- cbPhase b concentration
C++ Type:std::vector<VariableName>
Controllable:No
Description:Phase b concentration
- fa_nameBase name of the free energy function Fa (f_name in the corresponding derivative function material)
C++ Type:MaterialPropertyName
Controllable:No
Description:Base name of the free energy function Fa (f_name in the corresponding derivative function material)
- fb_nameBase name of the free energy function Fb (f_name in the corresponding derivative function material)
C++ Type:MaterialPropertyName
Controllable:No
Description:Base name of the free energy function Fb (f_name in the corresponding derivative function material)
- variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on
KKSPhaseChemicalPotential
KKS model kernel to enforce the pointwise equality of phase chemical potentials . The non-linear variable of this kernel is .
Enforces the point wise equality of the phase chemical potentials
The non-linear variable of this Kernel is .
Residual
Jacobian
For the Jacobian we need to calculate
On-Diagonal
Off-Diagonal
With the union of the argument vectors of and (represented in the code by _coupled_moose_vars[]) we get
Again the is non-zero only if , which is the case if is the argument selected through jvar.
Note that in the code jvar is not an index into _coupled_moose_vars[] but has to be resolved through the _jvar_map.
Input Parameters
- args_aVector of further parameters to Fa (optional, to add in second cross derivatives of Fa)
C++ Type:std::vector<VariableName>
Controllable:No
Description:Vector of further parameters to Fa (optional, to add in second cross derivatives of Fa)
- args_bVector of further parameters to Fb (optional, to add in second cross derivatives of Fb)
C++ Type:std::vector<VariableName>
Controllable:No
Description:Vector of further parameters to Fb (optional, to add in second cross derivatives of Fb)
- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements
- ka1Site fraction for the ca variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)
Default:1
C++ Type:double
Controllable:No
Description:Site fraction for the ca variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)
- kb1Site fraction for the cb variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)
Default:1
C++ Type:double
Controllable:No
Description:Site fraction for the cb variable (specify this if ca is a sublattice concentration, and make sure it is a true site fraction eg. 0.6666666)
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
- 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.
Optional Parameters
- absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill
Tagging Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
Input Files
- (modules/phase_field/test/tests/KKS_system/nonlinear.i)
- (modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i)
- (modules/phase_field/test/tests/KKS_system/auxkernel.i)
- (modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_split.i)
- (modules/combined/test/tests/surface_tension_KKS/surface_tension_VDWgas.i)
- (modules/phase_field/test/tests/KKS_system/kks_example.i)
- (modules/combined/test/tests/surface_tension_KKS/surface_tension_KKS.i)
- (modules/phase_field/test/tests/KKS_system/two_phase.i)
- (modules/phase_field/test/tests/KKS_system/kks_phase_concentration.i)
- (modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_offset.i)
- (modules/phase_field/test/tests/KKS_system/kks_multiphase.i)
- (modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i)
- (modules/phase_field/test/tests/KKS_system/lagrange_multiplier.i)
- (modules/phase_field/examples/slkks/CrFe.i)
- (modules/phase_field/test/tests/slkks/full_solve.i)
- (modules/combined/examples/publications/rapid_dev/fig6.i)
- (modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i)
(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_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/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/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
args = '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
args = 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
args = '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/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/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
[]
[Problem]
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'
[../]
[]
[Modules/TensorMechanics/Master]
[./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
args = 'cvm cvb cgm cgb'
[../]
[./ACBulkCv]
type = KKSACBulkC
variable = eta
ca = cvm
cb = cvb
fa_name = f_total_matrix
args = 'cgm'
[../]
[./ACBulkCg]
type = KKSACBulkC
variable = eta
ca = cgm
cb = cgb
fa_name = f_total_matrix
args = '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
args = ' '
[../]
# 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
args = ' '
[../]
# 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/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
[../]
[]
(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
[]
[Problem]
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'
[../]
[]
[Modules/TensorMechanics/Master]
[./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
args = '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
args = ' '
[../]
# 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
args = ' '
[../]
# 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/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/KKS_system/kks_phase_concentration.i)
#
# This test validates the phase concentration calculation for the KKS system
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = 0
xmax = 1
ymin = 0
ymax = 1
zmin = 0
zmax = 0
elem_type = QUAD4
[]
# We set c and eta...
[BCs]
# (and ca for debugging purposes)
[./left]
type = DirichletBC
variable = c
boundary = 'left'
value = 0.1
[../]
[./right]
type = DirichletBC
variable = c
boundary = 'right'
value = 0.9
[../]
[./top]
type = DirichletBC
variable = eta
boundary = 'top'
value = 0.1
[../]
[./bottom]
type = DirichletBC
variable = eta
boundary = 'bottom'
value = 0.9
[../]
[]
[Variables]
# concentration
[./c]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
# order parameter
[./eta]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# phase concentration a
[./ca]
order = FIRST
family = LAGRANGE
initial_condition = 0.2
[../]
# phase concentration b
[./cb]
order = FIRST
family = LAGRANGE
initial_condition = 0.3
[../]
[]
[Materials]
# simple toy free energy
[./fa]
type = DerivativeParsedMaterial
property_name = Fa
coupled_variables = 'ca'
expression = 'ca^2'
[../]
[./fb]
type = DerivativeParsedMaterial
property_name = Fb
coupled_variables = 'cb'
expression = '(1-cb)^2'
[../]
# h(eta)
[./h_eta]
type = SwitchingFunctionMaterial
h_order = HIGH
eta = eta
outputs = exodus
[../]
[]
[Kernels]
active = 'cdiff etadiff phaseconcentration chempot'
##active = 'cbdiff cdiff etadiff chempot'
#active = 'cadiff cdiff etadiff phaseconcentration'
##active = 'cadiff cbdiff cdiff etadiff'
[./cadiff]
type = Diffusion
variable = ca
[../]
[./cbdiff]
type = Diffusion
variable = cb
[../]
[./cdiff]
type = Diffusion
variable = c
[../]
[./etadiff]
type = Diffusion
variable = eta
[../]
# ...and solve for ca and cb
[./phaseconcentration]
type = KKSPhaseConcentration
ca = ca
variable = cb
c = c
eta = eta
[../]
[./chempot]
type = KKSPhaseChemicalPotential
variable = ca
cb = cb
fa_name = Fa
fb_namee = Fb
[../]
[]
[Executioner]
type = Steady
solve_type = 'PJFNK'
#solve_type = 'NEWTON'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero'
[]
[Preconditioning]
active = 'full'
#active = 'mydebug'
#active = ''
[./full]
type = SMP
full = true
[../]
[./mydebug]
type = FDP
full = true
[../]
[]
[Outputs]
execute_on = 'timestep_end'
file_base = kks_phase_concentration
exodus = true
[]
(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
args = ' '
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
args = ' '
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
args = '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_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_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
mob_name = 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
mob_name = L
[../]
# Kernels for the Lagrange multiplier equation
[./mult_lambda]
type = MatReaction
variable = lambda
mob_name = 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
mob_name = 1
[../]
[./eta1reaction]
type = MatReaction
variable = eta3
v = eta1
mob_name = 1
[../]
[./eta2reaction]
type = MatReaction
variable = eta3
v = eta2
mob_name = 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/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/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
mob_name = L
[]
# Kernels for the Lagrange multiplier equation
[mult_lambda]
type = MatReaction
variable = lambda
mob_name = 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
mob_name = 1
[]
[eta1reaction]
type = MatReaction
variable = eta2
v = eta1
mob_name = 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 -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
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/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.
#
[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
coupled_variables = eta1
[]
[diff_c2a]
type = MatDiffusion
variable = cCr
diffusivity = Dh2a
v = SIGMA_0CR
coupled_variables = eta2
[]
[diff_c2b]
type = MatDiffusion
variable = cCr
diffusivity = Dh2b
v = SIGMA_1CR
coupled_variables = eta2
[]
[diff_c2c]
type = MatDiffusion
variable = cCr
diffusivity = Dh2c
v = SIGMA_2CR
coupled_variables = 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/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/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
args = '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
args = 'eta2 eta3'
[../]
[./ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[../]
[./multipler1]
type = MatReaction
variable = eta1
v = lambda
mob_name = 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
args = '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
args = 'eta1 eta3'
[../]
[./ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[../]
[./multipler2]
type = MatReaction
variable = eta2
v = lambda
mob_name = L
[../]
# Kernels for the Lagrange multiplier equation
[./mult_lambda]
type = MatReaction
variable = lambda
mob_name = 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
args = '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
args = '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
args = '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
args = '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
args = '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
args = '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
mob_name = 1
[../]
[./eta1reaction]
type = MatReaction
variable = eta3
v = eta1
mob_name = 1
[../]
[./eta2reaction]
type = MatReaction
variable = eta3
v = eta2
mob_name = 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/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
[../]
[]