]
type = DirichletBC
variable = disp_z
boundary = top
value = 0
[../]
[./bottom_z]
type = DirichletBC
variable = disp_z
boundary = bottom
value = 0
[../]
[]
[Materials]
# Chemical free energy of the matrix
[./fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '6.55*(cm-0.13)^2'
[../]
# Chemical Free energy of the precipitate phase
[./fp]
type = DerivativeParsedMaterial
property_name = fp
coupled_variables = 'cp'
expression = '6.55*(cp-0.235)^2'
[../]
# Elastic energy of the precipitate
[./elastic_free_energy_p]
type = ElasticEnergyMaterial
f_name = f_el_mat
coupled_variables = 'eta'
outputs = exodus
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# 1- h(eta), putting in function explicitly
[./one_minus_h_eta_explicit]
type = DerivativeParsedMaterial
property_name = one_minus_h_explicit
coupled_variables = eta
expression = 1-eta^3*(6*eta^2-15*eta+10)
outputs = exodus
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L kappa misfit'
prop_values = '0.7 0.7 0.01704 0.00377'
[../]
#Mechanical properties
[./Stiffness_matrix]
type = ComputeElasticityTensor
base_name = C_matrix
C_ijkl = '103.3 74.25 74.25 103.3 74.25 103.3 46.75 46.75 46.75'
fill_method = symmetric9
[../]
[./Stiffness_ppt]
type = ComputeElasticityTensor
C_ijkl = '100.7 71.45 71.45 100.7 71.45 100.7 50.10 50.10 50.10'
base_name = C_ppt
fill_method = symmetric9
[../]
[./C]
type = CompositeElasticityTensor
coupled_variables = eta
tensors = 'C_matrix C_ppt'
weights = 'one_minus_h_explicit h'
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./strain]
type = ComputeSmallStrain
displacements = 'disp_x disp_y disp_z'
eigenstrain_names = 'eigenstrain_ppt'
[../]
[./eigen_strain]
type = ComputeVariableEigenstrain
eigen_base = '0.00377 0.00377 0.00377 0 0 0'
prefactor = h
args = eta
eigenstrain_name = 'eigenstrain_ppt'
[../]
[]
[Kernels]
[./TensorMechanics]
displacements = 'disp_x disp_y disp_z'
[../]
# enforce c = (1-h(eta))*cm + h(eta)*cp
[./PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cp
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cp
fa_name = fm
fb_name = fp
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cm
fa_name = fm
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fm
fb_name = fp
w = 0.0264
coupled_variables = 'cp cm'
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cp
fa_name = fm
[../]
[./ACBulk_el] #This adds df_el/deta for strain interpolation
type = AllenCahn
variable = eta
f_name = f_el_mat
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-11
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.5
[../]
[]
[Postprocessors]
[./f_el_int]
type = ElementIntegralMaterialProperty
mat_prop = f_el_mat
[../]
[./c_alpha]
type = SideAverageValue
boundary = left
variable = c
[../]
[./c_beta]
type = SideAverageValue
boundary = right
variable = c
[../]
[./e11_alpha]
type = SideAverageValue
boundary = left
variable = e11
[../]
[./e11_beta]
type = SideAverageValue
boundary = right
variable = e11
[../]
[./s11_alpha]
type = SideAverageValue
boundary = left
variable = sigma11
[../]
[./s22_alpha]
type = SideAverageValue
boundary = left
variable = sigma22
[../]
[./s33_alpha]
type = SideAverageValue
boundary = left
variable = sigma33
[../]
[./s11_beta]
type = SideAverageValue
boundary = right
variable = sigma11
[../]
[./s22_beta]
type = SideAverageValue
boundary = right
variable = sigma22
[../]
[./s33_beta]
type = SideAverageValue
boundary = right
variable = sigma33
[../]
[./f_el_alpha]
type = SideAverageValue
boundary = left
variable = f_el
[../]
[./f_el_beta]
type = SideAverageValue
boundary = right
variable = f_el
[../]
[./f_c_alpha]
type = SideAverageValue
boundary = left
variable = Fglobal
[../]
[./f_c_beta]
type = SideAverageValue
boundary = right
variable = Fglobal
[../]
[./chem_pot_alpha]
type = SideAverageValue
boundary = left
variable = w
[../]
[./chem_pot_beta]
type = SideAverageValue
boundary = right
variable = w
[../]
[./psi_alpha]
type = SideAverageValue
boundary = left
variable = psi
[../]
[./psi_beta]
type = SideAverageValue
boundary = right
variable = psi
[../]
[./total_energy]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
[../]
# Get simulation cell size from postprocessor
[./volume]
type = ElementIntegralMaterialProperty
mat_prop = 1
[../]
[./psi_eq_int]
type = FunctionValuePostprocessor
function = psi_eq_int
[../]
[./psi_int]
type = ElementIntegralVariablePostprocessor
variable = psi
[../]
[./gamma]
type = FunctionValuePostprocessor
function = gamma
[../]
[./int_position]
type = FindValueOnLine
start_point = '-10 0 0'
end_point = '10 0 0'
v = eta
target = 0.5
[../]
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Outputs]
[./exodus]
type = Exodus
time_step_interval = 20
[../]
checkpoint = true
[./csv]
type = CSV
execute_on = 'final'
[../]
[]
(modules/combined/test/tests/surface_tension_KKS/surface_tension_VDWgas.i)
# Test for ComputeExtraStressVDWGas
# Gas bubble with r = 15 nm in a solid matrix
# The gas pressure is counterbalanced by the surface tension of the solid-gas interface,
# which is included with ComputeSurfaceTensionKKS
[Mesh]
type = GeneratedMesh
dim = 1
nx = 300
xmin = 0
xmax = 30
coord_type = RSPHERICAL
[]
[GlobalParams]
displacements = 'disp_x'
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# gas concentration
[./cg]
order = FIRST
family = LAGRANGE
[../]
# vacancy concentration
[./cv]
order = FIRST
family = LAGRANGE
[../]
# gas chemical potential
[./wg]
order = FIRST
family = LAGRANGE
[../]
# vacancy chemical potential
[./wv]
order = FIRST
family = LAGRANGE
[../]
# Matrix phase gas concentration
[./cgm]
order = FIRST
family = LAGRANGE
initial_condition = 1.01e-31
[../]
# Matrix phase vacancy concentration
[./cvm]
order = FIRST
family = LAGRANGE
initial_condition = 2.25e-11
[../]
# Bubble phase gas concentration
[./cgb]
order = FIRST
family = LAGRANGE
initial_condition = 0.2714
[../]
# Bubble phase vacancy concentration
[./cvb]
order = FIRST
family = LAGRANGE
initial_condition = 0.7286
[../]
[]
[ICs]
[./eta_ic]
variable = eta
type = FunctionIC
function = ic_func_eta
[../]
[./cv_ic]
variable = cv
type = FunctionIC
function = ic_func_cv
[../]
[./cg_ic]
variable = cg
type = FunctionIC
function = ic_func_cg
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2+z^2);0.5*(1.0-tanh((r-r0)/delta_eta/sqrt(2.0)))'
symbol_names = 'delta_eta r0'
symbol_values = '0.321 15'
[../]
[./ic_func_cv]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2+z^2);eta_an:=0.5*(1.0-tanh((r-r0)/delta/sqrt(2.0)));cvbubinit*eta_an^3*(6*eta_an^2-15*eta_an+10)+cvmatrixinit*(1-eta_an^3*(6*eta_an^2-15*eta_an+10))'
symbol_names = 'delta r0 cvbubinit cvmatrixinit'
symbol_values = '0.321 15 0.7286 2.25e-11'
[../]
[./ic_func_cg]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2+z^2);eta_an:=0.5*(1.0-tanh((r-r0)/delta/sqrt(2.0)));cgbubinit*eta_an^3*(6*eta_an^2-15*eta_an+10)+cgmatrixinit*(1-eta_an^3*(6*eta_an^2-15*eta_an+10))'
symbol_names = 'delta r0 cgbubinit cgmatrixinit'
symbol_values = '0.321 15 0.2714 1.01e-31'
[../]
[]
[Physics/SolidMechanics/QuasiStatic]
[./all]
add_variables = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz'
[../]
[]
[Kernels]
# enforce cg = (1-h(eta))*cgm + h(eta)*cgb
[./PhaseConc_g]
type = KKSPhaseConcentration
ca = cgm
variable = cgb
c = cg
eta = eta
[../]
# enforce cv = (1-h(eta))*cvm + h(eta)*cvb
[./PhaseConc_v]
type = KKSPhaseConcentration
ca = cvm
variable = cvb
c = cv
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cvm
cb = cvb
fa_name = f_total_matrix
fb_name = f_total_bub
args_a = 'cgm'
args_b = 'cgb'
[../]
[./ChemPotGas]
type = KKSPhaseChemicalPotential
variable = cgm
cb = cgb
fa_name = f_total_matrix
fb_name = f_total_bub
args_a = 'cvm'
args_b = 'cvb'
[../]
#
# Cahn-Hilliard Equations
#
[./CHBulk_g]
type = KKSSplitCHCRes
variable = cg
ca = cgm
fa_name = f_total_matrix
w = wg
args_a = 'cvm'
[../]
[./CHBulk_v]
type = KKSSplitCHCRes
variable = cv
ca = cvm
fa_name = f_total_matrix
w = wv
args_a = 'cgm'
[../]
[./dcgdt]
type = CoupledTimeDerivative
variable = wg
v = cg
[../]
[./dcvdt]
type = CoupledTimeDerivative
variable = wv
v = cv
[../]
[./wgkernel]
type = SplitCHWRes
mob_name = M
variable = wg
[../]
[./wvkernel]
type = SplitCHWRes
mob_name = M
variable = wv
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = f_total_matrix
fb_name = f_total_bub
w = 0.356
coupled_variables = 'cvm cvb cgm cgb'
[../]
[./ACBulkCv]
type = KKSACBulkC
variable = eta
ca = cvm
cb = cvb
fa_name = f_total_matrix
coupled_variables = 'cgm'
[../]
[./ACBulkCg]
type = KKSACBulkC
variable = eta
ca = cgm
cb = cgb
fa_name = f_total_matrix
coupled_variables = 'cvm'
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[Materials]
# Chemical free energy of the matrix
[./fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cvm cgm'
material_property_names = 'kvmatrix kgmatrix cvmatrixeq cgmatrixeq'
expression = '0.5*kvmatrix*(cvm-cvmatrixeq)^2 + 0.5*kgmatrix*(cgm-cgmatrixeq)^2'
[../]
# Elastic energy of the matrix
[./elastic_free_energy_m]
type = ElasticEnergyMaterial
base_name = matrix
f_name = fe_m
coupled_variables = ' '
[../]
# Total free energy of the matrix
[./Total_energy_matrix]
type = DerivativeSumMaterial
property_name = f_total_matrix
sum_materials = 'fm fe_m'
coupled_variables = 'cvm cgm'
[../]
# Free energy of the bubble phase
[./fb]
type = DerivativeParsedMaterial
property_name = fb
coupled_variables = 'cvb cgb'
material_property_names = 'kToverV nQ Va b f0 kpen kgbub kvbub cvbubeq cgbubeq'
expression = '0.5*kgbub*(cvb-cvbubeq)^2 + 0.5*kvbub*(cgb-cgbubeq)^2'
[../]
# Elastic energy of the bubble
[./elastic_free_energy_p]
type = ElasticEnergyMaterial
base_name = bub
f_name = fe_b
coupled_variables = ' '
[../]
# Total free energy of the bubble
[./Total_energy_bub]
type = DerivativeSumMaterial
property_name = f_total_bub
sum_materials = 'fb fe_b'
# sum_materials = 'fb'
coupled_variables = 'cvb cgb'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L kappa Va kvmatrix kgmatrix kgbub kvbub f0 kpen cvbubeq cgbubeq b T'
prop_values = '0.7 0.7 0.0368 0.03629 223.16 223.16 2.23 2.23 0.0224 1.0 0.6076 0.3924 0.085 800'
[../]
[./cvmatrixeq]
type = ParsedMaterial
property_name = cvmatrixeq
material_property_names = 'T'
constant_names = 'kB Efv'
constant_expressions = '8.6173324e-5 1.69'
expression = 'exp(-Efv/(kB*T))'
[../]
[./cgmatrixeq]
type = ParsedMaterial
property_name = cgmatrixeq
material_property_names = 'T'
constant_names = 'kB Efg'
constant_expressions = '8.6173324e-5 4.92'
expression = 'exp(-Efg/(kB*T))'
[../]
[./kToverV]
type = ParsedMaterial
property_name = kToverV
material_property_names = 'T Va'
constant_names = 'k C44dim' #k in J/K and dimensional C44 in J/m^3
constant_expressions = '1.38e-23 63e9'
expression = 'k*T*1e27/Va/C44dim'
[../]
[./nQ]
type = ParsedMaterial
property_name = nQ
material_property_names = 'T'
constant_names = 'k Pi M hbar' #k in J/K, M is Xe atomic mass in kg, hbar in J s
constant_expressions = '1.38e-23 3.14159 2.18e-25 1.05459e-34'
expression = '(M*k*T/2/Pi/hbar^2)^1.5 * 1e-27' #1e-27 converts from #/m^3 to #/nm^3
[../]
#Mechanical properties
[./Stiffness_matrix]
type = ComputeElasticityTensor
C_ijkl = '0.778 0.7935'
fill_method = symmetric_isotropic
base_name = matrix
[../]
[./Stiffness_bub]
type = ComputeElasticityTensor
C_ijkl = '0.0778 0.07935'
fill_method = symmetric_isotropic
base_name = bub
[../]
[./strain_matrix]
type = ComputeRSphericalSmallStrain
base_name = matrix
[../]
[./strain_bub]
type = ComputeRSphericalSmallStrain
base_name = bub
[../]
[./stress_matrix]
type = ComputeLinearElasticStress
base_name = matrix
[../]
[./stress_bub]
type = ComputeLinearElasticStress
base_name = bub
[../]
[./global_stress]
type = TwoPhaseStressMaterial
base_A = matrix
base_B = bub
[../]
[./surface_tension]
type = ComputeSurfaceTensionKKS
v = eta
kappa_name = kappa
w = 0.356
[../]
[./gas_pressure]
type = ComputeExtraStressVDWGas
T = T
b = b
cg = cgb
Va = Va
nondim_factor = 63e9
base_name = bub
outputs = exodus
[../]
[]
[BCs]
[./left_r]
type = DirichletBC
variable = disp_x
boundary = left
value = 0
[../]
[]
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm lu nonzero'
l_max_its = 30
nl_max_its = 15
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1e-11
num_steps = 2
dt = 0.5
[]
[Outputs]
exodus = true
[]
(modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialMultiphase.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = -20
xmax = 20
ymin = -20
ymax = 20
[]
[GlobalParams]
op_num = 2
var_name_base = etab
[]
[Variables]
[w]
[]
[etaa0]
[]
[etab0]
[]
[etab1]
[]
[]
[AuxVariables]
[bnds]
order = FIRST
family = LAGRANGE
[]
[]
[ICs]
[IC_etaa0]
type = FunctionIC
variable = etaa0
function = ic_func_etaa0
[]
[IC_etab0]
type = FunctionIC
variable = etab0
function = ic_func_etab0
[]
[IC_etab1]
type = FunctionIC
variable = etab1
function = ic_func_etab1
[]
[IC_w]
type = ConstantIC
value = -0.05
variable = w
[]
[]
[Functions]
[ic_func_etaa0]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2);0.5*(1.0-tanh((r-10.0)/sqrt(2.0)))'
[]
[ic_func_etab0]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2);0.5*(1.0+tanh((r-10)/sqrt(2.0)))*0.5*(1.0+tanh((y)/sqrt(2.0)))'
[]
[ic_func_etab1]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2);0.5*(1.0+tanh((r-10)/sqrt(2.0)))*0.5*(1.0-tanh((y)/sqrt(2.0)))'
[]
[]
[BCs]
[]
[Kernels]
# Order parameter eta_alpha0
[ACa0_bulk]
type = ACGrGrMulti
variable = etaa0
v = 'etab0 etab1'
gamma_names = 'gab gab'
[]
[ACa0_sw]
type = ACSwitching
variable = etaa0
Fj_names = 'omegaa omegab'
hj_names = 'ha hb'
coupled_variables = 'etab0 etab1 w'
[]
[ACa0_int]
type = ACInterface
variable = etaa0
kappa_name = kappa
[]
[ea0_dot]
type = TimeDerivative
variable = etaa0
[]
# Order parameter eta_beta0
[ACb0_bulk]
type = ACGrGrMulti
variable = etab0
v = 'etaa0 etab1'
gamma_names = 'gab gbb'
[]
[ACb0_sw]
type = ACSwitching
variable = etab0
Fj_names = 'omegaa omegab'
hj_names = 'ha hb'
coupled_variables = 'etaa0 etab1 w'
[]
[ACb0_int]
type = ACInterface
variable = etab0
kappa_name = kappa
[]
[eb0_dot]
type = TimeDerivative
variable = etab0
[]
# Order parameter eta_beta1
[ACb1_bulk]
type = ACGrGrMulti
variable = etab1
v = 'etaa0 etab0'
gamma_names = 'gab gbb'
[]
[ACb1_sw]
type = ACSwitching
variable = etab1
Fj_names = 'omegaa omegab'
hj_names = 'ha hb'
coupled_variables = 'etaa0 etab0 w'
[]
[ACb1_int]
type = ACInterface
variable = etab1
kappa_name = kappa
[]
[eb1_dot]
type = TimeDerivative
variable = etab1
[]
#Chemical potential
[w_dot]
type = SusceptibilityTimeDerivative
variable = w
f_name = chi
coupled_variables = '' # in this case chi (the susceptibility) is simply a constant
[]
[Diffusion]
type = MatDiffusion
variable = w
diffusivity = Dchi
args = ''
[]
[coupled_etaa0dot]
type = CoupledSwitchingTimeDerivative
variable = w
v = etaa0
Fj_names = 'rhoa rhob'
hj_names = 'ha hb'
coupled_variables = 'etaa0 etab0 etab1'
[]
[coupled_etab0dot]
type = CoupledSwitchingTimeDerivative
variable = w
v = etab0
Fj_names = 'rhoa rhob'
hj_names = 'ha hb'
coupled_variables = 'etaa0 etab0 etab1'
[]
[coupled_etab1dot]
type = CoupledSwitchingTimeDerivative
variable = w
v = etab1
Fj_names = 'rhoa rhob'
hj_names = 'ha hb'
coupled_variables = 'etaa0 etab0 etab1'
[]
[]
[AuxKernels]
[BndsCalc]
type = BndsCalcAux
variable = bnds
execute_on = timestep_end
[]
[]
# enable_jit set to false in many materials to make this test start up faster.
# It is recommended to set enable_jit = true or just remove these lines for
# production runs with this model
[Materials]
[ha]
type = SwitchingFunctionMultiPhaseMaterial
h_name = ha
all_etas = 'etaa0 etab0 etab1'
phase_etas = 'etaa0'
[]
[hb]
type = SwitchingFunctionMultiPhaseMaterial
h_name = hb
all_etas = 'etaa0 etab0 etab1'
phase_etas = 'etab0 etab1'
[]
[omegaa]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegaa
material_property_names = 'Vm ka caeq'
expression = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
derivative_order = 2
enable_jit = false
[]
[omegab]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegab
material_property_names = 'Vm kb cbeq'
expression = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
derivative_order = 2
enable_jit = false
[]
[rhoa]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhoa
material_property_names = 'Vm ka caeq'
expression = 'w/Vm^2/ka + caeq/Vm'
derivative_order = 2
enable_jit = false
[]
[rhob]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhob
material_property_names = 'Vm kb cbeq'
expression = 'w/Vm^2/kb + cbeq/Vm'
derivative_order = 2
enable_jit = false
[]
[const]
type = GenericConstantMaterial
prop_names = 'kappa_c kappa L D chi Vm ka caeq kb cbeq gab gbb mu'
prop_values = '0 1 1.0 1.0 1.0 1.0 10.0 0.1 10.0 0.9 4.5 1.5 1.0'
[]
[Mobility]
type = DerivativeParsedMaterial
property_name = Dchi
material_property_names = 'D chi'
expression = 'D*chi'
derivative_order = 2
enable_jit = false
[]
[]
[Preconditioning]
[SMP]
type = SMP
full = true
[]
[]
[Executioner]
type = Transient
scheme = bdf2
petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -pc_asm_overlap'
petsc_options_value = 'asm 31 lu 1'
l_tol = 1.0e-3
nl_rel_tol = 1.0e-8
nl_abs_tol = 1e-8
num_steps = 2
[TimeStepper]
type = TimeSequenceStepper
time_sequence = '0.1 0.21'
[]
[]
[Outputs]
exodus = true
[]
(modules/combined/examples/phase_field-mechanics/SimplePhaseTrans.i)
#
# Martensitic transformation
# One structural order parameter (SOP) governed by AllenCahn Eqn.
# Chemical driving force described by Landau Polynomial
# Coupled with elasticity (Mechanics)
# Eigenstrain as a function of SOP
#
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
type = GeneratedMesh
dim = 2
nx = 100
ny = 100
xmin = 0
xmax = 100
ymin = 0
ymax = 100
elem_type = QUAD4
[]
[Variables]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 50
y1 = 50
radius = 10.0
invalue = 1.0
outvalue = 0.0
int_width = 5.0
[../]
[../]
[]
[Physics/SolidMechanics/QuasiStatic]
[./all]
add_variables = true
generate_output = 'stress_xx stress_yy'
eigenstrain_names = 'eigenstrain'
[../]
[]
[Kernels]
[./eta_bulk]
type = AllenCahn
variable = eta
f_name = F
[../]
[./eta_interface]
type = ACInterface
variable = eta
kappa_name = kappa_eta
[../]
[./time]
type = TimeDerivative
variable = eta
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1 1'
[../]
[./chemical_free_energy]
type = DerivativeParsedMaterial
property_name = Fc
coupled_variables = 'eta'
constant_names = 'A2 A3 A4'
constant_expressions = '0.2 -12.6 12.4'
expression = A2/2*eta^2+A3/3*eta^3+A4/4*eta^4
enable_jit = true
derivative_order = 2
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '70 30 30 70 30 70 30 30 30'
fill_method = symmetric9
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./var_dependence]
type = DerivativeParsedMaterial
expression = eta
coupled_variables = 'eta'
property_name = var_dep
enable_jit = true
derivative_order = 2
[../]
[./eigenstrain]
type = ComputeVariableEigenstrain
eigen_base = '0.1 0.1 0 0 0 0'
prefactor = var_dep
#outputs = exodus
coupled_variables = 'eta'
eigenstrain_name = eigenstrain
[../]
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'eta'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeSumMaterial
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'eta'
derivative_order = 2
[../]
[]
[BCs]
[./all_y]
type = DirichletBC
variable = disp_y
boundary = 'top bottom left right'
value = 0
[../]
[./all_x]
type = DirichletBC
variable = disp_x
boundary = 'top bottom left right'
value = 0
[../]
[]
[Preconditioning]
# active = ' '
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
# this gives best performance on 4 cores
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type '
petsc_options_value = 'asm lu'
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 = 10
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 9
iteration_window = 2
growth_factor = 1.1
cutback_factor = 0.75
dt = 0.3
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i)
#
# KKS ternary (3 chemical component) system example in the split form
# We track c1 and c2 only, since c1 + c2 + c3 = 1
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 150
ny = 15
nz = 0
xmin = -25
xmax = 25
ymin = -2.5
ymax = 2.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[AuxVariables]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# solute 1 concentration
[./c1]
order = FIRST
family = LAGRANGE
[../]
# solute 2 concentration
[./c2]
order = FIRST
family = LAGRANGE
[../]
# chemical potential solute 1
[./w1]
order = FIRST
family = LAGRANGE
[../]
# chemical potential solute 2
[./w2]
order = FIRST
family = LAGRANGE
[../]
# Liquid phase solute 1 concentration
[./c1l]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# Liquid phase solute 2 concentration
[./c2l]
order = FIRST
family = LAGRANGE
initial_condition = 0.05
[../]
# Solid phase solute 1 concentration
[./c1s]
order = FIRST
family = LAGRANGE
initial_condition = 0.8
[../]
# Solid phase solute 2 concentration
[./c2s]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = '0.5*(1.0-tanh((x)/sqrt(2.0)))'
[../]
[./ic_func_c1]
type = ParsedFunction
expression = '0.8*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.1*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
[../]
[./ic_func_c2]
type = ParsedFunction
expression = '0.1*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.05*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
[../]
[]
[ICs]
[./eta]
variable = eta
type = FunctionIC
function = ic_func_eta
[../]
[./c1]
variable = c1
type = FunctionIC
function = ic_func_c1
[../]
[./c2]
variable = c2
type = FunctionIC
function = ic_func_c2
[../]
[]
[Materials]
# Free energy of the liquid
[./fl]
type = DerivativeParsedMaterial
property_name = fl
coupled_variables = 'c1l c2l'
expression = '(0.1-c1l)^2+(0.05-c2l)^2'
[../]
# Free energy of the solid
[./fs]
type = DerivativeParsedMaterial
property_name = fs
coupled_variables = 'c1s c2s'
expression = '(0.8-c1s)^2+(0.1-c2s)^2'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L eps_sq'
prop_values = '0.7 0.7 1.0 '
[../]
[]
[Kernels]
# enforce c1 = (1-h(eta))*c1l + h(eta)*c1s
[./PhaseConc1]
type = KKSPhaseConcentration
ca = c1l
variable = c1s
c = c1
eta = eta
[../]
# enforce c2 = (1-h(eta))*c2l + h(eta)*c2s
[./PhaseConc2]
type = KKSPhaseConcentration
ca = c2l
variable = c2s
c = c2
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotSolute1]
type = KKSPhaseChemicalPotential
variable = c1l
cb = c1s
fa_name = fl
fb_name = fs
args_a = 'c2l'
args_b = 'c2s'
[../]
[./ChemPotSolute2]
type = KKSPhaseChemicalPotential
variable = c2l
cb = c2s
fa_name = fl
fb_name = fs
args_a = 'c1l'
args_b = 'c1s'
[../]
#
# Cahn-Hilliard Equations
#
[./CHBulk1]
type = KKSSplitCHCRes
variable = c1
ca = c1l
fa_name = fl
w = w1
args_a = 'c2l'
[../]
[./CHBulk2]
type = KKSSplitCHCRes
variable = c2
ca = c2l
fa_name = fl
w = w2
args_a = 'c1l'
[../]
[./dc1dt]
type = CoupledTimeDerivative
variable = w1
v = c1
[../]
[./dc2dt]
type = CoupledTimeDerivative
variable = w2
v = c2
[../]
[./w1kernel]
type = SplitCHWRes
mob_name = M
variable = w1
[../]
[./w2kernel]
type = SplitCHWRes
mob_name = M
variable = w2
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fl
fb_name = fs
w = 1.0
coupled_variables = 'c1l c1s c2l c2s'
[../]
[./ACBulkC1]
type = KKSACBulkC
variable = eta
ca = c1l
cb = c1s
fa_name = fl
coupled_variables = 'c2l'
[../]
[./ACBulkC2]
type = KKSACBulkC
variable = eta
ca = c2l
cb = c2s
fa_name = fl
coupled_variables = 'c1l'
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = eps_sq
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fl
fb_name = fs
w = 1.0
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 50
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Outputs]
exodus = true
[]
(modules/phase_field/test/tests/MultiPhase/lagrangemult.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 14
ny = 10
nz = 0
xmin = 10
xmax = 40
ymin = 15
ymax = 35
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 30.0
y1 = 25.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'c eta2'
f_name = F
[../]
[./ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa_eta
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'c eta1'
f_name = F
[../]
[./ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa_eta
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2'
h_names = 'h1 h2'
epsilon = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = 'eta1 eta2'
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time1]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1 1 '
[../]
[./consts2]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1 1'
[../]
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
outputs = exodus
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
outputs = exodus
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2'
[../]
[./free_energy_A]
type = DerivativeParsedMaterial
property_name = Fa
coupled_variables = 'c'
expression = '(c-0.1)^2'
derivative_order = 2
enable_jit = true
[../]
[./free_energy_B]
type = DerivativeParsedMaterial
property_name = Fb
coupled_variables = 'c'
expression = '(c-0.9)^2'
derivative_order = 2
enable_jit = true
[../]
[./free_energy]
type = DerivativeMultiPhaseMaterial
property_name = F
fi_names = 'Fa Fb'
hi_names = 'h1 h2'
etas = 'eta1 eta2'
coupled_variables = 'c'
derivative_order = 2
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
#petsc_options = '-snes_ksp -snes_ksp_ew'
#petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
#petsc_options_iname = '-ksp_gmres_restart'
#petsc_options_value = '1000 '
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 1
dt = 0.01
dtmin = 0.01
[]
[Debug]
# show_var_residual_norms = true
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/test/tests/phase_field_kernels/AllenCahn.i)
#
# Test the parsed function free enery Allen-Cahn Bulk kernel
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
xmax = 12
ymax = 12
elem_type = QUAD4
[]
[Variables]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[]
[Kernels]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk]
type = AllenCahn
variable = eta
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = 1
variable_L = false
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L'
prop_values = '1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'eta'
expression = '2 * eta^2 * (1-eta)^2 - 0.2*eta'
derivative_order = 2
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
num_steps = 2
dt = 0.5
[]
[Outputs]
exodus = true
[]
(modules/combined/examples/publications/rapid_dev/fig7a.i)
#
# Fig. 7 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Solid gray curve (1)
# Eigenstrain and elastic energies ar computed per phase and then interpolated.
# Supply the RADIUS parameter (10-35) on the command line to generate data
# for all curves in the plot.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 32
xmin = 0
xmax = 100
second_order = true
coord_type = RSPHERICAL
[]
[GlobalParams]
displacements = 'disp_r'
[]
[Functions]
[./diff]
type = ParsedFunction
expression = '${RADIUS}-pos_c'
symbol_names = pos_c
symbol_values = pos_c
[../]
[]
# 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'
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
[./w]
[../]
# Phase order parameter
[./eta]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
# Mesh displacement
[./disp_r]
order = SECOND
[../]
[./Fe_fit]
order = SECOND
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Split Cahn-Hilliard kernels
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
coupled_variables = 'eta'
kappa_name = kappa_c
w = w
[../]
[./wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk1]
type = AllenCahn
variable = eta
coupled_variables = 'c'
mob_name = L
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
mob_name = L
kappa_name = kappa_eta
[../]
[./Fe]
type = MaterialPropertyValue
prop_name = Fe
variable = Fe_fit
[../]
[./autoadjust]
type = MaskedBodyForce
variable = w
function = diff
mask = mask
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M L kappa_c kappa_eta'
prop_values = '1.0 1.0 0.5 1'
[../]
# forcing function mask
[./mask]
type = ParsedMaterial
property_name = mask
expression = grad/dt
material_property_names = 'grad dt'
[../]
[./grad]
type = VariableGradientMaterial
variable = c
prop = grad
[../]
[./time]
type = TimeStepMaterial
[../]
# global mechanical properties
[./elasticity_tensor_1]
type = ComputeElasticityTensor
C_ijkl = '1 1'
base_name = phase1
fill_method = symmetric_isotropic
[../]
[./elasticity_tensor_2]
type = ComputeElasticityTensor
C_ijkl = '1 1'
base_name = phase2
fill_method = symmetric_isotropic
[../]
[./strain_1]
type = ComputeRSphericalSmallStrain
base_name = phase1
[../]
[./strain_2]
type = ComputeRSphericalSmallStrain
base_name = phase2
eigenstrain_names = eigenstrain
[../]
[./stress_1]
type = ComputeLinearElasticStress
base_name = phase1
[../]
[./stress_2]
type = ComputeLinearElasticStress
base_name = phase2
[../]
# eigenstrain per phase
[./eigenstrain2]
type = ComputeEigenstrain
eigen_base = '0.05 0.05 0.05 0 0 0'
base_name = phase2
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching]
type = SwitchingFunctionMaterial
function_name = h
eta = eta
h_order = SIMPLE
[../]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = 'c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(1-c)^2'
coupled_variables = 'c'
derivative_order = 2
[../]
# elastic free energies
[./elastic_free_energy_1]
type = ElasticEnergyMaterial
f_name = Fe1
coupled_variables = ''
base_name = phase1
derivative_order = 2
[../]
[./elastic_free_energy_2]
type = ElasticEnergyMaterial
f_name = Fe2
coupled_variables = ''
base_name = phase2
derivative_order = 2
[../]
# per phase free energies
[./free_energy_1]
type = DerivativeSumMaterial
property_name = F1
sum_materials = 'Fc1 Fe1'
coupled_variables = 'c'
derivative_order = 2
[../]
[./free_energy_2]
type = DerivativeSumMaterial
property_name = F2
sum_materials = 'Fc2 Fe2'
coupled_variables = 'c'
derivative_order = 2
[../]
# global chemical free energy
[./global_free_energy]
type = DerivativeTwoPhaseMaterial
f_name = F
fa_name = F1
fb_name = F2
eta = eta
coupled_variables = 'c'
W = 4
[../]
# global stress
[./global_stress]
type = TwoPhaseStressMaterial
base_A = phase1
base_B = phase2
[../]
[./elastic_free_energy]
type = DerivativeTwoPhaseMaterial
f_name = Fe
fa_name = Fe1
fb_name = Fe2
eta = eta
coupled_variables = 'c'
W = 0
[../]
[]
[BCs]
[./left_r]
type = DirichletBC
variable = disp_r
boundary = 'left'
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
variable = local_energy
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_c]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = c
target = 0.582
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_eta]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = eta
target = 0.5
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./c_min]
type = ElementExtremeValue
value_type = min
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[]
[VectorPostprocessors]
[./line]
type = LineValueSampler
variable = 'Fe_fit c w'
start_point = '0 0 0'
end_point = '100 0 0'
num_points = 5000
sort_by = x
outputs = vpp
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 30
nl_max_its = 15
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 2.0e-9
start_time = 0.0
end_time = 100000.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 7
iteration_window = 1
dt = 1
[../]
[./Adaptivity]
initial_adaptivity = 5
interval = 10
max_h_level = 5
refine_fraction = 0.9
coarsen_fraction = 0.1
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
execute_on = 'INITIAL TIMESTEP_END'
[./table]
type = CSV
delimiter = ' '
file_base = radius_${RADIUS}/energy_pp
[../]
[./vpp]
type = CSV
delimiter = ' '
sync_times = '10 50 100 500 1000 5000 10000 50000 100000'
sync_only = true
time_data = true
file_base = radius_${RADIUS}/energy_vpp
[../]
[]
(modules/phase_field/examples/multiphase/GrandPotential3Phase.i)
# This is an example of implementation of the multi-phase, multi-order parameter
# grand potential based phase-field model described in Phys. Rev. E, 98, 023309
# (2018). It includes 3 phases with 1 grain of each phase. This example was used
# to generate the results shown in Fig. 3 of the paper.
[Mesh]
type = GeneratedMesh
dim = 1
nx = 60
xmin = -15
xmax = 15
[]
[Variables]
[./w]
[../]
[./etaa0]
[../]
[./etab0]
[../]
[./etad0]
[../]
[]
[ICs]
[./IC_etaa0]
type = FunctionIC
variable = etaa0
function = ic_func_etaa0
[../]
[./IC_etab0]
type = FunctionIC
variable = etab0
function = ic_func_etab0
[../]
[./IC_etad0]
type = ConstantIC
variable = etad0
value = 0.1
[../]
[./IC_w]
type = FunctionIC
variable = w
function = ic_func_w
[../]
[]
[Functions]
[./ic_func_etaa0]
type = ParsedFunction
expression = '0.9*0.5*(1.0-tanh((x)/sqrt(2.0)))'
[../]
[./ic_func_etab0]
type = ParsedFunction
expression = '0.9*0.5*(1.0+tanh((x)/sqrt(2.0)))'
[../]
[./ic_func_w]
type = ParsedFunction
expression = 0
[../]
[]
[Kernels]
# Order parameter eta_alpha0
[./ACa0_bulk]
type = ACGrGrMulti
variable = etaa0
v = 'etab0 etad0'
gamma_names = 'gab gad'
[../]
[./ACa0_sw]
type = ACSwitching
variable = etaa0
Fj_names = 'omegaa omegab omegad'
hj_names = 'ha hb hd'
coupled_variables = 'etab0 etad0 w'
[../]
[./ACa0_int]
type = ACInterface
variable = etaa0
kappa_name = kappa
[../]
[./ea0_dot]
type = TimeDerivative
variable = etaa0
[../]
# Order parameter eta_beta0
[./ACb0_bulk]
type = ACGrGrMulti
variable = etab0
v = 'etaa0 etad0'
gamma_names = 'gab gbd'
[../]
[./ACb0_sw]
type = ACSwitching
variable = etab0
Fj_names = 'omegaa omegab omegad'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etad0 w'
[../]
[./ACb0_int]
type = ACInterface
variable = etab0
kappa_name = kappa
[../]
[./eb0_dot]
type = TimeDerivative
variable = etab0
[../]
# Order parameter eta_delta0
[./ACd0_bulk]
type = ACGrGrMulti
variable = etad0
v = 'etaa0 etab0'
gamma_names = 'gad gbd'
[../]
[./ACd0_sw]
type = ACSwitching
variable = etad0
Fj_names = 'omegaa omegab omegad'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etab0 w'
[../]
[./ACd0_int]
type = ACInterface
variable = etad0
kappa_name = kappa
[../]
[./ed0_dot]
type = TimeDerivative
variable = etad0
[../]
#Chemical potential
[./w_dot]
type = SusceptibilityTimeDerivative
variable = w
f_name = chi
coupled_variables = 'etaa0 etab0 etad0'
[../]
[./Diffusion]
type = MatDiffusion
variable = w
diffusivity = Dchi
args = ''
[../]
[./coupled_etaa0dot]
type = CoupledSwitchingTimeDerivative
variable = w
v = etaa0
Fj_names = 'rhoa rhob rhod'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etab0 etad0'
[../]
[./coupled_etab0dot]
type = CoupledSwitchingTimeDerivative
variable = w
v = etab0
Fj_names = 'rhoa rhob rhod'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etab0 etad0'
[../]
[./coupled_etad0dot]
type = CoupledSwitchingTimeDerivative
variable = w
v = etad0
Fj_names = 'rhoa rhob rhod'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etab0 etad0'
[../]
[]
[Materials]
[./ha_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = ha
all_etas = 'etaa0 etab0 etad0'
phase_etas = 'etaa0'
[../]
[./hb_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = hb
all_etas = 'etaa0 etab0 etad0'
phase_etas = 'etab0'
[../]
[./hd_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = hd
all_etas = 'etaa0 etab0 etad0'
phase_etas = 'etad0'
[../]
[./omegaa]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegaa
material_property_names = 'Vm ka caeq'
expression = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
derivative_order = 2
[../]
[./omegab]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegab
material_property_names = 'Vm kb cbeq'
expression = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
derivative_order = 2
[../]
[./omegad]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegad
material_property_names = 'Vm kd cdeq'
expression = '-0.5*w^2/Vm^2/kd-w/Vm*cdeq'
derivative_order = 2
[../]
[./rhoa]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhoa
material_property_names = 'Vm ka caeq'
expression = 'w/Vm^2/ka + caeq/Vm'
derivative_order = 2
[../]
[./rhob]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhob
material_property_names = 'Vm kb cbeq'
expression = 'w/Vm^2/kb + cbeq/Vm'
derivative_order = 2
[../]
[./rhod]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhod
material_property_names = 'Vm kd cdeq'
expression = 'w/Vm^2/kd + cdeq/Vm'
derivative_order = 2
[../]
[./c]
type = ParsedMaterial
material_property_names = 'Vm rhoa rhob rhod ha hb hd'
expression = 'Vm * (ha * rhoa + hb * rhob + hd * rhod)'
property_name = c
[../]
[./const]
type = GenericConstantMaterial
prop_names = 'kappa_c kappa L D Vm ka caeq kb cbeq kd cdeq gab gad gbd mu tgrad_corr_mult'
prop_values = '0 1 1.0 1.0 1.0 10.0 0.1 10.0 0.9 10.0 0.5 1.5 1.5 1.5 1.0 0.0'
[../]
[./Mobility]
type = DerivativeParsedMaterial
property_name = Dchi
material_property_names = 'D chi'
expression = 'D*chi'
derivative_order = 2
[../]
[./chi]
type = DerivativeParsedMaterial
property_name = chi
material_property_names = 'Vm ha(etaa0,etab0,etad0) ka hb(etaa0,etab0,etad0) kb hd(etaa0,etab0,etad0) kd'
expression = '(ha/ka + hb/kb + hd/kd) / Vm^2'
coupled_variables = 'etaa0 etab0 etad0'
derivative_order = 2
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[VectorPostprocessors]
[./etaa0]
type = LineValueSampler
variable = etaa0
start_point = '-15 0 0'
end_point = '15 0 0'
num_points = 61
sort_by = x
execute_on = 'initial timestep_end final'
[../]
[./etab0]
type = LineValueSampler
variable = etab0
start_point = '-15 0 0'
end_point = '15 0 0'
num_points = 61
sort_by = x
execute_on = 'initial timestep_end final'
[../]
[./etad0]
type = LineValueSampler
variable = etad0
start_point = '-15 0 0'
end_point = '15 0 0'
num_points = 61
sort_by = x
execute_on = 'initial timestep_end final'
[../]
[]
[Executioner]
type = Transient
nl_max_its = 15
scheme = bdf2
solve_type = PJFNK
petsc_options_iname = -pc_type
petsc_options_value = asm
l_max_its = 15
l_tol = 1.0e-3
nl_rel_tol = 1.0e-8
start_time = 0.0
num_steps = 20
nl_abs_tol = 1e-10
dt = 1.0
[]
[Outputs]
[./exodus]
type = Exodus
execute_on = 'initial timestep_end final'
time_step_interval = 1
[../]
[./csv]
type = CSV
execute_on = 'initial timestep_end final'
time_step_interval = 1
[../]
[]
(modules/phase_field/test/tests/phase_field_kernels/AllenCahnVariableL.i)
#
# Test the parsed function free enery Allen-Cahn Bulk kernel
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
xmax = 12
ymax = 12
elem_type = QUAD4
[]
[AuxVariables]
[./chi]
[./InitialCondition]
type = FunctionIC
function = 'x/24+0.5'
[../]
[../]
[]
[Variables]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[]
[Kernels]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk]
type = AllenCahn
variable = eta
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = 1
variable_L = true
coupled_variables = chi
[../]
[]
[Materials]
[./L]
type = DerivativeParsedMaterial
property_name = L
coupled_variables = 'eta chi'
expression = '0.1 * eta^2 + chi^2'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'eta'
expression = '2 * eta^2 * (1-eta)^2 - 0.2*eta'
derivative_order = 2
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
num_steps = 2
dt = 1
[]
[Outputs]
exodus = true
[]
(modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialPFM.i)
# this input file test the implementation of the grand-potential phase-field model based on M.Plapp PRE 84,031601(2011)
# in this simple example, the liquid and solid free energies are parabola with the same curvature and the material properties are constant
# Note that this example also test The SusceptibilityTimeDerivative kernels
[Mesh]
type = GeneratedMesh
dim = 2
nx = 16
ny = 16
xmax = 32
ymax = 32
[]
[GlobalParams]
radius = 20.0
int_width = 4.0
x1 = 0
y1 = 0
[]
[Variables]
[./w]
[../]
[./eta]
[../]
[]
[ICs]
[./w]
type = SmoothCircleIC
variable = w
# note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
outvalue = -0.2
invalue = 0.2
[../]
[./eta]
type = SmoothCircleIC
variable = eta
outvalue = 0.0
invalue = 1.0
[../]
[]
[Kernels]
[./w_dot]
type = SusceptibilityTimeDerivative
variable = w
f_name = chi
coupled_variables = '' # in this case chi (the susceptibility) is simply a constant
[../]
[./Diffusion]
type = MatDiffusion
variable = w
diffusivity = D
args = ''
[../]
[./coupled_etadot]
type = CoupledSusceptibilityTimeDerivative
variable = w
v = eta
f_name = ft
coupled_variables = 'eta'
[../]
[./AC_bulk]
type = AllenCahn
variable = eta
f_name = F
coupled_variables = 'w'
[../]
[./AC_int]
type = ACInterface
variable = eta
[../]
[./e_dot]
type = TimeDerivative
variable = eta
[../]
[]
[Materials]
[./constants]
type = GenericConstantMaterial
prop_names = 'kappa_op D L chi cseq cleq A'
prop_values = '4.0 1.0 1.0 1.0 0.0 1.0 1.0'
[../]
[./liquid_GrandPotential]
type = DerivativeParsedMaterial
expression = '-0.5 * w^2/A - cleq * w'
coupled_variables = 'w'
property_name = f1
material_property_names = 'cleq A'
[../]
[./solid_GrandPotential]
type = DerivativeParsedMaterial
expression = '-0.5 * w^2/A - cseq * w'
coupled_variables = 'w'
property_name = f2
material_property_names = 'cseq A'
[../]
[./switching_function]
type = SwitchingFunctionMaterial
eta = eta
h_order = HIGH
[../]
[./barrier_function]
type = BarrierFunctionMaterial
eta = eta
[../]
[./cs]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = cs
material_property_names = 'A cseq'
expression = 'w/A + cseq' # since w = A*(c-cseq)
derivative_order = 2
[../]
[./cl]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = cl
material_property_names = 'A cleq'
expression = 'w/A + cleq' # since w = A*(c-cleq)
derivative_order = 2
[../]
[./total_GrandPotential]
type = DerivativeTwoPhaseMaterial
coupled_variables = 'w'
eta = eta
fa_name = f1
fb_name = f2
derivative_order = 2
W = 1.0
[../]
[./coupled_eta_function]
type = DerivativeParsedMaterial
expression = '(cs - cl) * dh'
coupled_variables = 'eta w'
property_name = ft
material_property_names = 'cs cl dh:=D[h,eta]'
derivative_order = 1
outputs = exodus
[../]
[./concentration]
type = ParsedMaterial
property_name = c
material_property_names = 'dF:=D[F,w]'
expression = '-dF'
outputs = exodus
[../]
[]
[Postprocessors]
[./C]
type = ElementIntegralMaterialProperty
mat_prop = c
execute_on = 'initial timestep_end'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
l_max_its = 15
l_tol = 1e-3
nl_max_its = 15
nl_rel_tol = 1e-8
nl_abs_tol = 1e-8
num_steps = 5
dt = 10.0
[]
[Outputs]
exodus = true
csv = true
execute_on = 'TIMESTEP_END'
[]
(modules/phase_field/test/tests/phase_field_kernels/CoupledCoefAllenCahn.i)
#
# Test the CoefReaction kernel (which adds -L*v to the residual) for the case
# where v is a coupled variable
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
nz = 0
xmin = 0
xmax = 50
ymin = 0
ymax = 50
zmin = 0
zmax = 50
elem_type = QUAD4
[]
[Variables]
[./w]
[../]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 6.0
invalue = 1.0
outvalue = 0.0
int_width = 3.0
[../]
[../]
[]
[Kernels]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk]
type = CoupledAllenCahn
variable = w
v = eta
f_name = F
mob_name = 1
[../]
[./W]
type = MatReaction
variable = w
reaction_rate = -1
[../]
[./CoupledBulk]
type = MatReaction
variable = eta
v = w
reaction_rate = L
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = 1
mob_name = L
coupled_variables = w
[../]
[]
[Materials]
[./mobility]
type = DerivativeParsedMaterial
property_name = L
coupled_variables = 'eta w'
expression = '(1.5-eta)^2+(1.5-w)^2'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'eta'
expression = 'eta^2 * (1-eta)^2'
derivative_order = 2
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
l_max_its = 15
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-11
start_time = 0.0
num_steps = 2
dt = 0.5
[]
[Outputs]
hide = w
exodus = true
[]
(modules/phase_field/examples/rigidbodymotion/AC_CH_advection_constforce_rect.i)
#
# Tests the Rigid Body Motion of grains due to applied forces.
# Concenterated forces and torques have been applied and corresponding
# advection velocities are calculated.
# Grain motion kernels make the grains translate and rotate as a rigidbody,
# applicable to grain movement in porous media
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 50
ny = 25
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./vadvx]
order = CONSTANT
family = MONOMIAL
[../]
[./vadvy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = eta
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
# advection kernel corrsponding to CH equation
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./eta_dot]
type = TimeDerivative
variable = eta
[../]
[./vadv_eta]
# advection kernel corrsponding to AC equation
type = SingleGrainRigidBodyMotion
variable = eta
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./acint_eta]
type = ACInterface
variable = eta
mob_name = M
coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta]
type = AllenCahn
variable = eta
mob_name = M
f_name = F
coupled_variables = c
[../]
[]
[AuxKernels]
[./vadv_x]
type = GrainAdvectionAux
component = x
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
variable = vadvx
[../]
[./vadv_y]
type = GrainAdvectionAux
component = y
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
variable = vadvy
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '1.0 2.0 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'c eta'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+(c-eta)^2
derivative_order = 2
[../]
[]
[VectorPostprocessors]
[./forces]
# VectorPostprocessor for outputting grain forces and torques
type = GrainForcesPostprocessor
grain_force = grain_force
[../]
[./grain_volumes]
type = FeatureVolumeVectorPostprocessor
flood_counter = grain_center
execute_on = 'initial timestep_begin'
[../]
[]
[UserObjects]
[./grain_center]
type = GrainTracker
variable = eta
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ConstantGrainForceAndTorque
execute_on = 'linear nonlinear'
force = '0.2 0.0 0.0 ' # size should be 3 * no. of grains
torque = '0.0 0.0 5.0 ' # size should be 3 * no. of grains
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
nl_max_its = 30
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 lu 1'
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
dt = 0.1
end_time = 10
[]
[Outputs]
exodus = true
[]
[ICs]
[./rect_c]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = c
x1 = 10.0
type = BoundingBoxIC
[../]
[./rect_eta]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = eta
x1 = 10.0
type = BoundingBoxIC
[../]
[]
(modules/phase_field/test/tests/mobility_derivative/AC_mobility_derivative_test.i)
[Mesh]
type = GeneratedMesh
dim = 1
nx = 40
xmax = 25
[]
[Variables]
[./op]
[../]
[]
[ICs]
[./op_IC]
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 6.0
invalue = 1
outvalue = 0
int_width = 3.0
variable = op
[../]
[]
[Kernels]
[./op_dot]
type = TimeDerivative
variable = op
[../]
[./op_bulk]
type = AllenCahn
variable = op
f_name = F
mob_name = L
[../]
[./op_interface]
type = ACInterface
variable = op
kappa_name = 1
mob_name = L
[../]
[]
[Materials]
[./consts]
type = DerivativeParsedMaterial
property_name = L
expression = 'if(op<0, 0.01, if(op>1, 0.01, 1*op^2*(1-op)^2+0.01))'
coupled_variables = 'op'
outputs = exodus
output_properties = 'L dL/dop dL/dv'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'op'
expression = '2*op^2*(1-op)^2 - 0.2*op'
derivative_order = 2
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu'
l_max_its = 15
l_tol = 1.0e-4
nl_max_its = 15
nl_rel_tol = 1.0e-9
start_time = 0.0
num_steps = 20
dt = 2.0
[]
[Outputs]
exodus = true
print_linear_residuals = false
[]
(modules/phase_field/test/tests/phase_field_kernels/MatGradSquareCoupled.i)
#
# Test the MatGradSquareCoupled kernel
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
nz = 0
xmin = 0
xmax = 50
ymin = 0
ymax = 50
zmin = 0
zmax = 50
elem_type = QUAD4
[]
[Variables]
[./w]
[../]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 6.0
invalue = 1.0
outvalue = 0.0
int_width = 3.0
[../]
[../]
[]
[Kernels]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk]
type = CoupledAllenCahn
variable = w
v = eta
f_name = F
mob_name = 1
[../]
[./W]
type = MatReaction
variable = w
reaction_rate = -1
[../]
[./CoupledBulk]
type = MatReaction
variable = eta
v = w
reaction_rate = L
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = 1
mob_name = L
coupled_variables = w
[../]
# MatGradSquareCoupled kernel
[./nabla_eta]
type = MatGradSquareCoupled
variable = w
elec_potential = eta
prefactor = 0.5
[../]
[]
[Materials]
[./mobility]
type = DerivativeParsedMaterial
property_name = L
coupled_variables = 'eta w'
expression = '(1.5-eta)^2+(1.5-w)^2'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'eta'
expression = 'eta^2 * (1-eta)^2'
derivative_order = 2
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
l_max_its = 15
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-11
start_time = 0.0
num_steps = 2
dt = 0.5
[]
[Outputs]
hide = w
exodus = true
console = true
[]
(modules/phase_field/test/tests/rigidbodymotion/update_orientation_verify.i)
# test file for applyting advection term and observing rigid body motion of grains
[Mesh]
type = GeneratedMesh
dim = 3
nx = 14
ny = 7
nz = 7
xmax = 40
ymax = 25
zmax = 25
elem_type = HEX8
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = eta
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./eta_dot]
type = TimeDerivative
variable = eta
[../]
[./vadv_eta]
type = SingleGrainRigidBodyMotion
variable = eta
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./acint_eta]
type = ACInterface
variable = eta
mob_name = M
coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta]
type = AllenCahn
variable = eta
mob_name = M
f_name = F
coupled_variables = c
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '5.0 2.0 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'c eta'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+(c-eta)^2
derivative_order = 2
[../]
[]
[AuxVariables]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./var_indices]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[./vadv_x]
order = CONSTANT
family = MONOMIAL
[../]
[./vadv_y]
order = CONSTANT
family = MONOMIAL
[../]
[./angle_initial]
order = CONSTANT
family = MONOMIAL
[../]
[./euler_angle]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./unique_grains]
type = FeatureFloodCountAux
variable = unique_grains
flood_counter = grain_center
field_display = UNIQUE_REGION
execute_on = timestep_begin
[../]
[./var_indices]
type = FeatureFloodCountAux
variable = var_indices
flood_counter = grain_center
field_display = VARIABLE_COLORING
execute_on = timestep_begin
[../]
[./centroids]
type = FeatureFloodCountAux
variable = centroids
execute_on = timestep_begin
field_display = CENTROID
flood_counter = grain_center
[../]
[./vadv_x]
type = GrainAdvectionAux
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
execute_on = timestep_begin
component = x
variable = vadv_x
[../]
[./vadv_y]
type = GrainAdvectionAux
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
execute_on = timestep_begin
component = y
variable = vadv_y
[../]
[./angle_initial]
type = OutputEulerAngles
variable = angle_initial
euler_angle_provider = euler_angle_initial
grain_tracker = grain_center
output_euler_angle = phi2
execute_on = timestep_begin
[../]
[./angle]
type = OutputEulerAngles
variable = euler_angle
euler_angle_provider = euler_angle
grain_tracker = grain_center
output_euler_angle = phi2
execute_on = timestep_begin
[../]
[]
[VectorPostprocessors]
[./forces]
type = GrainForcesPostprocessor
grain_force = grain_force
[../]
[./grain_volumes]
type = FeatureVolumeVectorPostprocessor
flood_counter = grain_center
execute_on = 'initial timestep_begin'
[../]
[./angle_check]
type = EulerAngleUpdaterCheck
grain_tracker_object = grain_center
euler_angle_updater = euler_angle
grain_torques_object = grain_force
grain_volumes = grain_volumes
execute_on = timestep_begin
[../]
[]
[UserObjects]
[./grain_center]
type = GrainTracker
variable = eta
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ConstantGrainForceAndTorque
execute_on = 'initial timestep_begin linear nonlinear'
force = '0.5 0.0 0.0 '
torque = '-200.0 -120.0 1000.0'
[../]
[./euler_angle_initial]
type = RandomEulerAngleProvider
grain_tracker_object = grain_center
seed = 12356
execute_on = 'initial timestep_begin'
[../]
[./euler_angle]
type = EulerAngleUpdater
grain_tracker_object = grain_center
euler_angle_provider = euler_angle_initial
grain_torques_object = grain_force
grain_volumes = grain_volumes
execute_on = timestep_begin
[../]
[]
[Preconditioning]
[./SMP]
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 lu 1'
nl_max_its = 30
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
dt = 0.2
num_steps = 2
[]
[Outputs]
csv = true
exodus = true
[]
[ICs]
[./rect_c]
y2 = 20.0
y1 = 5.0
z1 = 5.0
z2 = 20.0
inside = 1.0
x2 = 30.0
variable = c
x1 = 10.0
type = BoundingBoxIC
[../]
[./rect_eta]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = eta
x1 = 10.0
z1 = 5.0
z2 = 20.0
type = BoundingBoxIC
[../]
[]
(modules/combined/examples/phase_field-mechanics/LandauPhaseTrans.i)
#
# Martensitic transformation
# Chemical driving force described by Landau Polynomial
# Coupled with elasticity (Mechanics)
#
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Mesh]
type = GeneratedMesh
dim = 2
nx = 100
ny = 100
xmin = 0
xmax = 100
ymin = 0
ymax = 100
elem_type = QUAD4
[]
[Variables]
[./eta1]
[./InitialCondition]
type = RandomIC
min = 0
max = 0.1
[../]
[../]
[./eta2]
[./InitialCondition]
type = RandomIC
min = 0
max = 0.1
[../]
[../]
[]
[Physics/SolidMechanics/QuasiStatic]
[./all]
add_variables = true
generate_output = 'stress_xx stress_yy'
eigenstrain_names = 'eigenstrain1 eigenstrain2'
[../]
[]
[Kernels]
[./eta_bulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2'
f_name = F
[../]
[./eta_bulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1'
f_name = F
[../]
[./eta_interface1]
type = ACInterface
variable = eta1
kappa_name = kappa_eta
[../]
[./eta_interface2]
type = ACInterface
variable = eta2
kappa_name = kappa_eta
[../]
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1 1'
[../]
[./chemical_free_energy]
type = DerivativeParsedMaterial
property_name = Fc
coupled_variables = 'eta1 eta2'
constant_names = 'A2 A3 A4'
constant_expressions = '0.2 -12.6 12.4'
expression = 'A2/2*(eta1^2+eta2^2) + A3/3*(eta1^3+eta2^3) + A4/4*(eta1^2+eta2^2)^2'
enable_jit = true
derivative_order = 2
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '700 300 300 700 300 700 300 300 300'
fill_method = symmetric9
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
[./var_dependence1]
type = DerivativeParsedMaterial
property_name = var_dep1
coupled_variables = 'eta1'
expression = eta1
enable_jit = true
derivative_order = 2
[../]
[./var_dependence2]
type = DerivativeParsedMaterial
property_name = var_dep2
coupled_variables = 'eta2'
expression = eta2
enable_jit = true
derivative_order = 2
[../]
[./eigenstrain1]
type = ComputeVariableEigenstrain
eigen_base = '0.1 -0.1 0 0 0 0'
prefactor = var_dep1
args = 'eta1'
eigenstrain_name = eigenstrain1
[../]
[./eigenstrain2]
type = ComputeVariableEigenstrain
eigen_base = '-0.1 0.1 0 0 0 0'
prefactor = var_dep2
args = 'eta2'
eigenstrain_name = eigenstrain2
[../]
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'eta1 eta2'
derivative_order = 2
[../]
[./totol_free_energy]
type = DerivativeSumMaterial
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'eta1 eta2'
derivative_order = 2
[../]
[]
[BCs]
[./all_y]
type = DirichletBC
variable = disp_y
boundary = 'top bottom left right'
value = 0
[../]
[./all_x]
type = DirichletBC
variable = disp_x
boundary = 'top bottom left right'
value = 0
[../]
[]
[Preconditioning]
# active = ' '
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
# this gives best performance on 4 cores
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type '
petsc_options_value = 'asm lu'
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 = 10
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 9
iteration_window = 2
growth_factor = 1.1
cutback_factor = 0.75
dt = 0.3
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/lagrange_multiplier.i)
#
# This test ensures that the equilibrium solution using two order parameters with a
# Lagrange multiplier constraint is identical to the dedicated two phase formulation
# in two_phase.i
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 20
xmax = 5
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = x/5
[]
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# phase concentration 1
[c1]
order = FIRST
family = LAGRANGE
initial_condition = 0.2
[]
# phase concentration 2
[c2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# Lagrange multiplier
[lambda]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
[]
[Materials]
# simple toy free energies
[f1] # = fd
type = DerivativeParsedMaterial
property_name = F1
coupled_variables = 'c1'
expression = '(0.9-c1)^2'
[]
[f2] # = fm
type = DerivativeParsedMaterial
property_name = F2
coupled_variables = 'c2'
expression = '(0.1-c2)^2'
[]
# Switching functions for each phase
[h1_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta1
function_name = h1
[]
[h2_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta2
function_name = h2
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1'
expression = D*h1
property_name = Dh1
[]
[Dh2]
type = DerivativeParsedMaterial
material_property_names = 'D h2'
expression = D*h2
property_name = Dh2
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '0.7 0.7 0.2'
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = c
[]
[diff_c1]
type = MatDiffusion
variable = c
diffusivity = Dh1
v = c1
[]
[diff_c2]
type = MatDiffusion
variable = c
diffusivity = Dh2
v = c2
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gi_name = g1
eta_i = eta1
wi = 0.2
coupled_variables = 'c1 c2 eta2'
[]
[ACBulkC1]
type = KKSMultiACBulkC
variable = eta1
Fj_names = 'F1 F2'
hj_names = 'h1 h2'
cj_names = 'c1 c2'
eta_i = eta1
coupled_variables = 'eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
[multipler1]
type = MatReaction
variable = eta1
v = lambda
reaction_rate = L
[]
# Kernels for the Lagrange multiplier equation
[mult_lambda]
type = MatReaction
variable = lambda
reaction_rate = 2
[]
[mult_ACBulkF_1]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gi_name = g1
eta_i = eta1
wi = 0.2
mob_name = 1
coupled_variables = 'c1 c2 eta2 '
[]
[mult_ACBulkC_1]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2'
hj_names = 'h1 h2'
cj_names = 'c1 c2'
eta_i = eta1
coupled_variables = 'eta2 '
mob_name = 1
[]
[mult_CoupledACint_1]
type = SimpleCoupledACInterface
variable = lambda
v = eta1
kappa_name = kappa
mob_name = 1
[]
[mult_ACBulkF_2]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gi_name = g2
eta_i = eta2
wi = 0.2
mob_name = 1
coupled_variables = 'c1 c2 eta1 '
[]
[mult_ACBulkC_2]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2'
hj_names = 'h1 h2'
cj_names = 'c1 c2'
eta_i = eta2
coupled_variables = 'eta1 '
mob_name = 1
[]
[mult_CoupledACint_2]
type = SimpleCoupledACInterface
variable = lambda
v = eta2
kappa_name = kappa
mob_name = 1
[]
# Kernels for constraint equation eta1 + eta2 = 1
# eta2 is the nonlinear variable for the constraint equation
[eta2reaction]
type = MatReaction
variable = eta2
reaction_rate = 1
[]
[eta1reaction]
type = MatReaction
variable = eta2
v = eta1
reaction_rate = 1
[]
[one]
type = BodyForce
variable = eta2
value = -1.0
[]
# Phase concentration constraints
[chempot12]
type = KKSPhaseChemicalPotential
variable = c1
cb = c2
fa_name = F1
fb_name = F2
[]
[phaseconcentration]
type = KKSMultiPhaseConcentration
variable = c2
cj = 'c1 c2'
hj_names = 'h1 h2'
etas = 'eta1 eta2'
c = c
[]
[]
[AuxKernels]
[Fglobal_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gj_names = 'g1 g2 '
variable = Fglobal
w = 0.2
interfacial_vars = 'eta1 eta2 '
kappa_names = 'kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = NEWTON
petsc_options_iname = '-pc_type -pc_factor_shift_type'
petsc_options_value = 'lu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 35
dt = 10
[]
[VectorPostprocessors]
[c]
type = LineValueSampler
variable = c
start_point = '0 0 0'
end_point = '5 0 0'
num_points = 21
sort_by = x
[]
[]
[Outputs]
csv = true
execute_on = FINAL
[]
(modules/phase_field/test/tests/rigidbodymotion/grain_motion_fauxGT.i)
# test file for showing reaction forces between particles
[GlobalParams]
var_name_base = eta
op_num = 2
[]
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 5
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
uniform_refine = 1
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta0]
[../]
[./eta1]
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
coupled_variables = 'eta0 eta1'
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = 'eta0 eta1'
grain_force = grain_force
grain_tracker_object = grain_center
grain_volumes = grain_volumes
[../]
[./eta0_dot]
type = TimeDerivative
variable = eta0
[../]
[./vadv_eta]
type = SingleGrainRigidBodyMotion
variable = eta0
c = c
v = 'eta0 eta1'
grain_force = grain_force
grain_tracker_object = grain_center
grain_volumes = grain_volumes
op_index = 0
[../]
[./acint_eta0]
type = ACInterface
variable = eta0
mob_name = M
#coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta0]
type = AllenCahn
variable = eta0
mob_name = M
f_name = F
coupled_variables = 'c eta1'
[../]
[./eta1_dot]
type = TimeDerivative
variable = eta1
[../]
[./vadv_eta1]
type = SingleGrainRigidBodyMotion
variable = eta1
c = c
v = 'eta0 eta1'
op_index = 1
grain_force = grain_force
grain_tracker_object = grain_center
grain_volumes = grain_volumes
[../]
[./acint_eta1]
type = ACInterface
variable = eta1
mob_name = M
#coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta1]
type = AllenCahn
variable = eta1
mob_name = M
f_name = F
coupled_variables = 'c eta0'
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '1.0 0.5 0.5'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'c eta0 eta1'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+eta0*(1-eta0)*c+eta1*(1-eta1)*c
derivative_order = 2
[../]
[./force_density]
type = ForceDensityMaterial
c = c
etas ='eta0 eta1'
[../]
[]
[AuxVariables]
[./bnds]
[../]
[./df00]
order = CONSTANT
family = MONOMIAL
[../]
[./df01]
order = CONSTANT
family = MONOMIAL
[../]
[./df10]
order = CONSTANT
family = MONOMIAL
[../]
[./df11]
order = CONSTANT
family = MONOMIAL
[../]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./var_indices]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./bnds]
type = BndsCalcAux
variable = bnds
var_name_base = eta
op_num = 2
v = 'eta0 eta1'
[../]
[./df01]
type = MaterialStdVectorRealGradientAux
variable = df01
index = 0
component = 1
property = force_density
[../]
[./df11]
type = MaterialStdVectorRealGradientAux
variable = df11
index = 1
component = 1
property = force_density
[../]
[./df00]
type = MaterialStdVectorRealGradientAux
variable = df00
index = 0
component = 0
property = force_density
[../]
[./df10]
type = MaterialStdVectorRealGradientAux
variable = df10
index = 1
component = 0
property = force_density
[../]
[./unique_grains]
type = FeatureFloodCountAux
variable = unique_grains
flood_counter = grain_center
field_display = UNIQUE_REGION
execute_on = 'initial timestep_end'
[../]
[./var_indices]
type = FeatureFloodCountAux
variable = var_indices
flood_counter = grain_center
field_display = VARIABLE_COLORING
execute_on = 'initial timestep_end'
[../]
[./centroids]
type = FeatureFloodCountAux
variable = centroids
execute_on = 'initial timestep_end'
field_display = CENTROID
flood_counter = grain_center
[../]
[]
[ICs]
[./ic_eta0]
int_width = 1.0
x1 = 20.0
y1 = 0.0
radius = 14.0
outvalue = 0.0
variable = eta0
invalue = 1.0
type = SmoothCircleIC
[../]
[./IC_eta1]
int_width = 1.0
x1 = 30.0
y1 = 25.0
radius = 14.0
outvalue = 0.0
variable = eta1
invalue = 1.0
type = SmoothCircleIC
[../]
[./ic_c]
type = SpecifiedSmoothCircleIC
invalue = 1.0
outvalue = 0.1
int_width = 1.0
x_positions = '20.0 30.0 '
z_positions = '0.0 0.0 '
y_positions = '0.0 25.0 '
radii = '14.0 14.0'
3D_spheres = false
variable = c
block = 0
[../]
[]
[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 = FauxGrainTracker
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
variable = 'eta0 eta1'
[../]
[./grain_force]
type = ComputeGrainForceAndTorque
execute_on = 'linear nonlinear'
grain_data = grain_center
force_density = force_density
c = c
etas = 'eta0 eta1'
[../]
[]
[Preconditioning]
[./SMP]
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 lu 1'
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 1
dt = 0.1
[]
[Outputs]
exodus = true
csv = true
[]
(modules/combined/examples/publications/rapid_dev/fig6.i)
#
# Fig. 6 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Three phase interface simulation demonstrating the interfacial stability
# w.r.t. formation of a tspurious third phase
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 120
ny = 120
nz = 0
xmin = 0
xmax = 40
ymin = 0
ymax = 40
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[Variables]
# concentration
[./c]
[../]
# order parameter 1
[./eta1]
[../]
# order parameter 2
[./eta2]
[../]
# order parameter 3
[./eta3]
[../]
# phase concentration 1
[./c1]
initial_condition = 0.4
[../]
# phase concentration 2
[./c2]
initial_condition = 0.5
[../]
# phase concentration 3
[./c3]
initial_condition = 0.8
[../]
# Lagrange multiplier
[./lambda]
initial_condition = 0.0
[../]
[]
[AuxVariables]
[./T]
[./InitialCondition]
type = FunctionIC
function = 'x-10'
[../]
[../]
[]
[Functions]
[./ic_func_eta1]
type = ParsedFunction
expression = '0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0)))'
[../]
[./ic_func_eta2]
type = ParsedFunction
expression = '0.5*(1.0-tanh((x-10)/sqrt(2.0)))'
[../]
[./ic_func_eta3]
type = ParsedFunction
expression = '1 - 0.5*(1.0-tanh((x-10)/sqrt(2.0)))
- 0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0)))'
[../]
[./ic_func_c]
type = ParsedFunction
expression = '0.5 * 0.5*(1.0-tanh((x-10)/sqrt(2.0)))
+ 0.4 * 0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0)))
+ 0.8 * (1 - 0.5*(1.0-tanh((x-10)/sqrt(2.0)))
- 0.5*(1.0+tanh((x-10)/sqrt(2.0))) * 0.5*(1.0+tanh((y-10)/sqrt(2.0))))'
[../]
[]
[ICs]
[./eta1]
variable = eta1
type = FunctionIC
function = ic_func_eta1
[../]
[./eta2]
variable = eta2
type = FunctionIC
function = ic_func_eta2
[../]
[./eta3]
variable = eta3
type = FunctionIC
function = ic_func_eta3
[../]
[./c]
variable = c
type = FunctionIC
function = ic_func_c
[../]
[]
[Materials]
# simple toy free energies
[./f1]
type = DerivativeParsedMaterial
property_name = F1
coupled_variables = 'c1'
expression = '20*(c1-0.4)^2'
[../]
[./f2]
type = DerivativeParsedMaterial
property_name = F2
coupled_variables = 'c2 T'
expression = '20*(c2-0.5)^2 + 0.01*T'
[../]
[./f3]
type = DerivativeParsedMaterial
property_name = F3
coupled_variables = 'c3'
expression = '20*(c3-0.8)^2'
[../]
# Switching functions for each phase
# h1(eta1, eta2, eta3)
[./h1]
type = SwitchingFunction3PhaseMaterial
eta_i = eta1
eta_j = eta2
eta_k = eta3
f_name = h1
[../]
# h2(eta1, eta2, eta3)
[./h2]
type = SwitchingFunction3PhaseMaterial
eta_i = eta2
eta_j = eta3
eta_k = eta1
f_name = h2
[../]
# h3(eta1, eta2, eta3)
[./h3]
type = SwitchingFunction3PhaseMaterial
eta_i = eta3
eta_j = eta1
eta_k = eta2
f_name = h3
[../]
# Coefficients for diffusion equation
[./Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1'
expression = D*h1
property_name = Dh1
[../]
[./Dh2]
type = DerivativeParsedMaterial
material_property_names = 'D h2'
expression = D*h2
property_name = Dh2
[../]
[./Dh3]
type = DerivativeParsedMaterial
material_property_names = 'D h3'
expression = D*h3
property_name = Dh3
[../]
# Barrier functions for each phase
[./g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[../]
[./g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[../]
[./g3]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta3
function_name = g3
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'L kappa D'
prop_values = '1.0 1.0 1'
[../]
[]
[Kernels]
#Kernels for diffusion equation
[./diff_time]
type = TimeDerivative
variable = c
[../]
[./diff_c1]
type = MatDiffusion
variable = c
diffusivity = Dh1
v = c1
[../]
[./diff_c2]
type = MatDiffusion
variable = c
diffusivity = Dh2
v = c2
[../]
[./diff_c3]
type = MatDiffusion
variable = c
diffusivity = Dh3
v = c3
[../]
# Kernels for Allen-Cahn equation for eta1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g1
eta_i = eta1
wi = 1.0
coupled_variables = 'c1 c2 c3 eta2 eta3'
[../]
[./ACBulkC1]
type = KKSMultiACBulkC
variable = eta1
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta1
coupled_variables = 'eta2 eta3'
[../]
[./ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[../]
[./multipler1]
type = MatReaction
variable = eta1
v = lambda
reaction_rate = L
[../]
# Kernels for Allen-Cahn equation for eta2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g2
eta_i = eta2
wi = 1.0
coupled_variables = 'c1 c2 c3 eta1 eta3'
[../]
[./ACBulkC2]
type = KKSMultiACBulkC
variable = eta2
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta2
coupled_variables = 'eta1 eta3'
[../]
[./ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[../]
[./multipler2]
type = MatReaction
variable = eta2
v = lambda
reaction_rate = L
[../]
# Kernels for the Lagrange multiplier equation
[./mult_lambda]
type = MatReaction
variable = lambda
reaction_rate = 3
[../]
[./mult_ACBulkF_1]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g1
eta_i = eta1
wi = 1.0
mob_name = 1
coupled_variables = 'c1 c2 c3 eta2 eta3'
[../]
[./mult_ACBulkC_1]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta1
coupled_variables = 'eta2 eta3'
mob_name = 1
[../]
[./mult_CoupledACint_1]
type = SimpleCoupledACInterface
variable = lambda
v = eta1
kappa_name = kappa
mob_name = 1
[../]
[./mult_ACBulkF_2]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g2
eta_i = eta2
wi = 1.0
mob_name = 1
coupled_variables = 'c1 c2 c3 eta1 eta3'
[../]
[./mult_ACBulkC_2]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta2
coupled_variables = 'eta1 eta3'
mob_name = 1
[../]
[./mult_CoupledACint_2]
type = SimpleCoupledACInterface
variable = lambda
v = eta2
kappa_name = kappa
mob_name = 1
[../]
[./mult_ACBulkF_3]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g3
eta_i = eta3
wi = 1.0
mob_name = 1
coupled_variables = 'c1 c2 c3 eta1 eta2'
[../]
[./mult_ACBulkC_3]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta3
coupled_variables = 'eta1 eta2'
mob_name = 1
[../]
[./mult_CoupledACint_3]
type = SimpleCoupledACInterface
variable = lambda
v = eta3
kappa_name = kappa
mob_name = 1
[../]
# Kernels for constraint equation eta1 + eta2 + eta3 = 1
# eta3 is the nonlinear variable for the constraint equation
[./eta3reaction]
type = MatReaction
variable = eta3
reaction_rate = 1
[../]
[./eta1reaction]
type = MatReaction
variable = eta3
v = eta1
reaction_rate = 1
[../]
[./eta2reaction]
type = MatReaction
variable = eta3
v = eta2
reaction_rate = 1
[../]
[./one]
type = BodyForce
variable = eta3
value = -1.0
[../]
# Phase concentration constraints
[./chempot12]
type = KKSPhaseChemicalPotential
variable = c1
cb = c2
fa_name = F1
fb_name = F2
[../]
[./chempot23]
type = KKSPhaseChemicalPotential
variable = c2
cb = c3
fa_name = F2
fb_name = F3
[../]
[./phaseconcentration]
type = KKSMultiPhaseConcentration
variable = c3
cj = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
c = c
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 1000
[./TimeStepper]
type = IterationAdaptiveDT
dt = 0.2
optimal_iterations = 10
iteration_window = 2
[../]
[]
[Preconditioning]
active = 'full'
[./full]
type = SMP
full = true
[../]
[./mydebug]
type = FDP
full = true
[../]
[]
[Outputs]
exodus = true
checkpoint = true
print_linear_residuals = false
[./csv]
type = CSV
execute_on = 'final'
[../]
[]
#[VectorPostprocessors]
# [./c]
# type = LineValueSampler
# start_point = '-25 0 0'
# end_point = '25 0 0'
# variable = c
# num_points = 151
# sort_by = id
# execute_on = timestep_end
# [../]
# [./eta1]
# type = LineValueSampler
# start_point = '-25 0 0'
# end_point = '25 0 0'
# variable = eta1
# num_points = 151
# sort_by = id
# execute_on = timestep_end
# [../]
# [./eta2]
# type = LineValueSampler
# start_point = '-25 0 0'
# end_point = '25 0 0'
# variable = eta2
# num_points = 151
# sort_by = id
# execute_on = timestep_end
# [../]
# [./eta3]
# type = LineValueSampler
# start_point = '-25 0 0'
# end_point = '25 0 0'
# variable = eta3
# num_points = 151
# sort_by = id
# execute_on = timestep_end
# [../]
#[]
(modules/combined/examples/publications/rapid_dev/fig7b.i)
#
# Fig. 7 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Dashed black curve (2)
# Eigenstrain is globally applied. Single global elastic free energies.
# Supply the RADIUS parameter (10-35) on the command line to generate data
# for all curves in the plot.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 32
xmin = 0
xmax = 100
second_order = true
coord_type = RSPHERICAL
[]
[GlobalParams]
displacements = 'disp_r'
[]
[Functions]
[./diff]
type = ParsedFunction
expression = '${RADIUS}-pos_c'
symbol_names = pos_c
symbol_values = pos_c
[../]
[]
# 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'
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
[./w]
[../]
# Phase order parameter
[./eta]
[./InitialCondition]
type = SmoothCircleIC
invalue = 1
outvalue = 0
x1 = 0
y1 = 0
radius = ${RADIUS}
int_width = 3
[../]
[../]
[./Fe_fit]
order = SECOND
[../]
[]
[Physics/SolidMechanics/QuasiStatic/all]
add_variables = true
eigenstrain_names = eigenstrain
[]
[Kernels]
# Split Cahn-Hilliard kernels
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
coupled_variables = 'eta'
kappa_name = kappa_c
w = w
[../]
[./wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk1]
type = AllenCahn
variable = eta
coupled_variables = 'c'
mob_name = L
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
mob_name = L
kappa_name = kappa_eta
[../]
[./Fe]
type = MaterialPropertyValue
prop_name = Fe
variable = Fe_fit
[../]
[./autoadjust]
type = MaskedBodyForce
variable = w
function = diff
mask = mask
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M L kappa_c kappa_eta'
prop_values = '1.0 1.0 0.5 1'
[../]
# forcing function mask
[./mask]
type = ParsedMaterial
property_name = mask
expression = grad/dt
material_property_names = 'grad dt'
[../]
[./grad]
type = VariableGradientMaterial
variable = c
prop = grad
[../]
[./time]
type = TimeStepMaterial
[../]
# global mechanical properties
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '1 1'
fill_method = symmetric_isotropic
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# eigenstrain as a function of phase
[./eigenstrain]
type = ComputeVariableEigenstrain
eigen_base = '0.05 0.05 0.05 0 0 0'
prefactor = h
args = eta
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching]
type = SwitchingFunctionMaterial
function_name = h
eta = eta
h_order = SIMPLE
[../]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = 'c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(1-c)^2'
coupled_variables = 'c'
derivative_order = 2
[../]
# global chemical free energy
[./chemical_free_energy]
type = DerivativeTwoPhaseMaterial
f_name = Fc
fa_name = Fc1
fb_name = Fc2
eta = eta
coupled_variables = 'c'
W = 4
[../]
# global elastic free energy
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'eta'
output_properties = Fe
outputs = 'all'
derivative_order = 2
[../]
# free energy
[./free_energy]
type = DerivativeSumMaterial
property_name = F
sum_materials = 'Fc Fe'
coupled_variables = 'c eta'
derivative_order = 2
[../]
[]
[BCs]
[./left_r]
type = DirichletBC
variable = disp_r
boundary = 'left'
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
variable = local_energy
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_c]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = c
target = 0.582
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./pos_eta]
type = FindValueOnLine
start_point = '0 0 0'
end_point = '100 0 0'
v = eta
target = 0.5
tol = 1e-8
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[./c_min]
type = ElementExtremeValue
value_type = min
variable = c
execute_on = 'INITIAL TIMESTEP_END'
outputs = 'table console'
[../]
[]
[VectorPostprocessors]
[./line]
type = LineValueSampler
variable = 'Fe_fit c w'
start_point = '0 0 0'
end_point = '100 0 0'
num_points = 5000
sort_by = x
outputs = vpp
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 30
nl_max_its = 15
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 2.0e-9
start_time = 0.0
end_time = 100000.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
iteration_window = 1
dt = 1
[../]
[./Adaptivity]
initial_adaptivity = 5
interval = 10
max_h_level = 5
refine_fraction = 0.9
coarsen_fraction = 0.1
[../]
[]
[Outputs]
print_linear_residuals = false
perf_graph = true
execute_on = 'INITIAL TIMESTEP_END'
[./table]
type = CSV
delimiter = ' '
file_base = radius_${RADIUS}/eigenstrain_pp
[../]
[./vpp]
type = CSV
delimiter = ' '
sync_times = '10 50 100 500 1000 5000 10000 50000 100000'
sync_only = true
time_data = true
file_base = radius_${RADIUS}/eigenstrain_vpp
[../]
[]
(modules/phase_field/test/tests/rigidbodymotion/grain_forcedensity.i)
# test file for showing reaction forces between particles
[GlobalParams]
var_name_base = eta
op_num = 2
[]
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 5
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
uniform_refine = 1
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta0]
[../]
[./eta1]
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
coupled_variables = 'eta0 eta1'
w = w
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = 'eta0 eta1'
grain_force = grain_force
grain_tracker_object = grain_center
grain_volumes = grain_volumes
[../]
[./eta0_dot]
type = TimeDerivative
variable = eta0
[../]
[./vadv_eta]
type = SingleGrainRigidBodyMotion
variable = eta0
c = c
v = 'eta0 eta1'
grain_force = grain_force
grain_tracker_object = grain_center
grain_volumes = grain_volumes
op_index = 0
[../]
[./acint_eta0]
type = ACInterface
variable = eta0
mob_name = M
#coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta0]
type = AllenCahn
variable = eta0
mob_name = M
f_name = F
coupled_variables = 'c eta1'
[../]
[./eta1_dot]
type = TimeDerivative
variable = eta1
[../]
[./vadv_eta1]
type = SingleGrainRigidBodyMotion
variable = eta1
c = c
v = 'eta0 eta1'
op_index = 1
grain_force = grain_force
grain_tracker_object = grain_center
grain_volumes = grain_volumes
[../]
[./acint_eta1]
type = ACInterface
variable = eta1
mob_name = M
#coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta1]
type = AllenCahn
variable = eta1
mob_name = M
f_name = F
coupled_variables = 'c eta0'
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '1.0 0.5 0.5'
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'c eta0 eta1'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+eta0*(1-eta0)*c+eta1*(1-eta1)*c
derivative_order = 2
[../]
[./force_density]
type = ForceDensityMaterial
c = c
etas ='eta0 eta1'
[../]
[]
[AuxVariables]
[./bnds]
[../]
[./df00]
order = CONSTANT
family = MONOMIAL
[../]
[./df01]
order = CONSTANT
family = MONOMIAL
[../]
[./df10]
order = CONSTANT
family = MONOMIAL
[../]
[./df11]
order = CONSTANT
family = MONOMIAL
[../]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./var_indices]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./bnds]
type = BndsCalcAux
variable = bnds
var_name_base = eta
op_num = 2
v = 'eta0 eta1'
[../]
[./df01]
type = MaterialStdVectorRealGradientAux
variable = df01
index = 0
component = 1
property = force_density
[../]
[./df11]
type = MaterialStdVectorRealGradientAux
variable = df11
index = 1
component = 1
property = force_density
[../]
[./df00]
type = MaterialStdVectorRealGradientAux
variable = df00
index = 0
component = 0
property = force_density
[../]
[./df10]
type = MaterialStdVectorRealGradientAux
variable = df10
index = 1
component = 0
property = force_density
[../]
[./unique_grains]
type = FeatureFloodCountAux
variable = unique_grains
flood_counter = grain_center
field_display = UNIQUE_REGION
execute_on = timestep_begin
[../]
[./var_indices]
type = FeatureFloodCountAux
variable = var_indices
flood_counter = grain_center
field_display = VARIABLE_COLORING
execute_on = timestep_begin
[../]
[./centroids]
type = FeatureFloodCountAux
variable = centroids
execute_on = timestep_begin
field_display = CENTROID
flood_counter = grain_center
[../]
[]
[ICs]
[./ic_eta0]
int_width = 1.0
x1 = 20.0
y1 = 0.0
radius = 14.0
outvalue = 0.0
variable = eta0
invalue = 1.0
type = SmoothCircleIC
[../]
[./IC_eta1]
int_width = 1.0
x1 = 30.0
y1 = 25.0
radius = 14.0
outvalue = 0.0
variable = eta1
invalue = 1.0
type = SmoothCircleIC
[../]
[./ic_c]
type = SpecifiedSmoothCircleIC
invalue = 1.0
outvalue = 0.1
int_width = 1.0
x_positions = '20.0 30.0 '
z_positions = '0.0 0.0 '
y_positions = '0.0 25.0 '
radii = '14.0 14.0'
3D_spheres = false
variable = c
block = 0
[../]
[]
[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 = ComputeGrainForceAndTorque
execute_on = 'linear nonlinear'
grain_data = grain_center
force_density = force_density
c = c
etas = 'eta0 eta1'
[../]
[]
[Preconditioning]
[./SMP]
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 lu 1'
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
num_steps = 1
dt = 0.1
[]
[Outputs]
exodus = true
csv = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested_damped.i)
#
# This test is for the damped nested solve of 3-phase KKS model, and uses log-based free energies.
# The split-form of the Cahn-Hilliard equation instead of the Fick's diffusion equation is solved
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = 0
xmax = 40
ymin = 0
ymax = 40
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[BCs]
[Periodic]
[all]
auto_direction = 'x y'
[]
[]
[]
[AuxVariables]
[Energy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
[]
# order parameter 3
[eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# chemical potential
[mu]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# Lagrange multiplier
[lambda]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
[]
[ICs]
[eta1]
variable = eta1
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.9
outvalue = 0.1
int_width = 4
[]
[eta2]
variable = eta2
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.1
outvalue = 0.9
int_width = 4
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.2
outvalue = 0.5
int_width = 2
[]
[]
[Materials]
# simple toy free energies
[F1]
type = DerivativeParsedMaterial
property_name = F1
expression = 'c1*log(c1/1e-4) + (1-c1)*log((1-c1)/(1-1e-4))'
material_property_names = 'c1'
additional_derivative_symbols = 'c1'
compute = false
[]
[F2]
type = DerivativeParsedMaterial
property_name = F2
expression = 'c2*log(c2/0.5) + (1-c2)*log((1-c2)/(1-0.5))'
material_property_names = 'c2'
additional_derivative_symbols = 'c2'
compute = false
[]
[F3]
type = DerivativeParsedMaterial
property_name = F3
expression = 'c3*log(c3/0.9999) + (1-c3)*log((1-c3)/(1-0.9999))'
material_property_names = 'c3'
additional_derivative_symbols = 'c3'
compute = false
[]
[C]
type = DerivativeParsedMaterial
property_name = 'C'
material_property_names = 'c1 c2 c3'
expression = '(c1>0)&(c1<1)&(c2>0)&(c2<1)&(c3>0)&(c3<1)'
compute = false
[]
[KKSPhaseConcentrationMultiPhaseMaterial]
type = KKSPhaseConcentrationMultiPhaseMaterial
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
ci_IC = '0.2 0.5 0.8'
Fj_names = 'F1 F2 F3'
min_iterations = 1
max_iterations = 1000
absolute_tolerance = 1e-15
relative_tolerance = 1e-8
step_size_tolerance = 1e-05
damped_Newton = true
conditions = C
damping_factor = 0.8
[]
[KKSPhaseConcentrationMultiPhaseDerivatives]
type = KKSPhaseConcentrationMultiPhaseDerivatives
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
[]
# Switching functions for each phase
# h1(eta1, eta2, eta3)
[h1]
type = SwitchingFunction3PhaseMaterial
eta_i = eta1
eta_j = eta2
eta_k = eta3
property_name = h1
[]
# h2(eta1, eta2, eta3)
[h2]
type = SwitchingFunction3PhaseMaterial
eta_i = eta2
eta_j = eta3
eta_k = eta1
property_name = h2
[]
# h3(eta1, eta2, eta3)
[h3]
type = SwitchingFunction3PhaseMaterial
eta_i = eta3
eta_j = eta1
eta_k = eta2
property_name = h3
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
[g3]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta3
function_name = g3
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'L kappa M'
prop_values = '0.7 1.0 0.025'
[]
[]
[Kernels]
[lambda_lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-04
[]
[eta1_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2 eta3'
[]
[eta2_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1 eta3'
[]
[eta3_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
coupled_variables = 'eta1 eta2'
[]
#Kernels for Cahn-Hilliard equation
[diff_time]
type = CoupledTimeDerivative
variable = mu
v = c
[]
[CHBulk]
type = NestedKKSMultiSplitCHCRes
variable = c
all_etas = 'eta1 eta2 eta3'
global_cs = 'c'
w = mu
c1_names = 'c1'
F1_name = F1
coupled_variables = 'eta1 eta2 eta3 mu'
[]
[ckernel]
type = SplitCHWRes
variable = mu
mob_name = M
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = NestedKKSMultiACBulkF
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g1
mob_name = L
wi = 1.0
coupled_variables = 'c eta2 eta3'
[]
[ACBulkC1]
type = NestedKKSMultiACBulkC
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta2 eta3'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta2
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = NestedKKSMultiACBulkF
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g2
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta3'
[]
[ACBulkC2]
type = NestedKKSMultiACBulkC
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta3'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta3
[deta3dt]
type = TimeDerivative
variable = eta3
[]
[ACBulkF3]
type = NestedKKSMultiACBulkF
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g3
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta2'
[]
[ACBulkC3]
type = NestedKKSMultiACBulkC
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta2'
[]
[ACInterface3]
type = ACInterface
variable = eta3
kappa_name = kappa
[]
[]
[AuxKernels]
[Energy_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gj_names = 'g1 g2 g3'
variable = Energy
w = 1
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 2
dt = 0.01
[]
[Preconditioning]
active = 'full'
[full]
type = SMP
full = true
[]
[mydebug]
type = FDP
full = true
[]
[]
[Outputs]
file_base = kks_example_multiphase_nested_damped
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/two_phase.i)
#
# This test ensures that the equilibrium solution using the dedicated two phase
# formulation is identical to the two order parameters with a Lagrange multiplier
# constraint in lagrange_multiplier.i
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 20
xmax = 5
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# order parameter
[eta]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# hydrogen concentration
[c]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = x/5
[]
[]
# chemical potential
[w]
order = FIRST
family = LAGRANGE
[]
# hydrogen phase concentration (matrix)
[cm]
order = FIRST
family = LAGRANGE
initial_condition = 0.2
[]
# hydrogen phase concentration (delta phase)
[cd]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
[]
[Materials]
# Free energy of the matrix
[fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '(0.1-cm)^2'
[]
# Free energy of the delta phase
[fd]
type = DerivativeParsedMaterial
property_name = fd
coupled_variables = 'cd'
expression = '(0.9-cd)^2'
[]
# h(eta)
[h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[]
# g(eta)
[g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'M L kappa'
prop_values = '0.7 0.7 0.4 '
[]
[]
[Kernels]
# full transient
active = 'PhaseConc ChemPotVacancies CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'
# enforce c = (1-h(eta))*cm + h(eta)*cd
[PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cd
c = c
eta = eta
[]
# enforce pointwise equality of chemical potentials
[ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cd
fa_name = fm
fb_name = fd
[]
#
# Cahn-Hilliard Equation
#
[CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cm
fa_name = fm
w = w
[]
[dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[]
[ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[]
#
# Allen-Cahn Equation
#
[ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fm
fb_name = fd
coupled_variables = 'cm cd'
w = 0.4
[]
[ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cd
fa_name = fm
mob_name = L
[]
[ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
mob_name = L
[]
[detadt]
type = TimeDerivative
variable = eta
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fd
w = 0.4
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 35
dt = 10
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[full]
type = SMP
full = true
[]
[]
[VectorPostprocessors]
[c]
type = LineValueSampler
variable = c
start_point = '0 0 0'
end_point = '5 0 0'
num_points = 21
sort_by = x
[]
[]
[Outputs]
csv = true
execute_on = FINAL
[]
(modules/phase_field/test/tests/MultiPhase/penalty.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 14
ny = 10
nz = 0
xmin = 10
xmax = 40
ymin = 15
ymax = 35
elem_type = QUAD4
[]
[GlobalParams]
penalty = 5
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 30.0
y1 = 25.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
[]
[Kernels]
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'c eta2'
f_name = F
[../]
[./ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa_eta
[../]
[./penalty1]
type = SwitchingFunctionPenalty
variable = eta1
etas = 'eta1 eta2'
h_names = 'h1 h2'
[../]
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'c eta1'
f_name = F
[../]
[./ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa_eta
[../]
[./penalty2]
type = SwitchingFunctionPenalty
variable = eta2
etas = 'eta1 eta2'
h_names = 'h1 h2'
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = 'eta1 eta2'
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time1]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1 1 '
[../]
[./consts2]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1 1'
[../]
[./hsum]
type = ParsedMaterial
expression = h1+h2
property_name = hsum
material_property_names = 'h1 h2'
coupled_variables = 'c'
outputs = exodus
[../]
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2'
[../]
[./free_energy_A]
type = DerivativeParsedMaterial
property_name = Fa
coupled_variables = 'c'
expression = '(c-0.1)^2'
derivative_order = 2
[../]
[./free_energy_B]
type = DerivativeParsedMaterial
property_name = Fb
coupled_variables = 'c'
expression = '(c-0.9)^2'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeMultiPhaseMaterial
property_name = F
fi_names = 'Fa Fb'
hi_names = 'h1 h2'
etas = 'eta1 eta2'
coupled_variables = 'c'
derivative_order = 2
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-7
nl_abs_tol = 1.0e-9
start_time = 0.0
num_steps = 2
dt = 0.05
dtmin = 0.01
[]
[Debug]
# show_var_residual_norms = true
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/test/tests/rigidbodymotion/grain_motion2.i)
# test file for applyting advection term and observing rigid body motion of grains
[Mesh]
type = GeneratedMesh
dim = 2
nx = 25
ny = 15
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./vadvx]
order = CONSTANT
family = MONOMIAL
[../]
[./vadvy]
order = CONSTANT
family = MONOMIAL
[../]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = eta
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./eta_dot]
type = TimeDerivative
variable = eta
[../]
[./vadv_eta]
type = SingleGrainRigidBodyMotion
variable = eta
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./acint_eta]
type = ACInterface
variable = eta
mob_name = M
coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta]
type = AllenCahn
variable = eta
mob_name = M
f_name = F
coupled_variables = c
[../]
[]
[AuxKernels]
[./vadv_x]
type = GrainAdvectionAux
component = x
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
variable = vadvx
[../]
[./vadv_y]
type = GrainAdvectionAux
component = y
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
variable = vadvy
[../]
[./unique_grains]
type = FeatureFloodCountAux
variable = unique_grains
flood_counter = grain_center
field_display = UNIQUE_REGION
execute_on = 'initial timestep_begin'
[../]
[./centroids]
type = FeatureFloodCountAux
variable = centroids
execute_on = 'initial timestep_begin'
field_display = CENTROID
flood_counter = grain_center
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '5.0 2.0 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'c eta'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+(c-eta)^2
derivative_order = 2
[../]
[]
[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 = FauxGrainTracker
variable = eta
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ConstantGrainForceAndTorque
execute_on = 'initial linear nonlinear'
force = '0.5 0.0 0.0 '
torque = '0.0 0.0 10.0 '
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
nl_max_its = 30
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 lu 1'
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
dt = 0.5
num_steps = 1
[]
[Outputs]
exodus = true
[]
[ICs]
[./rect_c]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = c
x1 = 10.0
type = BoundingBoxIC
[../]
[./rect_eta]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = eta
x1 = 10.0
type = BoundingBoxIC
[../]
[]
(modules/phase_field/test/tests/MultiPhase/barrierfunctionmaterial.i)
# This is a test of the BarrierFunctionMaterial option = HIGH
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = 0
xmax = 20
ymin = 0
ymax = 20
elem_type = QUAD4
[]
[Variables]
[./eta]
[../]
[]
[ICs]
[./IC_eta]
type = SmoothCircleIC
variable = eta
x1 = 10
y1 = 10
radius = 5
invalue = 1
outvalue = 0
int_width = 1
[../]
[]
[Kernels]
[./eta_bulk]
type = AllenCahn
variable = eta
f_name = 0
mob_name = 1
[../]
[./eta_interface]
type = ACInterface
variable = eta
kappa_name = 1
mob_name = 1
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[Materials]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
g_order = HIGH
outputs = exodus
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
num_steps = 2
[]
[Problem]
solve = false
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_split.i)
#
# KKS toy problem in the split form
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
nz = 0
xmin = -2.5
xmax = 2.5
ymin = -2.5
ymax = 2.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[AuxVariables]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# hydrogen concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# hydrogen phase concentration (matrix)
[./cm]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[../]
# hydrogen phase concentration (delta phase)
[./cd]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[../]
[]
[ICs]
[./eta]
variable = eta
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.2
outvalue = 0.1
int_width = 0.75
[../]
[./c]
variable = c
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.6
outvalue = 0.4
int_width = 0.75
[../]
[]
[BCs]
[./Periodic]
[./all]
variable = 'eta w c cm cd'
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
# Free energy of the matrix
[./fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '(0.1-cm)^2'
[../]
# Free energy of the delta phase
[./fd]
type = DerivativeParsedMaterial
property_name = fd
coupled_variables = 'cd'
expression = '(0.9-cd)^2'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L kappa'
prop_values = '0.7 0.7 0.4 '
[../]
[]
[Kernels]
# full transient
active = 'PhaseConc ChemPotVacancies CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'
# enforce c = (1-h(eta))*cm + h(eta)*cd
[./PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cd
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cd
fa_name = fm
fb_name = fd
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cm
fa_name = fm
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fm
fb_name = fd
coupled_variables = 'cm cd'
w = 0.4
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cd
fa_name = fm
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fd
w = 0.4
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 3
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Outputs]
file_base = kks_example_split
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/auxkernel.i)
#
# This test checks if the two phase and lagrange multiplier solutions can be replicated
# with a two order parameter approach, where the second order parameter eta2 is an
# auxiliary variable that is set as eta2 := 1 - eta1
# The solution is reproduced, but convergence is suboptimal, as important Jacobian
# terms for eta1 (that should come indirectly from eta2) are missing.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 20
xmax = 5
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
[]
#
# With this approach the derivative w.r.t. eta1 is lost in all terms depending on
# eta2 a potential fix would be to make eta2 a material property with derivatives.
# This would require a major rewrite of the phase field kernels, though.
#
[AuxKernels]
[eta2]
type = ParsedAux
variable = eta2
expression = '1-eta1'
coupled_variables = eta1
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = x/5
[]
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# phase concentration 1
[c1]
order = FIRST
family = LAGRANGE
initial_condition = 0.9
[]
# phase concentration 2
[c2]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[]
[]
[Materials]
# simple toy free energies
[f1] # = fd
type = DerivativeParsedMaterial
property_name = F1
coupled_variables = 'c1'
expression = '(0.9-c1)^2'
[]
[f2] # = fm
type = DerivativeParsedMaterial
property_name = F2
coupled_variables = 'c2'
expression = '(0.1-c2)^2'
[]
# Switching functions for each phase
[h1_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta1
function_name = h1
[]
[h2_eta]
type = DerivativeParsedMaterial
material_property_names = 'h1(eta1)'
expression = '1-h1'
property_name = h2
coupled_variables = eta1
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
[]
[Dh2]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta1)'
expression = 'D*h2'
property_name = Dh2
coupled_variables = eta1
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '0.7 0.7 0.2'
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = c
[]
[diff_c1]
type = MatDiffusion
variable = c
diffusivity = Dh1
v = c1
args = eta1
[]
[diff_c2]
type = MatDiffusion
variable = c
diffusivity = Dh2
v = c2
args = eta1
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F1 F2'
hj_names = 'h1 h2'
gi_name = g1
eta_i = eta1
wi = 0.2
coupled_variables = 'c1 c2 eta2'
[]
[ACBulkC1]
type = KKSMultiACBulkC
variable = eta1
Fj_names = 'F1 F2'
hj_names = 'h1 h2'
cj_names = 'c1 c2'
eta_i = eta1
coupled_variables = 'eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
# Phase concentration constraints
[chempot12]
type = KKSPhaseChemicalPotential
variable = c1
cb = c2
fa_name = F1
fb_name = F2
[]
[phaseconcentration]
type = KKSMultiPhaseConcentration
variable = c2
cj = 'c1 c2'
hj_names = 'h1 h2'
etas = 'eta1 eta2'
c = c
[]
[]
[AuxKernels]
[Fglobal_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 '
hj_names = 'h1 h2 '
gj_names = 'g1 g2 '
variable = Fglobal
w = 0.2
interfacial_vars = 'eta1 eta2 '
kappa_names = 'kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = PJFNK
petsc_options_iname = '-pc_type'
petsc_options_value = 'lu '
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
end_time = 350
dt = 10
[]
[Preconditioning]
[full]
type = SMP
full = true
[]
[]
[VectorPostprocessors]
[c]
type = LineValueSampler
variable = c
start_point = '0 0 0'
end_point = '5 0 0'
num_points = 21
sort_by = x
[]
[]
[Outputs]
csv = true
execute_on = FINAL
[]
(modules/phase_field/test/tests/slkks/full_solve.i)
#
# SLKKS two phase example for the BCC and SIGMA phases. The sigma phase contains
# multiple sublattices. Free energy from
# Jacob, Aurelie, Erwin Povoden-Karadeniz, and Ernst Kozeschnik. "Revised thermodynamic
# description of the Fe-Cr system based on an improved sublattice model of the sigma phase."
# Calphad 60 (2018): 16-28.
#
# In this simulation we consider diffusion (Cahn-Hilliard) and phase transformation.
#
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 1
nx = 30
ny = 1
xmin = -25
xmax = 25
[]
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# order parameters
[eta1]
initial_condition = 0.5
[]
[eta2]
initial_condition = 0.5
[]
# solute concentration
[cCr]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
# sublattice concentrations (good guesses are needed here! - they can be obtained
# form a static solve like in sublattice_concentrations.i)
[BCC_CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
[SIGMA_0CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.17+0.01'
[]
[]
[SIGMA_1CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.36+0.02'
[]
[]
[SIGMA_2CR]
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.33+0.20'
[]
[]
# Lagrange multiplier
[lambda]
[]
[]
[Materials]
# CALPHAD free energies
[F_BCC_A2]
type = DerivativeParsedMaterial
property_name = F_BCC_A2
outputs = exodus
output_properties = F_BCC_A2
expression = 'BCC_FE:=1-BCC_CR; G := 8.3145*T*(1.0*if(BCC_CR > 1.0e-15,BCC_CR*log(BCC_CR),0) + '
'1.0*if(BCC_FE > 1.0e-15,BCC_FE*plog(BCC_FE,eps),0) + 3.0*if(BCC_VA > '
'1.0e-15,BCC_VA*log(BCC_VA),0))/(BCC_CR + BCC_FE) + 8.3145*T*if(T < '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - '
'1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(0.525599232981783*BCC_CR*BCC_FE*BCC_'
'VA*(BCC_CR - BCC_FE) - 0.894055608820709*BCC_CR*BCC_FE*BCC_VA + '
'0.298657718120805*BCC_CR*BCC_VA - BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
'4.65558036243985e-30*T^9/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
'1.3485349181899e-10*T^3/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
'0.905299382744392*(548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA + '
'1.0e-9)/T,if(T < -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + '
'1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(-0.525599232981783*BCC_CR*BCC_FE*BCC'
'_VA*(BCC_CR - BCC_FE) + 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - '
'0.298657718120805*BCC_CR*BCC_VA + BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
'4.65558036243985e-30*T^9/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) '
'+ 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
'1.3485349181899e-10*T^3/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
'0.905299382744392*(-548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA + '
'1.0e-9)/T,if(T > -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA & '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA < '
'0,-79209031311018.7*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
'3.83095660520737e+42*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
'1.22565886734485e+72*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,if(T > '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA & 548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - '
'BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA > '
'0,-79209031311018.7*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
'3.83095660520737e+42*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
'1.22565886734485e+72*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,0))))*log((2.15*BCC_CR*BCC_FE*BCC_VA - '
'0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA)*if(2.15*BCC_CR*BCC_FE*BCC_VA - '
'0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA <= 0,-1.0,1.0) + 1)/(BCC_CR + BCC_FE) + '
'1.0*(BCC_CR*BCC_VA*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + '
'BCC_FE*BCC_VA*if(T >= 298.15 & T < 1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T '
'- 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < '
'6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - 25383.581,0)))/(BCC_CR '
'+ BCC_FE) + 1.0*(BCC_CR*BCC_FE*BCC_VA*(500.0 - 1.5*T)*(BCC_CR - BCC_FE) + '
'BCC_CR*BCC_FE*BCC_VA*(24600.0 - 14.98*T) + BCC_CR*BCC_FE*BCC_VA*(9.15*T - '
'14000.0)*(BCC_CR - BCC_FE)^2)/(BCC_CR + BCC_FE); G/100000'
coupled_variables = 'BCC_CR'
constant_names = 'BCC_VA T eps'
constant_expressions = '1 1000 0.01'
[]
[F_SIGMA]
type = DerivativeParsedMaterial
property_name = F_SIGMA
outputs = exodus
output_properties = F_SIGMA
expression = 'SIGMA_0FE := 1-SIGMA_0CR; SIGMA_1FE := 1-SIGMA_1CR; SIGMA_2FE := 1-SIGMA_2CR; G := '
'8.3145*T*(10.0*if(SIGMA_0CR > 1.0e-15,SIGMA_0CR*plog(SIGMA_0CR,eps),0) + '
'10.0*if(SIGMA_0FE > 1.0e-15,SIGMA_0FE*plog(SIGMA_0FE,eps),0) + 4.0*if(SIGMA_1CR > '
'1.0e-15,SIGMA_1CR*plog(SIGMA_1CR,eps),0) + 4.0*if(SIGMA_1FE > '
'1.0e-15,SIGMA_1FE*plog(SIGMA_1FE,eps),0) + 16.0*if(SIGMA_2CR > '
'1.0e-15,SIGMA_2CR*plog(SIGMA_2CR,eps),0) + 16.0*if(SIGMA_2FE > '
'1.0e-15,SIGMA_2FE*plog(SIGMA_2FE,eps),0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + '
'4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
'(SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*SIGMA_2FE*(-70.0*T - 170400.0) + '
'SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*SIGMA_2FE*(-10.0*T - 330839.0))/(10.0*SIGMA_0CR + '
'10.0*SIGMA_0FE + 4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
'(SIGMA_0CR*SIGMA_1CR*SIGMA_2CR*(30.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
'26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= '
'2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) '
'+ 132000.0) + SIGMA_0CR*SIGMA_1CR*SIGMA_2FE*(-110.0*T + 16.0*if(T >= 298.15 & T < '
'1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
'5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - '
'46.0*T*log(T) + 299.31255*T - 25383.581,0)) + 14.0*if(T >= 298.15 & T < '
'2180.0,139250.0*1/T - 26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - '
'1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - '
'50.0*T*log(T) + 344.18*T - 34869.344,0)) + 123500.0) + '
'SIGMA_0CR*SIGMA_1FE*SIGMA_2CR*(4.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 26.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 140486.0) '
'+ SIGMA_0CR*SIGMA_1FE*SIGMA_2FE*(20.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 10.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 148800.0) '
'+ SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*(10.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 20.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 56200.0) + '
'SIGMA_0FE*SIGMA_1CR*SIGMA_2FE*(26.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 4.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 152700.0) '
'+ SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*(14.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 16.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 46200.0) + '
'SIGMA_0FE*SIGMA_1FE*SIGMA_2FE*(30.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 173333.0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + 4.0*SIGMA_1CR + '
'4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE); G/100000'
coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
constant_names = 'T eps'
constant_expressions = '1000 0.01'
[]
# h(eta)
[h1]
type = SwitchingFunctionMaterial
function_name = h1
h_order = HIGH
eta = eta1
[]
[h2]
type = SwitchingFunctionMaterial
function_name = h2
h_order = HIGH
eta = eta2
[]
# g(eta)
[g1]
type = BarrierFunctionMaterial
function_name = g1
g_order = SIMPLE
eta = eta1
[]
[g2]
type = BarrierFunctionMaterial
function_name = g2
g_order = SIMPLE
eta = eta2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '10 1 0.1 '
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
derivative_order = 1
[]
[Dh2a]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*10/30
property_name = Dh2a
coupled_variables = eta2
derivative_order = 1
[]
[Dh2b]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*4/30
property_name = Dh2b
coupled_variables = eta2
derivative_order = 1
[]
[Dh2c]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*16/30
property_name = Dh2c
coupled_variables = eta2
derivative_order = 1
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = cCr
[]
[diff_c1]
type = MatDiffusion
variable = cCr
diffusivity = Dh1
v = BCC_CR
args = eta1
[]
[diff_c2a]
type = MatDiffusion
variable = cCr
diffusivity = Dh2a
v = SIGMA_0CR
args = eta2
[]
[diff_c2b]
type = MatDiffusion
variable = cCr
diffusivity = Dh2b
v = SIGMA_1CR
args = eta2
[]
[diff_c2c]
type = MatDiffusion
variable = cCr
diffusivity = Dh2c
v = SIGMA_2CR
args = eta2
[]
# enforce pointwise equality of chemical potentials
[chempot1a2a]
# The BCC phase has only one sublattice
# we tie it to the first sublattice with site fraction 10/(10+4+16) in the sigma phase
type = KKSPhaseChemicalPotential
variable = BCC_CR
cb = SIGMA_0CR
kb = '${fparse 10/30}'
fa_name = F_BCC_A2
fb_name = F_SIGMA
args_b = 'SIGMA_1CR SIGMA_2CR'
[]
[chempot2a2b]
# This kernel ties the first two sublattices in the sigma phase together
type = SLKKSChemicalPotential
variable = SIGMA_0CR
a = 10
cs = SIGMA_1CR
as = 4
F = F_SIGMA
coupled_variables = 'SIGMA_2CR'
[]
[chempot2b2c]
# This kernel ties the remaining two sublattices in the sigma phase together
type = SLKKSChemicalPotential
variable = SIGMA_1CR
a = 4
cs = SIGMA_2CR
as = 16
F = F_SIGMA
coupled_variables = 'SIGMA_0CR'
[]
[phaseconcentration]
# This kernel ties the sum of the sublattice concentrations to the global concentration cCr
type = SLKKSMultiPhaseConcentration
variable = SIGMA_2CR
c = cCr
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g1
eta_i = eta1
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta2'
[]
[ACBulkC1]
type = SLKKSMultiACBulkC
variable = eta1
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
[lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g2
eta_i = eta2
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta1'
[]
[ACBulkC2]
type = SLKKSMultiACBulkC
variable = eta2
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
[lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1'
[]
# Lagrange-multiplier constraint kernel for lambda
[lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
h_names = 'h1 h2'
etas = 'eta1 eta2'
epsilon = 1e-6
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
type = KKSMultiFreeEnergy
variable = Fglobal
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gj_names = 'g1 g2'
interfacial_vars = 'eta1 eta2'
kappa_names = 'kappa kappa'
w = 0.1
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
line_search = none
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
petsc_options_value = 'asm lu nonzero 30'
l_max_its = 100
nl_max_its = 20
nl_abs_tol = 1e-10
end_time = 1000
[TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 12
iteration_window = 2
growth_factor = 2
cutback_factor = 0.5
dt = 0.1
[]
[]
[Postprocessors]
[F]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
[]
[cmin]
type = NodalExtremeValue
value_type = min
variable = cCr
[]
[cmax]
type = NodalExtremeValue
value_type = max
variable = cCr
[]
[]
[Outputs]
exodus = true
print_linear_residuals = false
# exclude lagrange multiplier from output, it can diff more easily
hide = lambda
[]
(modules/phase_field/test/tests/KKS_system/kks_multiphase.i)
#
# This test is for the 3-phase KKS model
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = 0
xmax = 40
ymin = 0
ymax = 40
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
[../]
[../]
[]
[AuxVariables]
[./Energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Variables]
# concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# order parameter 1
[./eta1]
order = FIRST
family = LAGRANGE
[../]
# order parameter 2
[./eta2]
order = FIRST
family = LAGRANGE
[../]
# order parameter 3
[./eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[../]
# phase concentration 1
[./c1]
order = FIRST
family = LAGRANGE
initial_condition = 0.2
[../]
# phase concentration 2
[./c2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
# phase concentration 3
[./c3]
order = FIRST
family = LAGRANGE
initial_condition = 0.8
[../]
# Lagrange multiplier
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[../]
[]
[ICs]
[./eta1]
variable = eta1
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.9
outvalue = 0.1
int_width = 4
[../]
[./eta2]
variable = eta2
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.1
outvalue = 0.9
int_width = 4
[../]
[./c]
variable = c
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.2
outvalue = 0.5
int_width = 2
[../]
[]
[Materials]
# simple toy free energies
[./f1]
type = DerivativeParsedMaterial
property_name = F1
coupled_variables = 'c1'
expression = '20*(c1-0.2)^2'
[../]
[./f2]
type = DerivativeParsedMaterial
property_name = F2
coupled_variables = 'c2'
expression = '20*(c2-0.5)^2'
[../]
[./f3]
type = DerivativeParsedMaterial
property_name = F3
coupled_variables = 'c3'
expression = '20*(c3-0.8)^2'
[../]
# Switching functions for each phase
# h1(eta1, eta2, eta3)
[./h1]
type = SwitchingFunction3PhaseMaterial
eta_i = eta1
eta_j = eta2
eta_k = eta3
property_name = h1
[../]
# h2(eta1, eta2, eta3)
[./h2]
type = SwitchingFunction3PhaseMaterial
eta_i = eta2
eta_j = eta3
eta_k = eta1
property_name = h2
[../]
# h3(eta1, eta2, eta3)
[./h3]
type = SwitchingFunction3PhaseMaterial
eta_i = eta3
eta_j = eta1
eta_k = eta2
property_name = h3
[../]
# Coefficients for diffusion equation
[./Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1'
expression = D*h1
property_name = Dh1
[../]
[./Dh2]
type = DerivativeParsedMaterial
material_property_names = 'D h2'
expression = D*h2
property_name = Dh2
[../]
[./Dh3]
type = DerivativeParsedMaterial
material_property_names = 'D h3'
expression = D*h3
property_name = Dh3
[../]
# Barrier functions for each phase
[./g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[../]
[./g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[../]
[./g3]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta3
function_name = g3
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'L kappa D'
prop_values = '0.7 1.0 1'
[../]
[]
[Kernels]
#Kernels for diffusion equation
[./diff_time]
type = TimeDerivative
variable = c
[../]
[./diff_c1]
type = MatDiffusion
variable = c
diffusivity = Dh1
v = c1
[../]
[./diff_c2]
type = MatDiffusion
variable = c
diffusivity = Dh2
v = c2
[../]
[./diff_c3]
type = MatDiffusion
variable = c
diffusivity = Dh3
v = c3
[../]
# Kernels for Allen-Cahn equation for eta1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g1
eta_i = eta1
wi = 1.0
coupled_variables = 'c1 c2 c3 eta2 eta3'
[../]
[./ACBulkC1]
type = KKSMultiACBulkC
variable = eta1
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta1
coupled_variables = 'eta2 eta3'
[../]
[./ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[../]
[./multipler1]
type = MatReaction
variable = eta1
v = lambda
reaction_rate = L
[../]
# Kernels for Allen-Cahn equation for eta2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g2
eta_i = eta2
wi = 1.0
coupled_variables = 'c1 c2 c3 eta1 eta3'
[../]
[./ACBulkC2]
type = KKSMultiACBulkC
variable = eta2
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta2
coupled_variables = 'eta1 eta3'
[../]
[./ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[../]
[./multipler2]
type = MatReaction
variable = eta2
v = lambda
reaction_rate = L
[../]
# Kernels for the Lagrange multiplier equation
[./mult_lambda]
type = MatReaction
variable = lambda
reaction_rate = 3
[../]
[./mult_ACBulkF_1]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g1
eta_i = eta1
wi = 1.0
mob_name = 1
coupled_variables = 'c1 c2 c3 eta2 eta3'
[../]
[./mult_ACBulkC_1]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta1
coupled_variables = 'eta2 eta3'
mob_name = 1
[../]
[./mult_CoupledACint_1]
type = SimpleCoupledACInterface
variable = lambda
v = eta1
kappa_name = kappa
mob_name = 1
[../]
[./mult_ACBulkF_2]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g2
eta_i = eta2
wi = 1.0
mob_name = 1
coupled_variables = 'c1 c2 c3 eta1 eta3'
[../]
[./mult_ACBulkC_2]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta2
coupled_variables = 'eta1 eta3'
mob_name = 1
[../]
[./mult_CoupledACint_2]
type = SimpleCoupledACInterface
variable = lambda
v = eta2
kappa_name = kappa
mob_name = 1
[../]
[./mult_ACBulkF_3]
type = KKSMultiACBulkF
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gi_name = g3
eta_i = eta3
wi = 1.0
mob_name = 1
coupled_variables = 'c1 c2 c3 eta1 eta2'
[../]
[./mult_ACBulkC_3]
type = KKSMultiACBulkC
variable = lambda
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
cj_names = 'c1 c2 c3'
eta_i = eta3
coupled_variables = 'eta1 eta2'
mob_name = 1
[../]
[./mult_CoupledACint_3]
type = SimpleCoupledACInterface
variable = lambda
v = eta3
kappa_name = kappa
mob_name = 1
[../]
# Kernels for constraint equation eta1 + eta2 + eta3 = 1
# eta3 is the nonlinear variable for the constraint equation
[./eta3reaction]
type = MatReaction
variable = eta3
reaction_rate = 1
[../]
[./eta1reaction]
type = MatReaction
variable = eta3
v = eta1
reaction_rate = 1
[../]
[./eta2reaction]
type = MatReaction
variable = eta3
v = eta2
reaction_rate = 1
[../]
[./one]
type = BodyForce
variable = eta3
value = -1.0
[../]
# Phase concentration constraints
[./chempot12]
type = KKSPhaseChemicalPotential
variable = c1
cb = c2
fa_name = F1
fb_name = F2
[../]
[./chempot23]
type = KKSPhaseChemicalPotential
variable = c2
cb = c3
fa_name = F2
fb_name = F3
[../]
[./phaseconcentration]
type = KKSMultiPhaseConcentration
variable = c3
cj = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
c = c
[../]
[]
[AuxKernels]
[./Energy_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gj_names = 'g1 g2 g3'
variable = Energy
w = 1
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa kappa kappa'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 2
dt = 0.5
[]
[Preconditioning]
active = 'full'
[./full]
type = SMP
full = true
[../]
[./mydebug]
type = FDP
full = true
[../]
[]
[Outputs]
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested.i)
#
# This test is for the nested solve of 3-phase KKS model
# The split-form of the Cahn-Hilliard equation instead of the Fick's diffusion equation is solved
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = 0
xmax = 40
ymin = 0
ymax = 40
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[BCs]
[Periodic]
[all]
auto_direction = 'x y'
[]
[]
[]
[AuxVariables]
[Energy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
[]
# order parameter 3
[eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# chemical potential
[mu]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# Lagrange multiplier
[lambda]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
[]
[ICs]
[eta1]
variable = eta1
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.9
outvalue = 0.1
int_width = 4
[]
[eta2]
variable = eta2
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.1
outvalue = 0.9
int_width = 4
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.2
outvalue = 0.5
int_width = 2
[]
[]
[Materials]
# simple toy free energies
[F1]
type = DerivativeParsedMaterial
property_name = F1
expression = '20*(c1-0.2)^2'
material_property_names = 'c1'
additional_derivative_symbols = 'c1'
compute = false
[]
[F2]
type = DerivativeParsedMaterial
property_name = F2
expression = '20*(c2-0.5)^2'
material_property_names = 'c2'
additional_derivative_symbols = 'c2'
compute = false
[]
[F3]
type = DerivativeParsedMaterial
property_name = F3
expression = '20*(c3-0.8)^2'
material_property_names = 'c3'
additional_derivative_symbols = 'c3'
compute = false
[]
[KKSPhaseConcentrationMultiPhaseMaterial]
type = KKSPhaseConcentrationMultiPhaseMaterial
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
ci_IC = '0.2 0.5 0.8'
Fj_names = 'F1 F2 F3'
min_iterations = 1
max_iterations = 1000
absolute_tolerance = 1e-11
relative_tolerance = 1e-10
[]
[KKSPhaseConcentrationMultiPhaseDerivatives]
type = KKSPhaseConcentrationMultiPhaseDerivatives
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
[]
# Switching functions for each phase
# h1(eta1, eta2, eta3)
[h1]
type = SwitchingFunction3PhaseMaterial
eta_i = eta1
eta_j = eta2
eta_k = eta3
property_name = h1
[]
# h2(eta1, eta2, eta3)
[h2]
type = SwitchingFunction3PhaseMaterial
eta_i = eta2
eta_j = eta3
eta_k = eta1
property_name = h2
[]
# h3(eta1, eta2, eta3)
[h3]
type = SwitchingFunction3PhaseMaterial
eta_i = eta3
eta_j = eta1
eta_k = eta2
property_name = h3
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
[g3]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta3
function_name = g3
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'L kappa M'
prop_values = '0.7 1.0 0.025'
[]
[]
[Kernels]
[lambda_lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-04
[]
[eta1_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2 eta3'
[]
[eta2_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1 eta3'
[]
[eta3_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
coupled_variables = 'eta1 eta2'
[]
#Kernels for Cahn-Hilliard equation
[diff_time]
type = CoupledTimeDerivative
variable = mu
v = c
[]
[CHBulk]
type = NestedKKSMultiSplitCHCRes
variable = c
all_etas = 'eta1 eta2 eta3'
global_cs = 'c'
w = mu
c1_names = 'c1'
F1_name = F1
coupled_variables = 'eta1 eta2 eta3 mu'
[]
[ckernel]
type = SplitCHWRes
variable = mu
mob_name = M
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = NestedKKSMultiACBulkF
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g1
mob_name = L
wi = 1.0
coupled_variables = 'c eta2 eta3'
[]
[ACBulkC1]
type = NestedKKSMultiACBulkC
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta2 eta3'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta2
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = NestedKKSMultiACBulkF
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g2
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta3'
[]
[ACBulkC2]
type = NestedKKSMultiACBulkC
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta3'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta3
[deta3dt]
type = TimeDerivative
variable = eta3
[]
[ACBulkF3]
type = NestedKKSMultiACBulkF
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g3
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta2'
[]
[ACBulkC3]
type = NestedKKSMultiACBulkC
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta2'
[]
[ACInterface3]
type = ACInterface
variable = eta3
kappa_name = kappa
[]
[]
[AuxKernels]
[Energy_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gj_names = 'g1 g2 g3'
variable = Energy
w = 1
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 2
dt = 0.5
[]
[Preconditioning]
active = 'full'
[full]
type = SMP
full = true
[]
[mydebug]
type = FDP
full = true
[]
[]
[Outputs]
file_base = kks_example_multiphase_nested
exodus = true
[]
(modules/phase_field/test/tests/mobility_derivative/AC_mobility_derivative_coupled_test.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 10
xmax = 50
ymin = 25
ymax = 50
[]
[Variables]
[./op]
[../]
[./v]
[../]
[]
[ICs]
[./op_IC]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 15.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
variable = op
[../]
[./v_IC]
type = BoundingBoxIC
x1 = 0.0
x2 = 25.0
y1 = 0.0
y2 = 50.0
inside = 1.0
outside = 0.0
variable = v
[../]
[]
[Kernels]
[./op_dot]
type = TimeDerivative
variable = op
[../]
[./op_bulk]
type = AllenCahn
variable = op
f_name = F
mob_name = L
coupled_variables = v
[../]
[./op_interface]
type = ACInterface
variable = op
kappa_name = 1
mob_name = L
coupled_variables = v
[../]
[./v_dot]
type = TimeDerivative
variable = v
[../]
[./v_diff]
type = MatDiffusion
variable = v
diffusivity = 50.0
[../]
[]
[Materials]
[./consts]
type = DerivativeParsedMaterial
property_name = L
expression = 'l:=0.1+1*(v+op)^2; if(l<0.01, 0.01, l)'
coupled_variables = 'op v'
outputs = exodus
output_properties = 'L dL/dop dL/dv'
derivative_order = 2
[../]
[./free_energy]
type = DerivativeParsedMaterial
property_name = F
coupled_variables = 'op'
expression = '2*op^2*(1-op)^2 - 0.2*op'
derivative_order = 2
[../]
[]
[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 = 15
l_tol = 1.0e-4
nl_max_its = 15
nl_rel_tol = 1.0e-9
start_time = 0.0
num_steps = 10
dt = 0.2
[]
[Outputs]
time_step_interval = 5
print_linear_residuals = false
exodus = true
[]
(modules/phase_field/examples/slkks/CrFe.i)
#
# SLKKS two phase example for the BCC and SIGMA phases. The sigma phase contains
# multiple sublattices. Free energy from
# Jacob, Aurelie, Erwin Povoden-Karadeniz, and Ernst Kozeschnik. "Revised thermodynamic
# description of the Fe-Cr system based on an improved sublattice model of the sigma phase."
# Calphad 60 (2018): 16-28.
#
# In this simulation we consider diffusion (Cahn-Hilliard) and phase transformation.
#
# This example requires CrFe_sigma_out_var_0001.csv file, which generated by first
# running the CrFe_sigma.i input file.
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 160
ny = 1
nz = 0
xmin = -25
xmax = 25
ymin = -2.5
ymax = 2.5
elem_type = QUAD4
[]
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[sigma_cr0]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 2
xy_in_file_only = false
[]
[sigma_cr1]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 3
xy_in_file_only = false
[]
[sigma_cr2]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 4
xy_in_file_only = false
[]
[]
[Variables]
# order parameters
[eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
[eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# solute concentration
[cCr]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
# sublattice concentrations
[BCC_CR]
initial_condition = 0.45
[]
[SIGMA_0CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr0
v = cCr
variable = SIGMA_0CR
[]
[]
[SIGMA_1CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr1
v = cCr
variable = SIGMA_1CR
[]
[]
[SIGMA_2CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr2
v = cCr
variable = SIGMA_2CR
[]
[]
# Lagrange multiplier
[lambda]
[]
[]
[Materials]
# CALPHAD free energies
[F_BCC_A2]
type = DerivativeParsedMaterial
property_name = F_BCC_A2
outputs = exodus
output_properties = F_BCC_A2
expression = 'BCC_FE:=1-BCC_CR; G := 8.3145*T*(1.0*if(BCC_CR > 1.0e-15,BCC_CR*log(BCC_CR),0) + '
'1.0*if(BCC_FE > 1.0e-15,BCC_FE*plog(BCC_FE,eps),0) + 3.0*if(BCC_VA > '
'1.0e-15,BCC_VA*log(BCC_VA),0))/(BCC_CR + BCC_FE) + 8.3145*T*if(T < '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - '
'1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(0.525599232981783*BCC_CR*BCC_FE*BCC_'
'VA*(BCC_CR - BCC_FE) - 0.894055608820709*BCC_CR*BCC_FE*BCC_VA + '
'0.298657718120805*BCC_CR*BCC_VA - BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
'4.65558036243985e-30*T^9/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
'1.3485349181899e-10*T^3/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
'0.905299382744392*(548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA + '
'1.0e-9)/T,if(T < -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + '
'1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(-0.525599232981783*BCC_CR*BCC_FE*BCC'
'_VA*(BCC_CR - BCC_FE) + 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - '
'0.298657718120805*BCC_CR*BCC_VA + BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
'4.65558036243985e-30*T^9/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) '
'+ 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
'1.3485349181899e-10*T^3/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
'0.905299382744392*(-548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA + '
'1.0e-9)/T,if(T > -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA & '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA < '
'0,-79209031311018.7*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
'3.83095660520737e+42*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
'1.22565886734485e+72*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,if(T > '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA & 548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - '
'BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA > '
'0,-79209031311018.7*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
'3.83095660520737e+42*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
'1.22565886734485e+72*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,0))))*log((2.15*BCC_CR*BCC_FE*BCC_VA - '
'0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA)*if(2.15*BCC_CR*BCC_FE*BCC_VA - '
'0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA <= 0,-1.0,1.0) + 1)/(BCC_CR + BCC_FE) + '
'1.0*(BCC_CR*BCC_VA*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + '
'BCC_FE*BCC_VA*if(T >= 298.15 & T < 1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T '
'- 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < '
'6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - 25383.581,0)))/(BCC_CR '
'+ BCC_FE) + 1.0*(BCC_CR*BCC_FE*BCC_VA*(500.0 - 1.5*T)*(BCC_CR - BCC_FE) + '
'BCC_CR*BCC_FE*BCC_VA*(24600.0 - 14.98*T) + BCC_CR*BCC_FE*BCC_VA*(9.15*T - '
'14000.0)*(BCC_CR - BCC_FE)^2)/(BCC_CR + BCC_FE); G/100000'
coupled_variables = 'BCC_CR'
constant_names = 'BCC_VA T eps'
constant_expressions = '1 1000 0.01'
[]
[F_SIGMA]
type = DerivativeParsedMaterial
property_name = F_SIGMA
outputs = exodus
output_properties = F_SIGMA
expression = 'SIGMA_0FE := 1-SIGMA_0CR; SIGMA_1FE := 1-SIGMA_1CR; SIGMA_2FE := 1-SIGMA_2CR; G := '
'8.3145*T*(10.0*if(SIGMA_0CR > 1.0e-15,SIGMA_0CR*plog(SIGMA_0CR,eps),0) + '
'10.0*if(SIGMA_0FE > 1.0e-15,SIGMA_0FE*plog(SIGMA_0FE,eps),0) + 4.0*if(SIGMA_1CR > '
'1.0e-15,SIGMA_1CR*plog(SIGMA_1CR,eps),0) + 4.0*if(SIGMA_1FE > '
'1.0e-15,SIGMA_1FE*plog(SIGMA_1FE,eps),0) + 16.0*if(SIGMA_2CR > '
'1.0e-15,SIGMA_2CR*plog(SIGMA_2CR,eps),0) + 16.0*if(SIGMA_2FE > '
'1.0e-15,SIGMA_2FE*plog(SIGMA_2FE,eps),0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + '
'4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
'(SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*SIGMA_2FE*(-70.0*T - 170400.0) + '
'SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*SIGMA_2FE*(-10.0*T - 330839.0))/(10.0*SIGMA_0CR + '
'10.0*SIGMA_0FE + 4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
'(SIGMA_0CR*SIGMA_1CR*SIGMA_2CR*(30.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
'26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= '
'2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) '
'+ 132000.0) + SIGMA_0CR*SIGMA_1CR*SIGMA_2FE*(-110.0*T + 16.0*if(T >= 298.15 & T < '
'1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
'5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - '
'46.0*T*log(T) + 299.31255*T - 25383.581,0)) + 14.0*if(T >= 298.15 & T < '
'2180.0,139250.0*1/T - 26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - '
'1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - '
'50.0*T*log(T) + 344.18*T - 34869.344,0)) + 123500.0) + '
'SIGMA_0CR*SIGMA_1FE*SIGMA_2CR*(4.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 26.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 140486.0) '
'+ SIGMA_0CR*SIGMA_1FE*SIGMA_2FE*(20.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 10.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 148800.0) '
'+ SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*(10.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 20.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 56200.0) + '
'SIGMA_0FE*SIGMA_1CR*SIGMA_2FE*(26.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 4.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 152700.0) '
'+ SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*(14.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 16.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 46200.0) + '
'SIGMA_0FE*SIGMA_1FE*SIGMA_2FE*(30.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 173333.0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + 4.0*SIGMA_1CR + '
'4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE); G/100000'
coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
constant_names = 'T eps'
constant_expressions = '1000 0.01'
[]
# h(eta)
[h1]
type = SwitchingFunctionMaterial
function_name = h1
h_order = HIGH
eta = eta1
[]
[h2]
type = SwitchingFunctionMaterial
function_name = h2
h_order = HIGH
eta = eta2
[]
# g(eta)
[g1]
type = BarrierFunctionMaterial
function_name = g1
g_order = SIMPLE
eta = eta1
[]
[g2]
type = BarrierFunctionMaterial
function_name = g2
g_order = SIMPLE
eta = eta2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '10 1 0.1 '
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
derivative_order = 1
[]
[Dh2a]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*10/30
property_name = Dh2a
coupled_variables = eta2
derivative_order = 1
[]
[Dh2b]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*4/30
property_name = Dh2b
coupled_variables = eta2
derivative_order = 1
[]
[Dh2c]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*16/30
property_name = Dh2c
coupled_variables = eta2
derivative_order = 1
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = cCr
[]
[diff_c1]
type = MatDiffusion
variable = cCr
diffusivity = Dh1
v = BCC_CR
args = eta1
[]
[diff_c2a]
type = MatDiffusion
variable = cCr
diffusivity = Dh2a
v = SIGMA_0CR
args = eta2
[]
[diff_c2b]
type = MatDiffusion
variable = cCr
diffusivity = Dh2b
v = SIGMA_1CR
args = eta2
[]
[diff_c2c]
type = MatDiffusion
variable = cCr
diffusivity = Dh2c
v = SIGMA_2CR
args = eta2
[]
# enforce pointwise equality of chemical potentials
[chempot1a2a]
# The BCC phase has only one sublattice
# we tie it to the first sublattice with site fraction 10/(10+4+16) in the sigma phase
type = KKSPhaseChemicalPotential
variable = BCC_CR
cb = SIGMA_0CR
kb = '${fparse 10/30}'
fa_name = F_BCC_A2
fb_name = F_SIGMA
args_b = 'SIGMA_1CR SIGMA_2CR'
[]
[chempot2a2b]
# This kernel ties the first two sublattices in the sigma phase together
type = SLKKSChemicalPotential
variable = SIGMA_0CR
a = 10
cs = SIGMA_1CR
as = 4
F = F_SIGMA
coupled_variables = 'SIGMA_2CR'
[]
[chempot2b2c]
# This kernel ties the remaining two sublattices in the sigma phase together
type = SLKKSChemicalPotential
variable = SIGMA_1CR
a = 4
cs = SIGMA_2CR
as = 16
F = F_SIGMA
coupled_variables = 'SIGMA_0CR'
[]
[phaseconcentration]
# This kernel ties the sum of the sublattice concentrations to the global concentration cCr
type = SLKKSMultiPhaseConcentration
variable = SIGMA_2CR
c = cCr
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g1
eta_i = eta1
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta2'
[]
[ACBulkC1]
type = SLKKSMultiACBulkC
variable = eta1
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
[lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g2
eta_i = eta2
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta1'
[]
[ACBulkC2]
type = SLKKSMultiACBulkC
variable = eta2
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
[lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1'
[]
# Lagrange-multiplier constraint kernel for lambda
[lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
h_names = 'h1 h2'
etas = 'eta1 eta2'
epsilon = 1e-6
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
type = KKSMultiFreeEnergy
variable = Fglobal
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gj_names = 'g1 g2'
interfacial_vars = 'eta1 eta2'
kappa_names = 'kappa kappa'
w = 0.1
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
line_search = none
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
petsc_options_value = 'asm lu nonzero 30'
l_max_its = 100
nl_max_its = 20
nl_abs_tol = 1e-10
end_time = 10000
[TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 12
iteration_window = 2
growth_factor = 1.5
cutback_factor = 0.7
dt = 0.1
[]
[]
[VectorPostprocessors]
[var]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = 'cCr eta1 eta2 SIGMA_0CR SIGMA_1CR SIGMA_2CR'
num_points = 151
sort_by = id
execute_on = 'initial timestep_end'
[]
[mat]
type = LineMaterialRealSampler
start = '-25 0 0'
end = '25 0 0'
property = 'F_BCC_A2 F_SIGMA'
sort_by = id
execute_on = 'initial timestep_end'
[]
[]
[Postprocessors]
[F]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
execute_on = 'initial timestep_end'
[]
[cmin]
type = NodalExtremeValue
value_type = min
variable = cCr
execute_on = 'initial timestep_end'
[]
[cmax]
type = NodalExtremeValue
value_type = max
variable = cCr
execute_on = 'initial timestep_end'
[]
[ctotal]
type = ElementIntegralVariablePostprocessor
variable = cCr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
exodus = true
print_linear_residuals = false
csv = true
perf_graph = true
[]
(modules/phase_field/test/tests/rigidbodymotion/update_orientation.i)
# test file for applyting advection term and observing rigid body motion of grains
[Mesh]
type = GeneratedMesh
dim = 2
nx = 25
ny = 15
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = eta
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./eta_dot]
type = TimeDerivative
variable = eta
[../]
[./vadv_eta]
type = SingleGrainRigidBodyMotion
variable = eta
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./acint_eta]
type = ACInterface
variable = eta
mob_name = M
coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta]
type = AllenCahn
variable = eta
mob_name = M
f_name = F
coupled_variables = c
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '5.0 2.0 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'c eta'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+(c-eta)^2
derivative_order = 2
[../]
[]
[AuxVariables]
[./unique_grains]
order = CONSTANT
family = MONOMIAL
[../]
[./var_indices]
order = CONSTANT
family = MONOMIAL
[../]
[./centroids]
order = CONSTANT
family = MONOMIAL
[../]
[./vadv_x]
order = CONSTANT
family = MONOMIAL
[../]
[./vadv_y]
order = CONSTANT
family = MONOMIAL
[../]
[./angle_initial]
order = CONSTANT
family = MONOMIAL
[../]
[./euler_angle]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./unique_grains]
type = FeatureFloodCountAux
variable = unique_grains
flood_counter = grain_center
field_display = UNIQUE_REGION
execute_on = timestep_begin
[../]
[./var_indices]
type = FeatureFloodCountAux
variable = var_indices
flood_counter = grain_center
field_display = VARIABLE_COLORING
execute_on = timestep_begin
[../]
[./centroids]
type = FeatureFloodCountAux
variable = centroids
execute_on = timestep_begin
field_display = CENTROID
flood_counter = grain_center
[../]
[./vadv_x]
type = GrainAdvectionAux
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
execute_on = timestep_begin
component = x
variable = vadv_x
[../]
[./vadv_y]
type = GrainAdvectionAux
grain_force = grain_force
grain_volumes = grain_volumes
grain_tracker_object = grain_center
execute_on = timestep_begin
component = y
variable = vadv_y
[../]
[./angle_initial]
type = OutputEulerAngles
variable = angle_initial
euler_angle_provider = euler_angle_initial
grain_tracker = grain_center
output_euler_angle = phi2
execute_on = timestep_begin
[../]
[./angle]
type = OutputEulerAngles
variable = euler_angle
euler_angle_provider = euler_angle
grain_tracker = grain_center
output_euler_angle = phi2
execute_on = timestep_begin
[../]
[]
[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
variable = eta
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ConstantGrainForceAndTorque
execute_on = 'initial timestep_begin linear nonlinear'
force = '0.5 0.0 0.0 '
torque = '0.0 0.0 10.0'
[../]
[./euler_angle_initial]
type = RandomEulerAngleProvider
grain_tracker_object = grain_center
execute_on = 'initial timestep_begin'
[../]
[./euler_angle]
type = EulerAngleUpdater
grain_tracker_object = grain_center
euler_angle_provider = euler_angle_initial
grain_torques_object = grain_force
grain_volumes = grain_volumes
execute_on = timestep_begin
[../]
[]
[Preconditioning]
[./SMP]
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 lu 1'
nl_max_its = 30
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
dt = 0.2
num_steps = 5
[]
[Outputs]
exodus = true
[]
[ICs]
[./rect_c]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = c
x1 = 10.0
type = BoundingBoxIC
[../]
[./rect_eta]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = eta
x1 = 10.0
type = BoundingBoxIC
[../]
[]
(modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i)
# KKS phase-field model coupled with elasticity using the Voigt-Taylor scheme as
# described in L.K. Aagesen et al., Computational Materials Science, 140, 10-21 (2017)
# Original run #170329e
[Mesh]
type = GeneratedMesh
dim = 3
nx = 640
ny = 1
nz = 1
xmin = -10
xmax = 10
ymin = 0
ymax = 0.03125
zmin = 0
zmax = 0.03125
elem_type = HEX8
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# solute concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# solute phase concentration (matrix)
[./cm]
order = FIRST
family = LAGRANGE
[../]
# solute phase concentration (precipitate)
[./cp]
order = FIRST
family = LAGRANGE
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[./disp_z]
order = FIRST
family = LAGRANGE
[../]
[]
[ICs]
[./eta_ic]
variable = eta
type = FunctionIC
function = ic_func_eta
block = 0
[../]
[./c_ic]
variable = c
type = FunctionIC
function = ic_func_c
block = 0
[../]
[./w_ic]
variable = w
type = ConstantIC
value = 0.00991
block = 0
[../]
[./cm_ic]
variable = cm
type = ConstantIC
value = 0.131
block = 0
[../]
[./cp_ic]
variable = cp
type = ConstantIC
value = 0.236
block = 0
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = '0.5*(1.0+tanh((x)/delta_eta/sqrt(2.0)))'
symbol_names = 'delta_eta'
symbol_values = '0.8034'
[../]
[./ic_func_c]
type = ParsedFunction
expression = '0.2388*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10)+0.1338*(1-(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^3*(6*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))^2-15*(0.5*(1.0+tanh(x/delta/sqrt(2.0))))+10))'
symbol_names = 'delta'
symbol_values = '0.8034'
[../]
[./psi_eq_int]
type = ParsedFunction
expression = 'volume*psi_alpha'
symbol_names = 'volume psi_alpha'
symbol_values = 'volume psi_alpha'
[../]
[./gamma]
type = ParsedFunction
expression = '(psi_int - psi_eq_int) / dy / dz'
symbol_names = 'psi_int psi_eq_int dy dz'
symbol_values = 'psi_int psi_eq_int 0.03125 0.03125'
[../]
[]
[AuxVariables]
[./sigma11]
order = CONSTANT
family = MONOMIAL
[../]
[./sigma22]
order = CONSTANT
family = MONOMIAL
[../]
[./sigma33]
order = CONSTANT
family = MONOMIAL
[../]
[./e11]
order = CONSTANT
family = MONOMIAL
[../]
[./e12]
order = CONSTANT
family = MONOMIAL
[../]
[./e22]
order = CONSTANT
family = MONOMIAL
[../]
[./e33]
order = CONSTANT
family = MONOMIAL
[../]
[./e_el11]
order = CONSTANT
family = MONOMIAL
[../]
[./e_el12]
order = CONSTANT
family = MONOMIAL
[../]
[./e_el22]
order = CONSTANT
family = MONOMIAL
[../]
[./f_el]
order = CONSTANT
family = MONOMIAL
[../]
[./eigen_strain00]
order = CONSTANT
family = MONOMIAL
[../]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[./psi]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./matl_sigma11]
type = RankTwoAux
rank_two_tensor = stress
index_i = 0
index_j = 0
variable = sigma11
[../]
[./matl_sigma22]
type = RankTwoAux
rank_two_tensor = stress
index_i = 1
index_j = 1
variable = sigma22
[../]
[./matl_sigma33]
type = RankTwoAux
rank_two_tensor = stress
index_i = 2
index_j = 2
variable = sigma33
[../]
[./matl_e11]
type = RankTwoAux
rank_two_tensor = total_strain
index_i = 0
index_j = 0
variable = e11
[../]
[./matl_e12]
type = RankTwoAux
rank_two_tensor = total_strain
index_i = 0
index_j = 1
variable = e12
[../]
[./matl_e22]
type = RankTwoAux
rank_two_tensor = total_strain
index_i = 1
index_j = 1
variable = e22
[../]
[./matl_e33]
type = RankTwoAux
rank_two_tensor = total_strain
index_i = 2
index_j = 2
variable = e33
[../]
[./f_el]
type = MaterialRealAux
variable = f_el
property = f_el_mat
execute_on = timestep_end
[../]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fp
w = 0.0264
kappa_names = kappa
interfacial_vars = eta
[../]
[./psi_potential]
variable = psi
type = ParsedAux
coupled_variables = 'Fglobal w c f_el sigma11 e11'
expression = 'Fglobal - w*c + f_el - sigma11*e11'
[../]
[]
[BCs]
[./left_x]
type = DirichletBC
variable = disp_x
boundary = left
value = 0
[../]
[./right_x]
type = DirichletBC
variable = disp_x
boundary = right
value = 0
[../]
[./front_y]
type = DirichletBC
variable = disp_y
boundary = front
value = 0
[../]
[./back_y]
type = DirichletBC
variable = disp_y
boundary = back
value = 0
[../]
[./top_z]
type = DirichletBC
variable = disp_z
boundary = top
value = 0
[../]
[./bottom_z]
type = DirichletBC
variable = disp_z
boundary = bottom
value = 0
[../]
[]
[Materials]
# Chemical free energy of the matrix
[./fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '6.55*(cm-0.13)^2'
[../]
# Elastic energy of the matrix
[./elastic_free_energy_m]
type = ElasticEnergyMaterial
base_name = matrix
f_name = fe_m
coupled_variables = ' '
outputs = exodus
[../]
# Total free energy of the matrix
[./Total_energy_matrix]
type = DerivativeSumMaterial
property_name = f_total_matrix
sum_materials = 'fm fe_m'
coupled_variables = 'cm'
[../]
# Free energy of the precipitate phase
[./fp]
type = DerivativeParsedMaterial
property_name = fp
coupled_variables = 'cp'
expression = '6.55*(cp-0.235)^2'
[../]
# Elastic energy of the precipitate
[./elastic_free_energy_p]
type = ElasticEnergyMaterial
base_name = ppt
f_name = fe_p
coupled_variables = ' '
outputs = exodus
[../]
# Total free energy of the precipitate
[./Total_energy_ppt]
type = DerivativeSumMaterial
property_name = f_total_ppt
sum_materials = 'fp fe_p'
coupled_variables = 'cp'
[../]
# Total elastic energy
[./Total_elastic_energy]
type = DerivativeTwoPhaseMaterial
eta = eta
f_name = f_el_mat
fa_name = fe_m
fb_name = fe_p
outputs = exodus
W = 0
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L kappa misfit'
prop_values = '0.7 0.7 0.01704 0.00377'
[../]
#Mechanical properties
[./Stiffness_matrix]
type = ComputeElasticityTensor
C_ijkl = '103.3 74.25 74.25 103.3 74.25 103.3 46.75 46.75 46.75'
base_name = matrix
fill_method = symmetric9
[../]
[./Stiffness_ppt]
type = ComputeElasticityTensor
C_ijkl = '100.7 71.45 71.45 100.7 71.45 100.7 50.10 50.10 50.10'
base_name = ppt
fill_method = symmetric9
[../]
[./stress_matrix]
type = ComputeLinearElasticStress
base_name = matrix
[../]
[./stress_ppt]
type = ComputeLinearElasticStress
base_name = ppt
[../]
[./strain_matrix]
type = ComputeSmallStrain
displacements = 'disp_x disp_y disp_z'
base_name = matrix
[../]
[./strain_ppt]
type = ComputeSmallStrain
displacements = 'disp_x disp_y disp_z'
base_name = ppt
eigenstrain_names = 'eigenstrain_ppt'
[../]
[./eigen_strain]
type = ComputeEigenstrain
base_name = ppt
eigen_base = '1 1 1 0 0 0'
prefactor = misfit
eigenstrain_name = 'eigenstrain_ppt'
[../]
[./global_stress]
type = TwoPhaseStressMaterial
base_A = matrix
base_B = ppt
[../]
[./global_strain]
type = ComputeSmallStrain
displacements = 'disp_x disp_y disp_z'
[../]
[]
[Kernels]
[./TensorMechanics]
displacements = 'disp_x disp_y disp_z'
[../]
# enforce c = (1-h(eta))*cm + h(eta)*cp
[./PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cp
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cp
fa_name = f_total_matrix
fb_name = f_total_ppt
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cm
fa_name = f_total_matrix
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = f_total_matrix
fb_name = f_total_ppt
w = 0.0264
coupled_variables = 'cp cm'
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cp
fa_name = f_total_matrix
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-11
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.5
[../]
[]
[VectorPostprocessors]
#[./eta]
# type = LineValueSampler
# start_point = '-10 0 0'
# end_point = '10 0 0'
# variable = eta
# num_points = 321
# sort_by = id
#[../]
#[./eta_position]
# type = FindValueOnLineSample
# vectorpostprocessor = eta
# variable_name = eta
# search_value = 0.5
#[../]
# [./f_el]
# type = LineMaterialRealSampler
# start = '-20 0 0'
# end = '20 0 0'
# sort_by = id
# property = f_el
# [../]
# [./f_el_a]
# type = LineMaterialRealSampler
# start = '-20 0 0'
# end = '20 0 0'
# sort_by = id
# property = fe_m
# [../]
# [./f_el_b]
# type = LineMaterialRealSampler
# start = '-20 0 0'
# end = '20 0 0'
# sort_by = id
# property = fe_p
# [../]
# [./h_out]
# type = LineMaterialRealSampler
# start = '-20 0 0'
# end = '20 0 0'
# sort_by = id
# property = h
# [../]
# [./fm_out]
# type = LineMaterialRealSampler
# start = '-20 0 0'
# end = '20 0 0'
# sort_by = id
# property = fm
# [../]
[]
[Postprocessors]
[./f_el_int]
type = ElementIntegralMaterialProperty
mat_prop = f_el_mat
[../]
[./c_alpha]
type = SideAverageValue
boundary = left
variable = c
[../]
[./c_beta]
type = SideAverageValue
boundary = right
variable = c
[../]
[./e11_alpha]
type = SideAverageValue
boundary = left
variable = e11
[../]
[./e11_beta]
type = SideAverageValue
boundary = right
variable = e11
[../]
[./s11_alpha]
type = SideAverageValue
boundary = left
variable = sigma11
[../]
[./s22_alpha]
type = SideAverageValue
boundary = left
variable = sigma22
[../]
[./s33_alpha]
type = SideAverageValue
boundary = left
variable = sigma33
[../]
[./s11_beta]
type = SideAverageValue
boundary = right
variable = sigma11
[../]
[./s22_beta]
type = SideAverageValue
boundary = right
variable = sigma22
[../]
[./s33_beta]
type = SideAverageValue
boundary = right
variable = sigma33
[../]
[./f_el_alpha]
type = SideAverageValue
boundary = left
variable = f_el
[../]
[./f_el_beta]
type = SideAverageValue
boundary = right
variable = f_el
[../]
[./f_c_alpha]
type = SideAverageValue
boundary = left
variable = Fglobal
[../]
[./f_c_beta]
type = SideAverageValue
boundary = right
variable = Fglobal
[../]
[./chem_pot_alpha]
type = SideAverageValue
boundary = left
variable = w
[../]
[./chem_pot_beta]
type = SideAverageValue
boundary = right
variable = w
[../]
[./psi_alpha]
type = SideAverageValue
boundary = left
variable = psi
[../]
[./psi_beta]
type = SideAverageValue
boundary = right
variable = psi
[../]
[./total_energy]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
[../]
# Get simulation cell size from postprocessor
[./volume]
type = ElementIntegralMaterialProperty
mat_prop = 1
[../]
[./psi_eq_int]
type = FunctionValuePostprocessor
function = psi_eq_int
[../]
[./psi_int]
type = ElementIntegralVariablePostprocessor
variable = psi
[../]
[./gamma]
type = FunctionValuePostprocessor
function = gamma
[../]
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Outputs]
[./exodus]
type = Exodus
time_step_interval = 20
[../]
[./csv]
type = CSV
execute_on = 'final'
[../]
#[./console]
# type = Console
# output_file = true
# [../]
[]
(modules/phase_field/test/tests/KKS_system/kks_example.i)
#
# KKS toy problem in the non-split form
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 5
ny = 5
nz = 0
xmin = -0.5
xmax = 0.5
ymin = -0.5
ymax = 0.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[Variables]
# order parameter
[eta]
order = THIRD
family = HERMITE
[]
# hydrogen concentration
[c]
order = THIRD
family = HERMITE
[]
# hydrogen phase concentration (matrix)
[cm]
order = THIRD
family = HERMITE
initial_condition = 0.0
[]
# hydrogen phase concentration (delta phase)
[cd]
order = THIRD
family = HERMITE
initial_condition = 0.0
[]
[]
[ICs]
[eta]
variable = eta
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 0.2
invalue = 0.2
outvalue = 0.1
int_width = 0.05
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 0.2
invalue = 0.6
outvalue = 0.4
int_width = 0.05
[]
[]
[BCs]
[Periodic]
[all]
variable = 'eta c cm cd'
auto_direction = 'x y'
[]
[]
[]
[Materials]
# Free energy of the matrix
[fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '(0.1-cm)^2'
outputs = oversampling
[]
# Free energy of the delta phase
[fd]
type = DerivativeParsedMaterial
property_name = fd
coupled_variables = 'cd'
expression = '(0.9-cd)^2'
outputs = oversampling
[]
# h(eta)
[h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
outputs = oversampling
[]
# g(eta)
[g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
outputs = oversampling
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'L '
prop_values = '0.7 '
[]
[]
[Kernels]
# enforce c = (1-h(eta))*cm + h(eta)*cd
[PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cd
c = c
eta = eta
[]
# enforce pointwise equality of chemical potentials
[ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cd
fa_name = fm
fb_name = fd
[]
#
# Cahn-Hilliard Equation
#
[CHBulk]
type = KKSCHBulk
variable = c
ca = cm
cb = cd
fa_name = fm
fb_name = fd
mob_name = 0.7
[]
[dcdt]
type = TimeDerivative
variable = c
[]
#
# Allen-Cahn Equation
#
[ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fm
fb_name = fd
coupled_variables = 'cm cd'
w = 0.4
[]
[ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cd
fa_name = fm
[]
[ACInterface]
type = ACInterface
variable = eta
kappa_name = 0.4
[]
[detadt]
type = TimeDerivative
variable = eta
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero'
l_max_its = 100
nl_max_its = 100
nl_rel_tol = 1e-4
num_steps = 1
dt = 0.01
dtmin = 0.01
[]
[Preconditioning]
[mydebug]
type = SMP
full = true
[]
[]
[Outputs]
file_base = kks_example
[oversampling]
type = Exodus
refinements = 3
# To keep the same test results as before #30318 sampled output rework
hide = 'd^2fd/dcd^2 d^2fm/dcm^2 d^2g/deta^2 d^2h/deta^2 dfd/dcd dfm/dcm dg/deta dh/deta fd fm g h'
[]
[]
(modules/phase_field/examples/multiphase/GrandPotential3Phase_masscons.i)
# This is an example of implementation of the multi-phase, multi-order parameter
# grand potential based phase-field model described in Phys. Rev. E, 98, 023309
# (2018). It includes 3 phases with 1 grain of each phase.
# This is a revised version of the model that eliminates small variations in mass
# that have been observed with the original formulation. In this version, rather
# than evolving the chemical potential as a field variable, we evolve the composition
# field using a normal Cahn-Hilliard equation, then relate chemical potential to
# composition using Eq. (22) from the paper (this relationship is derived from the
# grand potential functional and is valid only for parabolic free energies).
[Mesh]
type = GeneratedMesh
dim = 2
nx = 60
ny = 60
xmin = -15
xmax = 15
ymin = -15
ymax = 15
[]
[Variables]
[w]
[]
[c]
[]
[etaa0]
[]
[etab0]
[]
[etad0]
[]
[]
[ICs]
[IC_etaa0]
type = BoundingBoxIC
variable = etaa0
x1 = -10
y1 = -10
x2 = 10
y2 = 10
inside = 1.0
outside = 0.0
[]
[IC_etad0]
type = BoundingBoxIC
variable = etad0
x1 = -10
y1 = -10
x2 = 10
y2 = 10
inside = 0.0
outside = 1.0
[]
[IC_c]
type = BoundingBoxIC
variable = c
x1 = -10
y1 = -10
x2 = 10
y2 = 10
inside = 0.1
outside = 0.5
[]
[IC_w]
type = FunctionIC
variable = w
function = ic_func_w
[]
[]
[Functions]
[ic_func_w]
type = ConstantFunction
value = 0
[]
[]
[Kernels]
# Order parameter eta_alpha0
[ACa0_bulk]
type = ACGrGrMulti
variable = etaa0
v = 'etab0 etad0'
gamma_names = 'gab gad'
[]
[ACa0_sw]
type = ACSwitching
variable = etaa0
Fj_names = 'omegaa omegab omegad'
hj_names = 'ha hb hd'
coupled_variables = 'etab0 etad0 w'
[]
[ACa0_int]
type = ACInterface
variable = etaa0
kappa_name = kappa
[]
[ea0_dot]
type = TimeDerivative
variable = etaa0
[]
# Order parameter eta_beta0
[ACb0_bulk]
type = ACGrGrMulti
variable = etab0
v = 'etaa0 etad0'
gamma_names = 'gab gbd'
[]
[ACb0_sw]
type = ACSwitching
variable = etab0
Fj_names = 'omegaa omegab omegad'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etad0 w'
[]
[ACb0_int]
type = ACInterface
variable = etab0
kappa_name = kappa
[]
[eb0_dot]
type = TimeDerivative
variable = etab0
[]
# Order parameter eta_delta0
[ACd0_bulk]
type = ACGrGrMulti
variable = etad0
v = 'etaa0 etab0'
gamma_names = 'gad gbd'
[]
[ACd0_sw]
type = ACSwitching
variable = etad0
Fj_names = 'omegaa omegab omegad'
hj_names = 'ha hb hd'
coupled_variables = 'etaa0 etab0 w'
[]
[ACd0_int]
type = ACInterface
variable = etad0
kappa_name = kappa
[]
[ed0_dot]
type = TimeDerivative
variable = etad0
[]
#Concentration
[c_dot]
type = TimeDerivative
variable = c
[]
[Diffusion]
type = MatDiffusion
variable = c
v = w
diffusivity = DchiVm
args = ''
[]
#The following relate chemical potential to composition using Eq. (22)
[w_rxn]
type = MatReaction
variable = w
v = c
reaction_rate = -1
[]
[ca_rxn]
type = MatReaction
variable = w
reaction_rate = 'hoverk_a'
args = 'etaa0 etab0 etad0'
[]
[ca_bodyforce]
type = MaskedBodyForce
variable = w
mask = ha
coupled_variables = 'etaa0 etab0 etad0'
value = 0.1 #caeq
[]
[cb_rxn]
type = MatReaction
variable = w
reaction_rate = 'hoverk_b'
args = 'etaa0 etab0 etad0'
[]
[cb_bodyforce]
type = MaskedBodyForce
variable = w
mask = hb
coupled_variables = 'etaa0 etab0 etad0'
value = 0.9 #cbeq
[]
[cd_rxn]
type = MatReaction
variable = w
reaction_rate = 'hoverk_d'
args = 'etaa0 etab0 etad0'
[]
[cd_bodyforce]
type = MaskedBodyForce
variable = w
mask = hd
coupled_variables = 'etaa0 etab0 etad0'
value = 0.5 #cdeq
[]
[]
[Materials]
[ha_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = ha
all_etas = 'etaa0 etab0 etad0'
phase_etas = 'etaa0'
[]
[hb_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = hb
all_etas = 'etaa0 etab0 etad0'
phase_etas = 'etab0'
[]
[hd_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = hd
all_etas = 'etaa0 etab0 etad0'
phase_etas = 'etad0'
[]
[omegaa]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegaa
material_property_names = 'Vm ka caeq'
expression = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
derivative_order = 2
[]
[omegab]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegab
material_property_names = 'Vm kb cbeq'
expression = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
derivative_order = 2
[]
[omegad]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = omegad
material_property_names = 'Vm kd cdeq'
expression = '-0.5*w^2/Vm^2/kd-w/Vm*cdeq'
derivative_order = 2
[]
[rhoa]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhoa
material_property_names = 'Vm ka caeq'
expression = 'w/Vm^2/ka + caeq/Vm'
derivative_order = 2
[]
[rhob]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhob
material_property_names = 'Vm kb cbeq'
expression = 'w/Vm^2/kb + cbeq/Vm'
derivative_order = 2
[]
[rhod]
type = DerivativeParsedMaterial
coupled_variables = 'w'
property_name = rhod
material_property_names = 'Vm kd cdeq'
expression = 'w/Vm^2/kd + cdeq/Vm'
derivative_order = 2
[]
[const]
type = GenericConstantMaterial
prop_names = 'kappa_c kappa L D Vm ka caeq kb cbeq kd cdeq gab gad gbd mu tgrad_corr_mult'
prop_values = '0 1 1.0 1.0 1.0 10.0 0.1 10.0 0.9 10.0 0.5 1.5 1.5 1.5 1.0 0.0'
[]
[Mobility]
type = DerivativeParsedMaterial
property_name = DchiVm
material_property_names = 'D chi Vm' #Factor of Vm is needed to evolve c instead of rho
expression = 'D*chi*Vm'
derivative_order = 2
[]
[chi]
type = DerivativeParsedMaterial
property_name = chi
material_property_names = 'Vm ha(etaa0,etab0,etad0) ka hb(etaa0,etab0,etad0) kb hd(etaa0,etab0,etad0) kd'
expression = '(ha/ka + hb/kb + hd/kd) / Vm^2'
coupled_variables = 'etaa0 etab0 etad0'
derivative_order = 2
[]
[hoverk_a]
type = DerivativeParsedMaterial
material_property_names = 'ha(etaa0,etab0,etad0) Vm ka'
property_name = hoverk_a
expression = 'ha / Vm / ka'
[]
[hoverk_b]
type = DerivativeParsedMaterial
material_property_names = 'hb(etaa0,etab0,etad0) Vm kb'
property_name = hoverk_b
expression = 'hb / Vm / kb'
[]
[hoverk_d]
type = DerivativeParsedMaterial
material_property_names = 'hd(etaa0,etab0,etad0) Vm kd'
property_name = hoverk_d
expression = 'hd / Vm / kd'
[]
[]
[Postprocessors]
[c_total]
type = ElementIntegralVariablePostprocessor
variable = c
[]
[]
[Executioner]
type = Transient
nl_max_its = 15
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = -pc_type
petsc_options_value = asm
l_max_its = 15
l_tol = 1.0e-3
nl_rel_tol = 1.0e-8
start_time = 0.0
num_steps = 20
nl_abs_tol = 1e-10
dt = 1.0
[]
[Outputs]
csv = true
exodus = true
[]
(modules/phase_field/test/tests/free_energy_material/CoupledValueFunctionFreeEnergy.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 10
ny = 10
nz = 0
xmin = 0
xmax = 500
ymin = 0
ymax = 500
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[GlobalParams]
op_num = 4
var_name_base = gr
[]
[Variables]
[PolycrystalVariables]
[]
[]
[Functions]
[grain_growth_energy]
type = PiecewiseMultilinear
data_file = grain_growth_energy.data
[]
[grain_growth_mu0]
type = PiecewiseMultilinear
data_file = grain_growth_mu0.data
[]
[grain_growth_mu1]
type = PiecewiseMultilinear
data_file = grain_growth_mu1.data
[]
[grain_growth_mu2]
type = PiecewiseMultilinear
data_file = grain_growth_mu2.data
[]
[grain_growth_mu3]
type = PiecewiseMultilinear
data_file = grain_growth_mu3.data
[]
[matrix]
type = ParsedFunction
expression = '1-x-y-z'
[]
[]
[ICs]
[gr1]
type = SmoothCircleIC
variable = gr1
x1 = 0
y1 = 0
radius = 150
int_width = 90
invalue = 1
outvalue = 0
[]
[gr2]
type = SmoothCircleIC
variable = gr2
x1 = 500
y1 = 0
radius = 120
int_width = 90
invalue = 1
outvalue = 0
[]
[gr3]
type = SmoothCircleIC
variable = gr3
x1 = 250
y1 = 500
radius = 300
int_width = 90
invalue = 1
outvalue = 0
[]
[gr0]
type = CoupledValueFunctionIC
variable = gr0
v = 'gr1 gr2 gr3'
function = matrix
[]
[]
[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
coupled_variables = 'gr1 gr2 gr3'
[]
[gr0int]
type = ACInterface
variable = gr0
kappa_name = kappa_op
[]
[gr1dot]
type = TimeDerivative
variable = gr1
[]
[gr1bulk]
type = AllenCahn
variable = gr1
f_name = F
coupled_variables = 'gr0 gr2 gr3'
[]
[gr1int]
type = ACInterface
variable = gr1
kappa_name = kappa_op
[]
[gr2dot]
type = TimeDerivative
variable = gr2
[]
[gr2bulk]
type = AllenCahn
variable = gr2
f_name = F
coupled_variables = 'gr0 gr1 gr3'
[]
[gr2int]
type = ACInterface
variable = gr2
kappa_name = kappa_op
[]
[gr3dot]
type = TimeDerivative
variable = gr3
[]
[gr3bulk]
type = AllenCahn
variable = gr3
f_name = F
coupled_variables = 'gr0 gr1 gr2'
[]
[gr3int]
type = ACInterface
variable = gr3
kappa_name = kappa_op
[]
[]
[AuxKernels]
[BndsCalc]
type = BndsCalcAux
variable = bnds
[]
[local_free_energy]
type = TotalFreeEnergy
variable = local_energy
kappa_names = 'kappa_op kappa_op kappa_op kappa_op'
interfacial_vars = 'gr0 gr1 gr2 gr3'
[]
[]
[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
[]
[Tabulated]
type = CoupledValueFunctionFreeEnergy
free_energy_function = grain_growth_energy
chemical_potential_functions = 'grain_growth_mu0 grain_growth_mu1 grain_growth_mu2 '
'grain_growth_mu3'
v = 'gr0 gr1 gr2 gr3'
[]
[]
[Postprocessors]
[total_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[]
[]
[Preconditioning]
[SMP]
type = SMP
coupled_groups = 'gr0,gr1 gr0,gr2 gr0,gr3'
[]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
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 = 3
dt = 100.0
[]
[Outputs]
exodus = true
print_linear_residuals = false
perf_graph = true
[]
(modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i)
#
# KKS simple example in the split form
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 150
ny = 15
nz = 0
xmin = -25
xmax = 25
ymin = -2.5
ymax = 2.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[AuxVariables]
[./Fglobal]
order = CONSTANT
family = MONOMIAL
[../]
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# solute concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# Liquid phase solute concentration
[./cl]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# Solid phase solute concentration
[./cs]
order = FIRST
family = LAGRANGE
initial_condition = 0.9
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = '0.5*(1.0-tanh((x)/sqrt(2.0)))'
[../]
[./ic_func_c]
type = ParsedFunction
expression = '0.9*(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10)+0.1*(1-(0.5*(1.0-tanh(x/sqrt(2.0))))^3*(6*(0.5*(1.0-tanh(x/sqrt(2.0))))^2-15*(0.5*(1.0-tanh(x/sqrt(2.0))))+10))'
[../]
[]
[ICs]
[./eta]
variable = eta
type = FunctionIC
function = ic_func_eta
[../]
[./c]
variable = c
type = FunctionIC
function = ic_func_c
[../]
[]
[Materials]
# Free energy of the liquid
[./fl]
type = DerivativeParsedMaterial
property_name = fl
coupled_variables = 'cl'
expression = '(0.1-cl)^2'
[../]
# Free energy of the solid
[./fs]
type = DerivativeParsedMaterial
property_name = fs
coupled_variables = 'cs'
expression = '(0.9-cs)^2'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L eps_sq'
prop_values = '0.7 0.7 1.0 '
[../]
[]
[Kernels]
active = 'PhaseConc ChemPotSolute CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'
# enforce c = (1-h(eta))*cl + h(eta)*cs
[./PhaseConc]
type = KKSPhaseConcentration
ca = cl
variable = cs
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotSolute]
type = KKSPhaseChemicalPotential
variable = cl
cb = cs
fa_name = fl
fb_name = fs
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cl
fa_name = fl
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = fl
fb_name = fs
w = 1.0
coupled_variables = 'cl cs'
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cl
cb = cs
fa_name = fl
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = eps_sq
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fl
fb_name = fs
w = 1.0
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 50
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[VectorPostprocessors]
[./c]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = c
num_points = 151
sort_by = id
execute_on = timestep_end
[../]
[./eta]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = eta
num_points = 151
sort_by = id
execute_on = timestep_end
[../]
[]
[Outputs]
exodus = true
[./csv]
type = CSV
execute_on = final
[../]
[]
(modules/phase_field/test/tests/phase_field_kernels/nonuniform_barrier_coefficient.i)
# This material tests the kernels ACBarrierFunction and ACKappaFunction for a
# multiphase system.
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = -200
xmax = 200
ymin = -200
ymax = 200
uniform_refine = 0
[]
[Variables]
[./gr0]
[../]
[./gr1]
[../]
[]
[ICs]
[./gr0_IC]
type = BoundingBoxIC
variable = gr0
x1 = -80
y1 = -80
x2 = 80
y2 = 80
inside = 0
outside = 1
[../]
[./gr1_IC]
type = BoundingBoxIC
variable = gr1
x1 = -80
y1 = -80
x2 = 80
y2 = 80
inside = 1
outside = 0
[../]
[]
[Materials]
[./constants]
type = GenericConstantMaterial
prop_names = 'L gamma E0 E1'
prop_values = '0.1 1.5 3 1'
[../]
[./h0]
type = DerivativeParsedMaterial
property_name = h0
coupled_variables = 'gr0 gr1'
expression = 'gr0^2 / (gr0^2 + gr1^2)'
derivative_order = 2
[../]
[./h1]
type = DerivativeParsedMaterial
property_name = h1
coupled_variables = 'gr0 gr1'
expression = 'gr1^2 / (gr0^2 + gr1^2)'
derivative_order = 2
[../]
[./mu]
type = DerivativeParsedMaterial
property_name = mu
coupled_variables = 'gr0 gr1'
constant_names = 'mag'
constant_expressions = '16'
expression = 'mag * (gr0^2 * gr1^2 + 0.1)'
derivative_order = 2
[../]
[./kappa]
type = DerivativeParsedMaterial
property_name = kappa
coupled_variables = 'gr0 gr1'
material_property_names = 'h0(gr0,gr1) h1(gr0,gr1)'
constant_names = 'mag0 mag1'
constant_expressions = '200 100'
expression = 'h0*mag0 + h1*mag1'
derivative_order = 2
[../]
[]
[Kernels]
[./gr0_time]
type = TimeDerivative
variable = gr0
[../]
[./gr0_interface]
type = ACInterface
variable = gr0
coupled_variables = 'gr1'
mob_name = L
kappa_name = 'kappa'
[../]
[./gr0_switching]
type = ACSwitching
variable = gr0
coupled_variables = 'gr1'
hj_names = 'h0 h1'
Fj_names = 'E0 E1'
mob_name = L
[../]
[./gr0_multi]
type = ACGrGrMulti
variable = gr0
v = 'gr1'
mob_name = L
gamma_names = 'gamma'
[../]
[./gr0_barrier]
type = ACBarrierFunction
variable = gr0
mob_name = L
gamma = gamma
v = 'gr1'
[../]
[./gr0_kappa]
type = ACKappaFunction
variable = gr0
mob_name = L
kappa_name = kappa
v = 'gr1'
[../]
[./gr1_time]
type = TimeDerivative
variable = gr1
[../]
[./gr1_interface]
type = ACInterface
variable = gr1
coupled_variables = 'gr0'
mob_name = L
kappa_name = 'kappa'
[../]
[./gr1_switching]
type = ACSwitching
variable = gr1
coupled_variables = 'gr0'
hj_names = 'h0 h1'
Fj_names = 'E0 E1'
mob_name = L
[../]
[./gr1_multi]
type = ACGrGrMulti
variable = gr1
v = 'gr0'
mob_name = L
gamma_names = 'gamma'
[../]
[./gr1_barrier]
type = ACBarrierFunction
variable = gr1
mob_name = L
gamma = gamma
v = 'gr0'
[../]
[./gr1_kappa]
type = ACKappaFunction
variable = gr1
mob_name = L
kappa_name = kappa
v = 'gr0'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = NEWTON
petsc_options_iname = '-pc_type -sub_pc_type -pc_asm_overlap -ksp_gmres_restart -sub_ksp_type'
petsc_options_value = ' asm ilu 1 31 preonly'
nl_max_its = 20
l_max_its = 30
l_tol = 1e-4
nl_rel_tol = 1e-12
nl_abs_tol = 1e-12
start_time = 0
num_steps = 3
dt = 1
[]
[Outputs]
exodus = 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
coupled_variables = gr1
[../]
[./gr0int]
type = ACInterface
variable = gr0
kappa_name = kappa_op
[../]
[./gr1dot]
type = TimeDerivative
variable = gr1
[../]
[./gr1bulk]
type = AllenCahn
variable = gr1
f_name = F
coupled_variables = 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
coupled_variables = 'gr0 gr1'
material_property_names = 'mu gamma_asymm'
expression = '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-10
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'
exodus = true
[]
(modules/phase_field/test/tests/MultiPhase/switchingfunctionmultiphasematerial.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 30
ny = 30
xmin = 0
xmax = 30
ymin = 0
ymax = 30
[]
[Variables]
[./c]
[../]
[./w]
[../]
[./eta1]
[../]
[./eta2]
[../]
[./eta3]
[../]
[./eta0]
[../]
[]
[ICs]
[./IC_eta2]
x1 = 0
y1 = 15
x2 = 30
y2 = 30
inside = 1.0
outside = 0.0
type = BoundingBoxIC
variable = eta2
int_width = 0
[../]
[./IC_eta3]
x1 = 15
y1 = 0
x2 = 30
y2 = 15
inside = 1.0
outside = 0.0
type = BoundingBoxIC
variable = eta3
int_width = 0
[../]
[./IC_eta4]
x1 = 0
y1 = 0
x2 = 15
y2 = 15
inside = 1.0
outside = 0.0
type = BoundingBoxIC
variable = eta0
int_width = 0
[../]
[./IC_c]
x1 = 15
y1 = 15
radius = 8.0
outvalue = 0.05
variable = c
invalue = 1.0
type = SmoothCircleIC
int_width = 3.0
[../]
[./IC_eta1]
x1 = 15
y1 = 15
radius = 8.0
outvalue = 0.0
variable = eta1
invalue = 1.0
type = SmoothCircleIC
int_width = 3.0
[../]
[]
# Not evalulating time evolution to improve test performance, since we are only testing
# the material property. However, the kernel and free energy are left in place to allow
# this test to be easily turned in to a working example
#[Kernels]
# [./c_dot]
# type = CoupledTimeDerivative
# variable = w
# v = c
# [../]
# [./c_res]
# type = SplitCHParsed
# variable = c
# f_name = F
# kappa_name = kappa_c
# w = w
# coupled_variables = 'eta1 eta2 eta3 eta0'
# [../]
# [./w_res]
# # coupled_variables = 'c'
# type = SplitCHWRes
# variable = w
# mob_name = M
# [../]
# [./AC1_bulk]
# type = AllenCahn
# variable = eta1
# f_name = F
# coupled_variables = 'c eta2 eta3 eta0'
# [../]
# [./AC1_int]
# type = ACInterface
# variable = eta1
# kappa_name = kappa_s
# [../]
# [./e1_dot]
# type = TimeDerivative
# variable = eta1
# [../]
# [./AC2_bulk]
# type = AllenCahn
# variable = eta2
# f_name = F
# coupled_variables = 'c eta1 eta3 eta0'
# [../]
# [./AC2_int]
# type = ACInterface
# variable = eta2
# [../]
# [./e2_dot]
# type = TimeDerivative
# variable = eta2
# [../]
# [./AC3_bulk]
# type = AllenCahn
# variable = eta3
# f_name = F
# coupled_variables = 'c eta2 eta1 eta0'
# [../]
# [./AC3_int]
# type = ACInterface
# variable = eta3
# [../]
# [./e3_dot]
# type = TimeDerivative
# variable = eta3
# [../]
# [./AC4_bulk]
# type = AllenCahn
# variable = eta0
# f_name = F
# coupled_variables = 'c eta2 eta3 eta1'
# [../]
# [./AC4_int]
# type = ACInterface
# variable = eta0
# [../]
# [./e4_dot]
# type = TimeDerivative
# variable = eta0
# [../]
#[]
[Materials]
[./ha_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = ha
all_etas = 'eta0 eta1 eta2 eta3'
phase_etas = 'eta1'
outputs = exodus
[../]
[./hb_test]
type = SwitchingFunctionMultiPhaseMaterial
h_name = hb
all_etas = 'eta0 eta1 eta2 eta3'
phase_etas = 'eta0 eta2 eta3'
outputs = exodus
[../]
#[./ha]
# type = DerivativeParsedMaterial
# coupled_variables = 'eta1 eta2 eta3 eta0'
# property_name = ha_parsed
# expression = 'eta1^2/(eta1^2+eta2^2+eta3^2+eta0^2)'
# derivative_order = 2
# outputs = exodus
#[../]
#[./hb]
# type = DerivativeParsedMaterial
# coupled_variables = 'eta1 eta2 eta3 eta0'
# property_name = hb_parsed
# expression = '(eta2^2+eta3^2+eta0^2)/(eta1^2+eta2^2+eta3^2+eta0^2)'
# derivative_order = 2
# outputs = exodus
#[../]
#[./FreeEng]
# type = DerivativeParsedMaterial
# coupled_variables = 'c eta1 eta2 eta3 eta0'
# property_name = F
# constant_names = 'c1 c2 s g d e h z'
# constant_expressions = '1.0 0.0 1.5 1.5 1.0 1.0 1 1.0'
# material_property_names = 'ha(eta1,eta2,eta3,eta0) hb(eta1,eta2,eta3,eta0)'
# expression = 'a:=eta1^2/(eta1^2+eta2^2+eta3^2+eta0^2);f1:=ha*(c-c1)^2;b:=(eta2^2+eta3^2+eta0^2)/(eta1^2+eta2^2+eta3^2+eta0^2);f2:=hb*(c-c2)^2
# ;f3:=1/4*eta1^4-1/2*eta1^2+1/4*eta2^4-1/2*eta2^2+1/4*eta3^4-1/2*eta3^2+1/4*eta0^4-1/2*eta0^2
# ;f4:=z*s*(eta1^2*eta2^2+eta1^2*eta3^2+eta1^2*eta0^2)+g*(eta2^2*eta3^2+eta2^2*eta0^2+eta3^2*eta0^2);f:=1/4+e*f1+d*f2+h*(f3+f4);f'
# derivative_order = 2
#[../]
[./const]
type = GenericConstantMaterial
prop_names = 'kappa_c kappa_s kappa_op L M'
prop_values = '0 3 3 1.0 1.0'
outputs = exodus
[../]
[]
[Executioner]
type = Transient
num_steps = 1
[]
[Problem]
solve = false
kernel_coverage_check = false
[]
[Outputs]
exodus = true
[]
(modules/phase_field/test/tests/MultiPhase/derivativetwophasematerial.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 14
ny = 10
nz = 0
xmin = 10
xmax = 40
ymin = 15
ymax = 35
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 30.0
y1 = 25.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[]
[Kernels]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[./ACBulk]
type = AllenCahn
variable = eta
coupled_variables = c
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa_eta
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = 'eta'
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1 1 '
[../]
[./consts2]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1 1'
[../]
[./switching]
type = SwitchingFunctionMaterial
eta = eta
h_order = SIMPLE
[../]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
g_order = SIMPLE
[../]
[./free_energy_A]
type = DerivativeParsedMaterial
property_name = Fa
coupled_variables = 'c'
expression = '(c-0.1)^2*(c-1)^2 + c*0.01'
derivative_order = 2
enable_jit = true
[../]
[./free_energy_B]
type = DerivativeParsedMaterial
property_name = Fb
coupled_variables = 'c'
expression = 'c^2*(c-0.9)^2 + (1-c)*0.01'
derivative_order = 2
enable_jit = true
[../]
[./free_energy]
type = DerivativeTwoPhaseMaterial
property_name = F
fa_name = Fa
fb_name = Fb
coupled_variables = 'c'
eta = eta
derivative_order = 2
outputs = exodus
output_properties = 'F dF/dc dF/deta d^2F/dc^2 d^2F/dcdeta d^2F/deta^2'
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'NEWTON'
l_max_its = 15
l_tol = 1.0e-4
nl_max_its = 10
nl_rel_tol = 1.0e-11
start_time = 0.0
num_steps = 1
dt = 0.1
[]
[Outputs]
exodus = true
[]
(modules/phase_field/test/tests/rigidbodymotion/grain_motion.i)
# test file for applyting advection term and observing rigid body motion of grains
[Mesh]
type = GeneratedMesh
dim = 2
nx = 25
ny = 15
nz = 0
xmax = 50
ymax = 25
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = eta
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./motion]
type = MultiGrainRigidBodyMotion
variable = w
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./eta_dot]
type = TimeDerivative
variable = eta
[../]
[./vadv_eta]
type = SingleGrainRigidBodyMotion
variable = eta
c = c
v = eta
grain_tracker_object = grain_center
grain_force = grain_force
grain_volumes = grain_volumes
[../]
[./acint_eta]
type = ACInterface
variable = eta
mob_name = M
coupled_variables = c
kappa_name = kappa_eta
[../]
[./acbulk_eta]
type = AllenCahn
variable = eta
mob_name = M
f_name = F
coupled_variables = c
[../]
[]
[Materials]
[./pfmobility]
type = GenericConstantMaterial
prop_names = 'M kappa_c kappa_eta'
prop_values = '5.0 2.0 0.1'
[../]
[./free_energy]
type = DerivativeParsedMaterial
coupled_variables = 'c eta'
constant_names = 'barr_height cv_eq'
constant_expressions = '0.1 1.0e-2'
expression = 16*barr_height*(c-cv_eq)^2*(1-cv_eq-c)^2+(c-eta)^2
derivative_order = 2
[../]
[]
[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
variable = eta
outputs = none
compute_var_to_feature_map = true
execute_on = 'initial timestep_begin'
[../]
[./grain_force]
type = ConstantGrainForceAndTorque
execute_on = 'linear nonlinear'
force = '0.5 0.0 0.0 '
torque = '0.0 0.0 10.0 '
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
nl_max_its = 30
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 lu 1'
l_max_its = 30
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
start_time = 0.0
dt = 0.2
num_steps = 1
[]
[Outputs]
exodus = true
[]
[ICs]
[./rect_c]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = c
x1 = 10.0
type = BoundingBoxIC
[../]
[./rect_eta]
y2 = 20.0
y1 = 5.0
inside = 1.0
x2 = 30.0
variable = eta
x1 = 10.0
type = BoundingBoxIC
[../]
[]
(modules/combined/test/tests/phase_field_fracture/crack2d_iso_wo_time.i)
#This input does not add time derivative kernel for phase field equation
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 20
ny = 10
ymax = 0.5
[]
[./noncrack]
type = BoundingBoxNodeSetGenerator
new_boundary = noncrack
bottom_left = '0.5 0 0'
top_right = '1 0 0'
input = gen
[../]
[]
[GlobalParams]
displacements = 'disp_x disp_y'
[]
[Physics]
[./SolidMechanics]
[./QuasiStatic]
[./mech]
add_variables = true
strain = SMALL
additional_generate_output = 'stress_yy'
save_in = 'resid_x resid_y'
[../]
[../]
[../]
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[../]
[]
[AuxVariables]
[./resid_x]
[../]
[./resid_y]
[../]
[]
[Kernels]
[./solid_x]
type = PhaseFieldFractureMechanicsOffDiag
variable = disp_x
component = 0
c = c
[../]
[./solid_y]
type = PhaseFieldFractureMechanicsOffDiag
variable = disp_y
component = 1
c = c
[../]
[./ACBulk]
type = AllenCahn
variable = c
f_name = F
[../]
[./ACInterface]
type = ACInterface
variable = c
kappa_name = kappa_op
[../]
[]
[BCs]
[./ydisp]
type = FunctionDirichletBC
variable = disp_y
boundary = top
function = 't'
[../]
[./yfix]
type = DirichletBC
variable = disp_y
boundary = noncrack
value = 0
[../]
[./xfix]
type = DirichletBC
variable = disp_x
boundary = top
value = 0
[../]
[]
[Materials]
[./pfbulkmat]
type = GenericConstantMaterial
prop_names = 'gc_prop l visco'
prop_values = '1e-3 0.04 1e-4'
[../]
[./define_mobility]
type = ParsedMaterial
material_property_names = 'gc_prop visco'
property_name = L
expression = '1.0/(gc_prop * visco)'
[../]
[./define_kappa]
type = ParsedMaterial
material_property_names = 'gc_prop l'
property_name = kappa_op
expression = 'gc_prop * l'
[../]
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '120.0 80.0'
fill_method = symmetric_isotropic
[../]
[./elastic]
type = ComputeLinearElasticPFFractureStress
c = c
E_name = 'elastic_energy'
D_name = 'degradation'
F_name = 'local_fracture_energy'
decomposition_type = strain_spectral
[../]
[./degradation]
type = DerivativeParsedMaterial
property_name = degradation
coupled_variables = 'c'
expression = '(1.0-c)^2*(1.0 - eta) + eta'
constant_names = 'eta'
constant_expressions = '0.0'
derivative_order = 2
[../]
[./local_fracture_energy]
type = DerivativeParsedMaterial
property_name = local_fracture_energy
coupled_variables = 'c'
material_property_names = 'gc_prop l'
expression = 'c^2 * gc_prop / 2 / l'
derivative_order = 2
[../]
[./fracture_driving_energy]
type = DerivativeSumMaterial
coupled_variables = c
sum_materials = 'elastic_energy local_fracture_energy'
derivative_order = 2
property_name = F
[../]
[]
[Postprocessors]
[./resid_x]
type = NodalSum
variable = resid_x
boundary = 2
[../]
[./resid_y]
type = NodalSum
variable = resid_y
boundary = 2
[../]
[]
[Preconditioning]
[./smp]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = PJFNK
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'
nl_rel_tol = 1e-8
l_max_its = 10
nl_max_its = 10
dt = 1e-4
dtmin = 1e-4
num_steps = 2
[]
[Outputs]
exodus = true
[]
(modules/combined/examples/phase_field-mechanics/Nonconserved.i)
#
# Example 2
# Phase change driven by a mechanical (elastic) driving force.
# An oversized phase inclusion grows under a uniaxial tensile stress.
# Check the file below for comments and suggestions for parameter modifications.
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 40
ny = 40
nz = 0
xmin = 0
xmax = 50
ymin = 0
ymax = 50
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[Variables]
[./eta]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 0
y1 = 0
radius = 30.0
invalue = 1.0
outvalue = 0.0
int_width = 10.0
[../]
[../]
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
[]
[Kernels]
[./TensorMechanics]
displacements = 'disp_x disp_y'
[../]
[./eta_bulk]
type = AllenCahn
variable = eta
f_name = F
[../]
[./eta_interface]
type = ACInterface
variable = eta
kappa_name = 1
[../]
[./time]
type = TimeDerivative
variable = eta
[../]
[]
#
# Try visualizing the stress tensor components as done in Conserved.i
#
[Materials]
[./consts]
type = GenericConstantMaterial
block = 0
prop_names = 'L'
prop_values = '1'
[../]
# matrix phase
[./stiffness_a]
type = ComputeElasticityTensor
base_name = phasea
block = 0
# lambda, mu values
C_ijkl = '7 7'
# Stiffness tensor is created from lambda=7, mu=7 for symmetric_isotropic fill method
fill_method = symmetric_isotropic
# See RankFourTensor.h for details on fill methods
[../]
[./strain_a]
type = ComputeSmallStrain
block = 0
displacements = 'disp_x disp_y'
base_name = phasea
[../]
[./stress_a]
type = ComputeLinearElasticStress
block = 0
base_name = phasea
[../]
[./elastic_free_energy_a]
type = ElasticEnergyMaterial
base_name = phasea
f_name = Fea
block = 0
coupled_variables = ''
[../]
# oversized precipitate phase (simulated using thermal expansion)
[./stiffness_b]
type = ComputeElasticityTensor
base_name = phaseb
block = 0
# Stiffness tensor lambda, mu values
# Note that the two phases could have different stiffnesses.
# Try reducing the precipitate stiffness (to '1 1') rather than making it oversized
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_b]
type = ComputeSmallStrain
block = 0
displacements = 'disp_x disp_y'
base_name = phaseb
eigenstrain_names = eigenstrain
[../]
[./eigenstrain_b]
type = ComputeEigenstrain
base_name = phaseb
eigen_base = '0.1 0.1 0.1'
eigenstrain_name = eigenstrain
[../]
[./stress_b]
type = ComputeLinearElasticStress
block = 0
base_name = phaseb
[../]
[./elastic_free_energy_b]
type = ElasticEnergyMaterial
base_name = phaseb
f_name = Feb
block = 0
coupled_variables = ''
[../]
# Generate the global free energy from the phase free energies
[./switching]
type = SwitchingFunctionMaterial
block = 0
eta = eta
h_order = SIMPLE
[../]
[./barrier]
type = BarrierFunctionMaterial
block = 0
eta = eta
g_order = SIMPLE
[../]
[./free_energy]
type = DerivativeTwoPhaseMaterial
block = 0
f_name = F
fa_name = Fea
fb_name = Feb
eta = eta
coupled_variables = ''
W = 0.1
derivative_order = 2
[../]
# Generate the global stress from the phase stresses
[./global_stress]
type = TwoPhaseStressMaterial
block = 0
base_A = phasea
base_B = phaseb
[../]
[]
[BCs]
[./bottom_y]
type = DirichletBC
variable = disp_y
boundary = 'bottom'
value = 0
[../]
[./top_y]
type = DirichletBC
variable = disp_y
boundary = 'top'
value = 5
[../]
[./left_x]
type = DirichletBC
variable = disp_x
boundary = 'left'
value = 0
[../]
[]
[Preconditioning]
# active = ' '
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
# this gives best performance on 4 cores
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type '
petsc_options_value = 'asm lu'
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 = 0.2
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_nested.i)
#
# Two-phase nested KKS toy problem
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 15
ny = 15
nz = 0
xmin = -2.5
xmax = 2.5
ymin = -2.5
ymax = 2.5
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# order parameter
[eta]
order = FIRST
family = LAGRANGE
[]
# hydrogen concentration
[c]
order = FIRST
family = LAGRANGE
[]
# chemical potential
[w]
order = FIRST
family = LAGRANGE
[]
[]
[ICs]
[eta]
variable = eta
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.2
outvalue = 0.1
int_width = 0.75
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 0.0
y1 = 0.0
radius = 1.5
invalue = 0.6
outvalue = 0.4
int_width = 0.75
[]
[]
[BCs]
[Periodic]
[all]
variable = 'eta w c'
auto_direction = 'x y'
[]
[]
[]
[Materials]
# Free energy of the matrix
[fm]
type = DerivativeParsedMaterial
property_name = fm
expression = '(0.1-cm)^2'
material_property_names = 'cm'
additional_derivative_symbols = 'cm'
compute = false
[]
# Free energy of the delta phase
[fd]
type = DerivativeParsedMaterial
property_name = fd
expression = '(0.9-cd)^2'
material_property_names = 'cd'
additional_derivative_symbols = 'cd'
compute = false
[]
# Compute phase concentrations
[PhaseConcentrationMaterial]
type = KKSPhaseConcentrationMaterial
global_cs = 'c'
ci_names = 'cm cd'
ci_IC = '0 0'
fa_name = fm
fb_name = fd
h_name = h
min_iterations = 1
max_iterations = 100
absolute_tolerance = 1e-9
relative_tolerance = 1e-9
nested_iterations = iter
outputs = exodus
[]
# Compute chain rule terms
[PhaseConcentrationDerivatives]
type = KKSPhaseConcentrationDerivatives
global_cs = 'c'
eta = eta
ci_names = 'cm cd'
fa_name = fm
fb_name = fd
h_name = h
[]
# h(eta)
[h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[]
# g(eta)
[g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'M L kappa'
prop_values = '0.7 0.7 0.4 '
[]
[]
[Kernels]
# full transient
active = 'CHBulk ACBulkF ACBulkC ACInterface dcdt detadt ckernel'
#
# Cahn-Hilliard Equation
#
[CHBulk]
type = NestedKKSSplitCHCRes
variable = c
global_cs = 'c'
w = w
all_etas = eta
ca_names = 'cm cd'
fa_name = fm
coupled_variables = 'eta w'
[]
[dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[]
[ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[]
#
# Allen-Cahn Equation
#
[ACBulkF]
type = NestedKKSACBulkF
variable = eta
global_cs = 'c'
ci_names = 'cm cd'
fa_name = fm
fb_name = fd
g_name = g
h_name = h
mob_name = L
w = 0.4
coupled_variables = 'c'
[]
[ACBulkC]
type = NestedKKSACBulkC
variable = eta
global_cs = 'c'
ci_names = 'cm cd'
fa_name = fm
h_name = h
mob_name = L
coupled_variables = 'c'
[]
[ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[]
[detadt]
type = TimeDerivative
variable = eta
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fd
w = 0.4
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 3
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[full]
type = SMP
full = true
[]
[]
[Outputs]
file_base = kks_example_nested
exodus = true
[]
(modules/phase_field/test/tests/MultiPhase/mixedswitchingfunctionmaterial.i)
# This is a test of the MixedSwitchingfunctionmaterial
# Several mixed type of switching function with ajustable weight parameter
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
xmin = 0
xmax = 20
ymin = 0
ymax = 20
elem_type = QUAD4
[]
[Variables]
[./eta]
[../]
[]
[ICs]
[./IC_eta]
type = SmoothCircleIC
variable = eta
x1 = 10
y1 = 10
radius = 5
invalue = 1
outvalue = 0
int_width = 1
[../]
[]
[Kernels]
[./eta_bulk]
type = AllenCahn
variable = eta
f_name = F
[../]
[./eta_interface]
type = ACInterface
variable = eta
kappa_name = kappa_eta
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1.0 1.0'
[../]
[./switching]
type = MixedSwitchingFunctionMaterial
function_name = h
eta = eta
h_order = MIX234
weight = 1.0
[../]
[./barrier]
type = BarrierFunctionMaterial
eta = eta
g_order = SIMPLE
[../]
# Total free energy: F = Fa*(1-h) + Fb*h
[./free_energy]
type = DerivativeTwoPhaseMaterial
property_name = F
fa_name = '0'
fb_name = '-1'
eta = eta
W = 3.1
derivative_order = 2
outputs = exodus
[../]
[]
[BCs]
[./Periodic]
[./all]
auto_direction = 'x y'
[../]
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-12
start_time = 0.0
num_steps = 2
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 9
iteration_window = 2
growth_factor = 1.1
cutback_factor = 0.75
dt = 0.3
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/combined/test/tests/surface_tension_KKS/surface_tension_KKS.i)
#
# KKS coupled with elasticity. Physical parameters for matrix and precipitate phases
# are gamma and gamma-prime phases, respectively, in the Ni-Al system.
# Parameterization is as described in L.K. Aagesen et al., Computational Materials
# Science, 140, 10-21 (2017), with isotropic elastic properties in both phases
# and without eigenstrain.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 200
xmax = 200
coord_type = RSPHERICAL
[]
[GlobalParams]
displacements = 'disp_x'
[]
[Variables]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
[../]
# solute concentration
[./c]
order = FIRST
family = LAGRANGE
[../]
# chemical potential
[./w]
order = FIRST
family = LAGRANGE
[../]
# solute phase concentration (matrix)
[./cm]
order = FIRST
family = LAGRANGE
initial_condition = 0.13
[../]
# solute phase concentration (precipitate)
[./cp]
order = FIRST
family = LAGRANGE
initial_condition = 0.235
[../]
[]
[AuxVariables]
[./energy_density]
family = MONOMIAL
[../]
[./extra_xx]
order = CONSTANT
family = MONOMIAL
[../]
[./extra_yy]
order = CONSTANT
family = MONOMIAL
[../]
[./extra_zz]
order = CONSTANT
family = MONOMIAL
[../]
[./strain_xx]
order = CONSTANT
family = MONOMIAL
[../]
[./strain_yy]
order = CONSTANT
family = MONOMIAL
[../]
[./strain_zz]
order = CONSTANT
family = MONOMIAL
[../]
[]
[ICs]
[./eta_ic]
variable = eta
type = FunctionIC
function = ic_func_eta
[../]
[./c_ic]
variable = c
type = FunctionIC
function = ic_func_c
[../]
[]
[Functions]
[./ic_func_eta]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2+z^2);0.5*(1.0-tanh((r-r0)/delta_eta/sqrt(2.0)))'
symbol_names = 'delta_eta r0'
symbol_values = '6.431 100'
[../]
[./ic_func_c]
type = ParsedFunction
expression = 'r:=sqrt(x^2+y^2+z^2);eta_an:=0.5*(1.0-tanh((r-r0)/delta/sqrt(2.0)));0.235*eta_an^3*(6*eta_an^2-15*eta_an+10)+0.13*(1-eta_an^3*(6*eta_an^2-15*eta_an+10))'
symbol_names = 'delta r0'
symbol_values = '6.431 100'
[../]
[]
[Physics/SolidMechanics/QuasiStatic]
[./all]
add_variables = true
generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz'
[../]
[]
[Kernels]
# enforce c = (1-h(eta))*cm + h(eta)*cp
[./PhaseConc]
type = KKSPhaseConcentration
ca = cm
variable = cp
c = c
eta = eta
[../]
# enforce pointwise equality of chemical potentials
[./ChemPotVacancies]
type = KKSPhaseChemicalPotential
variable = cm
cb = cp
fa_name = f_total_matrix
fb_name = f_total_ppt
[../]
#
# Cahn-Hilliard Equation
#
[./CHBulk]
type = KKSSplitCHCRes
variable = c
ca = cm
fa_name = f_total_matrix
w = w
[../]
[./dcdt]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[./ckernel]
type = SplitCHWRes
mob_name = M
variable = w
[../]
#
# Allen-Cahn Equation
#
[./ACBulkF]
type = KKSACBulkF
variable = eta
fa_name = f_total_matrix
fb_name = f_total_ppt
w = 0.0033
coupled_variables = 'cp cm'
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cp
fa_name = f_total_matrix
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./extra_xx]
type = RankTwoAux
rank_two_tensor = extra_stress
index_i = 0
index_j = 0
variable = extra_xx
[../]
[./extra_yy]
type = RankTwoAux
rank_two_tensor = extra_stress
index_i = 1
index_j = 1
variable = extra_yy
[../]
[./extra_zz]
type = RankTwoAux
rank_two_tensor = extra_stress
index_i = 2
index_j = 2
variable = extra_zz
[../]
[./strain_xx]
type = RankTwoAux
rank_two_tensor = mechanical_strain
index_i = 0
index_j = 0
variable = strain_xx
[../]
[./strain_yy]
type = RankTwoAux
rank_two_tensor = mechanical_strain
index_i = 1
index_j = 1
variable = strain_yy
[../]
[./strain_zz]
type = RankTwoAux
rank_two_tensor = mechanical_strain
index_i = 2
index_j = 2
variable = strain_zz
[../]
[]
[Materials]
# Chemical free energy of the matrix
[./fm]
type = DerivativeParsedMaterial
property_name = fm
coupled_variables = 'cm'
expression = '6.55*(cm-0.13)^2'
[../]
# Elastic energy of the matrix
[./elastic_free_energy_m]
type = ElasticEnergyMaterial
base_name = matrix
f_name = fe_m
coupled_variables = ' '
[../]
# Total free energy of the matrix
[./Total_energy_matrix]
type = DerivativeSumMaterial
property_name = f_total_matrix
sum_materials = 'fm fe_m'
coupled_variables = 'cm'
[../]
# Free energy of the precipitate phase
[./fp]
type = DerivativeParsedMaterial
property_name = fp
coupled_variables = 'cp'
expression = '6.55*(cp-0.235)^2'
[../]
# Elastic energy of the precipitate
[./elastic_free_energy_p]
type = ElasticEnergyMaterial
base_name = ppt
f_name = fe_p
coupled_variables = ' '
[../]
# Total free energy of the precipitate
[./Total_energy_ppt]
type = DerivativeSumMaterial
property_name = f_total_ppt
sum_materials = 'fp fe_p'
coupled_variables = 'cp'
[../]
# Total elastic energy
[./Total_elastic_energy]
type = DerivativeTwoPhaseMaterial
eta = eta
f_name = f_el_mat
fa_name = fe_m
fb_name = fe_p
outputs = exodus
W = 0
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
[../]
# g(eta)
[./g_eta]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta
outputs = exodus
[../]
# constant properties
[./constants]
type = GenericConstantMaterial
prop_names = 'M L kappa'
prop_values = '0.7 0.7 0.1365'
[../]
#Mechanical properties
[./Stiffness_matrix]
type = ComputeElasticityTensor
C_ijkl = '74.25 14.525'
base_name = matrix
fill_method = symmetric_isotropic
[../]
[./Stiffness_ppt]
type = ComputeElasticityTensor
C_ijkl = '74.25 14.525'
base_name = ppt
fill_method = symmetric_isotropic
[../]
[./strain_matrix]
type = ComputeRSphericalSmallStrain
base_name = matrix
[../]
[./strain_ppt]
type = ComputeRSphericalSmallStrain
base_name = ppt
[../]
[./stress_matrix]
type = ComputeLinearElasticStress
base_name = matrix
[../]
[./stress_ppt]
type = ComputeLinearElasticStress
base_name = ppt
[../]
[./global_stress]
type = TwoPhaseStressMaterial
base_A = matrix
base_B = ppt
[../]
[./interface_stress]
type = ComputeSurfaceTensionKKS
v = eta
kappa_name = kappa
w = 0.0033
[../]
[]
[BCs]
[./left_r]
type = DirichletBC
variable = disp_x
boundary = left
value = 0
[../]
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm lu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-9
nl_abs_tol = 1.0e-10
num_steps = 2
dt = 0.5
[]
[Outputs]
exodus = true
[./csv]
type = CSV
execute_on = 'final'
[../]
[]
(modules/phase_field/include/kernels/ACInterface2DMultiPhase1.h)
// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html
#pragma once
#include "Kernel.h"
#include "JvarMapInterface.h"
#include "DerivativeMaterialInterface.h"
#include "ACInterface.h"
/**
* Compute the Allen-Cahn interface term with the weak form residual
* \f$ \left(\nabla (L \psi), 1/2 {\partial \kappa} \over {\partial \nabla \eta_{\alpha i}}
* \sum \{(\nabla \eta_{\beta j})^2 \} \right) \f$
*/
class ACInterface2DMultiPhase1 : public ACInterface
{
public:
static InputParameters validParams();
ACInterface2DMultiPhase1(const InputParameters & parameters);
protected:
virtual Real computeQpResidual();
virtual Real computeQpJacobian();
virtual Real computeQpOffDiagJacobian(unsigned int jvar);
Real sumSquareGradEta();
/// Interfacial parameter
const MaterialProperty<RealGradient> & _dkappadgrad_etaa;
const MaterialProperty<RealTensorValue> & _d2kappadgrad_etaa;
/// Order parameters
unsigned int _num_etas;
std::vector<const VariableValue *> _eta;
std::vector<const VariableGradient *> _grad_eta;
};
(modules/phase_field/include/kernels/ACInterface2DMultiPhase2.h)
// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html
#pragma once
#include "Kernel.h"
#include "JvarMapInterface.h"
#include "DerivativeMaterialInterface.h"
#include "ACInterface.h"
/**
* Compute the Allen-Cahn interface term with the weak form residual
* \f$ \left( \kappa \nabla \eta_{\alpha i}, \nabla (L \psi) \right) \f$
* It is assumed kappa is a function of gradients of two order parameters eta_alpha and eta_beta.
* Therefore, kappa depends on multiple order parameters.
*/
class ACInterface2DMultiPhase2 : public ACInterface
{
public:
static InputParameters validParams();
ACInterface2DMultiPhase2(const InputParameters & parameters);
protected:
virtual Real computeQpJacobian();
virtual Real computeQpOffDiagJacobian(unsigned int jvar);
/// Interfacial parameter
const MaterialProperty<RealGradient> & _dkappadgrad_etaa;
};
(modules/phase_field/include/kernels/ACInterfaceChangedVariable.h)
// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html
/// Considers cleavage plane anisotropy in the crack propagation
#pragma once
#include "ACInterface.h"
class ACInterfaceChangedVariable : public ACInterface
{
public:
static InputParameters validParams();
ACInterfaceChangedVariable(const InputParameters & parameters);
virtual void initialSetup();
protected:
virtual Real computeQpResidual();
virtual Real computeQpJacobian();
/// Order parameter derivative
const MaterialProperty<Real> & _dopdu;
/// 2nd order parameter derivative
const MaterialProperty<Real> & _d2opdu2;
};
(modules/phase_field/include/kernels/ACInterfaceCleavageFracture.h)
// This file is part of the MOOSE framework
// https://mooseframework.inl.gov
//
// All rights reserved, see COPYRIGHT for full restrictions
// https://github.com/idaholab/moose/blob/master/COPYRIGHT
//
// Licensed under LGPL 2.1, please see LICENSE for details
// https://www.gnu.org/licenses/lgpl-2.1.html
/// Considers cleavage plane anisotropy in the crack propagation
#pragma once
#include "ACInterface.h"
class ACInterfaceCleavageFracture : public ACInterface
{
public:
static InputParameters validParams();
ACInterfaceCleavageFracture(const InputParameters & parameters);
protected:
virtual Real computeQpResidual();
virtual Real computeQpJacobian();
/// term with beta penalty
Real betaNablaPsi();
/// penalty for damage on planes not normal to the weak (favoured) cleavage
/// plane (Clayton & Knap, 2015)
const Real _beta_penalty;
/// Plane normal to the weak cleavage plane: M in (Clayton & Knap, 2015)
const RealVectorValue _cleavage_plane_normal;
};