- etaseta order parameters
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:eta order parameters
- variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable that this residual object operates on
SwitchingFunctionConstraintLagrange
Lagrange multiplier kernel to constrain the sum of all switching functions in a multiphase system. This kernel acts on the Lagrange multiplier variable.
Enforces the constraint . See Multiphase models for the full derivation.
Input Parameters
- blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
- displacementsThe displacements
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements
- epsilon1e-09Shift factor to avoid a zero pivot
Default:1e-09
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Shift factor to avoid a zero pivot
- h_namesSwitching function materials
C++ Type:std::vector<MaterialPropertyName>
Unit:(no unit assumed)
Controllable:No
Description:Switching function materials
- matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
Optional Parameters
- absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the matrices this Kernel should fill
- extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
Description:The extra tags for the vectors this Kernel should fill
- matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime, system
Controllable:No
Description:The tag for the matrices this Kernel should fill
- vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime, time
Controllable:No
Description:The tag for the vectors this Kernel should fill
Contribution To Tagged Field Data Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
- diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
- save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
- search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
- seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
- prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
- use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Material Property Retrieval Parameters
Input Files
- (modules/phase_field/test/tests/MultiPhase/acmultiinterface_aux.i)
- (modules/phase_field/examples/slkks/CrFe.i)
- (modules/phase_field/test/tests/MultiPhase/lagrangemult.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested_damped.i)
- (modules/combined/examples/publications/rapid_dev/fig8.i)
- (modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested.i)
- (modules/phase_field/test/tests/slkks/full_solve.i)
- (modules/combined/examples/phase_field-mechanics/Pattern1.i)
- (modules/phase_field/test/tests/MultiPhase/acmultiinterface.i)
(modules/phase_field/test/tests/MultiPhase/acmultiinterface_aux.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 10
nz = 0
xmin = -10
xmax = 10
ymin = -5
ymax = 5
elem_type = QUAD4
[]
[AuxVariables]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = -3.5
y1 = 0.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[]
[Variables]
[./eta2]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 3.5
y1 = 0.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[./eta3]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SpecifiedSmoothCircleIC
x_positions = '-4.0 4.0'
y_positions = ' 0.0 0.0'
z_positions = ' 0.0 0.0'
radii = '4.0 4.0'
invalue = 0.1
outvalue = 0.9
int_width = 2.0
[../]
[../]
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 0
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'Fx L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0 1 1 1 1 1 1 1 1 1 1 1 1 '
[../]
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
[./free_energy]
type = DerivativeMultiPhaseMaterial
property_name = F
# we use a constant free energy (GeneriConstantmaterial property Fx)
fi_names = 'Fx Fx Fx'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
# the free energy is given by the MultiBarrierFunctionMaterial only
W = 1
derivative_order = 2
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
#petsc_options = '-snes_ksp -snes_ksp_ew'
#petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
#petsc_options_iname = '-ksp_gmres_restart'
#petsc_options_value = '1000 '
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 2
dt = 0.2
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/examples/slkks/CrFe.i)
#
# SLKKS two phase example for the BCC and SIGMA phases. The sigma phase contains
# multiple sublattices. Free energy from
# Jacob, Aurelie, Erwin Povoden-Karadeniz, and Ernst Kozeschnik. "Revised thermodynamic
# description of the Fe-Cr system based on an improved sublattice model of the sigma phase."
# Calphad 60 (2018): 16-28.
#
# In this simulation we consider diffusion (Cahn-Hilliard) and phase transformation.
#
# This example requires CrFe_sigma_out_var_0001.csv file, which generated by first
# running the CrFe_sigma.i input file.
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
nx = 160
ny = 1
nz = 0
xmin = -25
xmax = 25
ymin = -2.5
ymax = 2.5
elem_type = QUAD4
[]
[]
[AuxVariables]
[Fglobal]
order = CONSTANT
family = MONOMIAL
[]
[]
[Functions]
[sigma_cr0]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 2
xy_in_file_only = false
[]
[sigma_cr1]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 3
xy_in_file_only = false
[]
[sigma_cr2]
type = PiecewiseLinear
data_file = CrFe_sigma_out_var_0001.csv
format = columns
x_index_in_file = 5
y_index_in_file = 4
xy_in_file_only = false
[]
[]
[Variables]
# order parameters
[eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
[eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[]
# solute concentration
[cCr]
order = FIRST
family = LAGRANGE
[InitialCondition]
type = FunctionIC
function = '(x+25)/50*0.5+0.1'
[]
[]
# sublattice concentrations
[BCC_CR]
initial_condition = 0.45
[]
[SIGMA_0CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr0
v = cCr
variable = SIGMA_0CR
[]
[]
[SIGMA_1CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr1
v = cCr
variable = SIGMA_1CR
[]
[]
[SIGMA_2CR]
[InitialCondition]
type = CoupledValueFunctionIC
function = sigma_cr2
v = cCr
variable = SIGMA_2CR
[]
[]
# Lagrange multiplier
[lambda]
[]
[]
[Materials]
# CALPHAD free energies
[F_BCC_A2]
type = DerivativeParsedMaterial
property_name = F_BCC_A2
outputs = exodus
output_properties = F_BCC_A2
expression = 'BCC_FE:=1-BCC_CR; G := 8.3145*T*(1.0*if(BCC_CR > 1.0e-15,BCC_CR*log(BCC_CR),0) + '
'1.0*if(BCC_FE > 1.0e-15,BCC_FE*plog(BCC_FE,eps),0) + 3.0*if(BCC_VA > '
'1.0e-15,BCC_VA*log(BCC_VA),0))/(BCC_CR + BCC_FE) + 8.3145*T*if(T < '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - '
'1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(0.525599232981783*BCC_CR*BCC_FE*BCC_'
'VA*(BCC_CR - BCC_FE) - 0.894055608820709*BCC_CR*BCC_FE*BCC_VA + '
'0.298657718120805*BCC_CR*BCC_VA - BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
'4.65558036243985e-30*T^9/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
'1.3485349181899e-10*T^3/(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
'0.905299382744392*(548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA + '
'1.0e-9)/T,if(T < -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + '
'1043.0*BCC_FE*BCC_VA,-8.13674105561218e-49*T^15/(-0.525599232981783*BCC_CR*BCC_FE*BCC'
'_VA*(BCC_CR - BCC_FE) + 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - '
'0.298657718120805*BCC_CR*BCC_VA + BCC_FE*BCC_VA + 9.58772770853308e-13)^15 - '
'4.65558036243985e-30*T^9/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) '
'+ 0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^9 - '
'1.3485349181899e-10*T^3/(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^3 + 1 - '
'0.905299382744392*(-548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA + '
'1.0e-9)/T,if(T > -548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'932.5*BCC_CR*BCC_FE*BCC_VA - 311.5*BCC_CR*BCC_VA + 1043.0*BCC_FE*BCC_VA & '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA < '
'0,-79209031311018.7*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
'3.83095660520737e+42*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
'1.22565886734485e+72*(-0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) + '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA - 0.298657718120805*BCC_CR*BCC_VA + '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,if(T > '
'548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + '
'311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA & 548.2*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - '
'BCC_FE) - 932.5*BCC_CR*BCC_FE*BCC_VA + 311.5*BCC_CR*BCC_VA - 1043.0*BCC_FE*BCC_VA > '
'0,-79209031311018.7*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^5/T^5 - '
'3.83095660520737e+42*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^15/T^15 - '
'1.22565886734485e+72*(0.525599232981783*BCC_CR*BCC_FE*BCC_VA*(BCC_CR - BCC_FE) - '
'0.894055608820709*BCC_CR*BCC_FE*BCC_VA + 0.298657718120805*BCC_CR*BCC_VA - '
'BCC_FE*BCC_VA + 9.58772770853308e-13)^25/T^25,0))))*log((2.15*BCC_CR*BCC_FE*BCC_VA - '
'0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA)*if(2.15*BCC_CR*BCC_FE*BCC_VA - '
'0.008*BCC_CR*BCC_VA + 2.22*BCC_FE*BCC_VA <= 0,-1.0,1.0) + 1)/(BCC_CR + BCC_FE) + '
'1.0*(BCC_CR*BCC_VA*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + '
'BCC_FE*BCC_VA*if(T >= 298.15 & T < 1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T '
'- 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < '
'6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - 25383.581,0)))/(BCC_CR '
'+ BCC_FE) + 1.0*(BCC_CR*BCC_FE*BCC_VA*(500.0 - 1.5*T)*(BCC_CR - BCC_FE) + '
'BCC_CR*BCC_FE*BCC_VA*(24600.0 - 14.98*T) + BCC_CR*BCC_FE*BCC_VA*(9.15*T - '
'14000.0)*(BCC_CR - BCC_FE)^2)/(BCC_CR + BCC_FE); G/100000'
coupled_variables = 'BCC_CR'
constant_names = 'BCC_VA T eps'
constant_expressions = '1 1000 0.01'
[]
[F_SIGMA]
type = DerivativeParsedMaterial
property_name = F_SIGMA
outputs = exodus
output_properties = F_SIGMA
expression = 'SIGMA_0FE := 1-SIGMA_0CR; SIGMA_1FE := 1-SIGMA_1CR; SIGMA_2FE := 1-SIGMA_2CR; G := '
'8.3145*T*(10.0*if(SIGMA_0CR > 1.0e-15,SIGMA_0CR*plog(SIGMA_0CR,eps),0) + '
'10.0*if(SIGMA_0FE > 1.0e-15,SIGMA_0FE*plog(SIGMA_0FE,eps),0) + 4.0*if(SIGMA_1CR > '
'1.0e-15,SIGMA_1CR*plog(SIGMA_1CR,eps),0) + 4.0*if(SIGMA_1FE > '
'1.0e-15,SIGMA_1FE*plog(SIGMA_1FE,eps),0) + 16.0*if(SIGMA_2CR > '
'1.0e-15,SIGMA_2CR*plog(SIGMA_2CR,eps),0) + 16.0*if(SIGMA_2FE > '
'1.0e-15,SIGMA_2FE*plog(SIGMA_2FE,eps),0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + '
'4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
'(SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*SIGMA_2FE*(-70.0*T - 170400.0) + '
'SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*SIGMA_2FE*(-10.0*T - 330839.0))/(10.0*SIGMA_0CR + '
'10.0*SIGMA_0FE + 4.0*SIGMA_1CR + 4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE) + '
'(SIGMA_0CR*SIGMA_1CR*SIGMA_2CR*(30.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - '
'26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= '
'2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) '
'+ 132000.0) + SIGMA_0CR*SIGMA_1CR*SIGMA_2FE*(-110.0*T + 16.0*if(T >= 298.15 & T < '
'1811.0,77358.5*1/T - 23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - '
'5.89269e-8*T^3.0 + 1225.7,if(T >= 1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - '
'46.0*T*log(T) + 299.31255*T - 25383.581,0)) + 14.0*if(T >= 298.15 & T < '
'2180.0,139250.0*1/T - 26.908*T*log(T) + 157.48*T + 0.00189435*T^2.0 - '
'1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < 6000.0,-2.88526e+32*T^(-9.0) - '
'50.0*T*log(T) + 344.18*T - 34869.344,0)) + 123500.0) + '
'SIGMA_0CR*SIGMA_1FE*SIGMA_2CR*(4.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 26.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 140486.0) '
'+ SIGMA_0CR*SIGMA_1FE*SIGMA_2FE*(20.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 10.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 148800.0) '
'+ SIGMA_0FE*SIGMA_1CR*SIGMA_2CR*(10.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 20.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 56200.0) + '
'SIGMA_0FE*SIGMA_1CR*SIGMA_2FE*(26.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 4.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 152700.0) '
'+ SIGMA_0FE*SIGMA_1FE*SIGMA_2CR*(14.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 16.0*if(T >= 298.15 & T < 2180.0,139250.0*1/T - 26.908*T*log(T) + '
'157.48*T + 0.00189435*T^2.0 - 1.47721e-6*T^3.0 - 8856.94,if(T >= 2180.0 & T < '
'6000.0,-2.88526e+32*T^(-9.0) - 50.0*T*log(T) + 344.18*T - 34869.344,0)) + 46200.0) + '
'SIGMA_0FE*SIGMA_1FE*SIGMA_2FE*(30.0*if(T >= 298.15 & T < 1811.0,77358.5*1/T - '
'23.5143*T*log(T) + 124.134*T - 0.00439752*T^2.0 - 5.89269e-8*T^3.0 + 1225.7,if(T >= '
'1811.0 & T < 6000.0,2.2960305e+31*T^(-9.0) - 46.0*T*log(T) + 299.31255*T - '
'25383.581,0)) + 173333.0))/(10.0*SIGMA_0CR + 10.0*SIGMA_0FE + 4.0*SIGMA_1CR + '
'4.0*SIGMA_1FE + 16.0*SIGMA_2CR + 16.0*SIGMA_2FE); G/100000'
coupled_variables = 'SIGMA_0CR SIGMA_1CR SIGMA_2CR'
constant_names = 'T eps'
constant_expressions = '1000 0.01'
[]
# h(eta)
[h1]
type = SwitchingFunctionMaterial
function_name = h1
h_order = HIGH
eta = eta1
[]
[h2]
type = SwitchingFunctionMaterial
function_name = h2
h_order = HIGH
eta = eta2
[]
# g(eta)
[g1]
type = BarrierFunctionMaterial
function_name = g1
g_order = SIMPLE
eta = eta1
[]
[g2]
type = BarrierFunctionMaterial
function_name = g2
g_order = SIMPLE
eta = eta2
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'D L kappa'
prop_values = '10 1 0.1 '
[]
# Coefficients for diffusion equation
[Dh1]
type = DerivativeParsedMaterial
material_property_names = 'D h1(eta1)'
expression = D*h1
property_name = Dh1
coupled_variables = eta1
derivative_order = 1
[]
[Dh2a]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*10/30
property_name = Dh2a
coupled_variables = eta2
derivative_order = 1
[]
[Dh2b]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*4/30
property_name = Dh2b
coupled_variables = eta2
derivative_order = 1
[]
[Dh2c]
type = DerivativeParsedMaterial
material_property_names = 'D h2(eta2)'
expression = D*h2*16/30
property_name = Dh2c
coupled_variables = eta2
derivative_order = 1
[]
[]
[Kernels]
#Kernels for diffusion equation
[diff_time]
type = TimeDerivative
variable = cCr
[]
[diff_c1]
type = MatDiffusion
variable = cCr
diffusivity = Dh1
v = BCC_CR
args = eta1
[]
[diff_c2a]
type = MatDiffusion
variable = cCr
diffusivity = Dh2a
v = SIGMA_0CR
args = eta2
[]
[diff_c2b]
type = MatDiffusion
variable = cCr
diffusivity = Dh2b
v = SIGMA_1CR
args = eta2
[]
[diff_c2c]
type = MatDiffusion
variable = cCr
diffusivity = Dh2c
v = SIGMA_2CR
args = eta2
[]
# enforce pointwise equality of chemical potentials
[chempot1a2a]
# The BCC phase has only one sublattice
# we tie it to the first sublattice with site fraction 10/(10+4+16) in the sigma phase
type = KKSPhaseChemicalPotential
variable = BCC_CR
cb = SIGMA_0CR
kb = '${fparse 10/30}'
fa_name = F_BCC_A2
fb_name = F_SIGMA
args_b = 'SIGMA_1CR SIGMA_2CR'
[]
[chempot2a2b]
# This kernel ties the first two sublattices in the sigma phase together
type = SLKKSChemicalPotential
variable = SIGMA_0CR
a = 10
cs = SIGMA_1CR
as = 4
F = F_SIGMA
coupled_variables = 'SIGMA_2CR'
[]
[chempot2b2c]
# This kernel ties the remaining two sublattices in the sigma phase together
type = SLKKSChemicalPotential
variable = SIGMA_1CR
a = 4
cs = SIGMA_2CR
as = 16
F = F_SIGMA
coupled_variables = 'SIGMA_0CR'
[]
[phaseconcentration]
# This kernel ties the sum of the sublattice concentrations to the global concentration cCr
type = SLKKSMultiPhaseConcentration
variable = SIGMA_2CR
c = cCr
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = KKSMultiACBulkF
variable = eta1
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g1
eta_i = eta1
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta2'
[]
[ACBulkC1]
type = SLKKSMultiACBulkC
variable = eta1
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
[lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2'
[]
# Kernels for Allen-Cahn equation for eta1
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = KKSMultiACBulkF
variable = eta2
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gi_name = g2
eta_i = eta2
wi = 0.1
coupled_variables = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR eta1'
[]
[ACBulkC2]
type = SLKKSMultiACBulkC
variable = eta2
F = F_BCC_A2
c = BCC_CR
ns = '1 3'
as = '1 10 4 16'
cs = 'BCC_CR SIGMA_0CR SIGMA_1CR SIGMA_2CR'
h_names = 'h1 h2'
eta = 'eta1 eta2'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
[lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1'
[]
# Lagrange-multiplier constraint kernel for lambda
[lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
h_names = 'h1 h2'
etas = 'eta1 eta2'
epsilon = 1e-6
[]
[]
[AuxKernels]
[GlobalFreeEnergy]
type = KKSMultiFreeEnergy
variable = Fglobal
Fj_names = 'F_BCC_A2 F_SIGMA'
hj_names = 'h1 h2'
gj_names = 'g1 g2'
interfacial_vars = 'eta1 eta2'
kappa_names = 'kappa kappa'
w = 0.1
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
line_search = none
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
petsc_options_value = 'asm lu nonzero 30'
l_max_its = 100
nl_max_its = 20
nl_abs_tol = 1e-10
end_time = 10000
[TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 12
iteration_window = 2
growth_factor = 1.5
cutback_factor = 0.7
dt = 0.1
[]
[]
[VectorPostprocessors]
[var]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = 'cCr eta1 eta2 SIGMA_0CR SIGMA_1CR SIGMA_2CR'
num_points = 151
sort_by = id
execute_on = 'initial timestep_end'
[]
[mat]
type = LineMaterialRealSampler
start = '-25 0 0'
end = '25 0 0'
property = 'F_BCC_A2 F_SIGMA'
sort_by = id
execute_on = 'initial timestep_end'
[]
[]
[Postprocessors]
[F]
type = ElementIntegralVariablePostprocessor
variable = Fglobal
execute_on = 'initial timestep_end'
[]
[cmin]
type = NodalExtremeValue
value_type = min
variable = cCr
execute_on = 'initial timestep_end'
[]
[cmax]
type = NodalExtremeValue
value_type = max
variable = cCr
execute_on = 'initial timestep_end'
[]
[ctotal]
type = ElementIntegralVariablePostprocessor
variable = cCr
execute_on = 'initial timestep_end'
[]
[]
[Outputs]
exodus = true
print_linear_residuals = false
csv = true
perf_graph = true
[]
(modules/phase_field/test/tests/MultiPhase/lagrangemult.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 14
ny = 10
nz = 0
xmin = 10
xmax = 40
ymin = 15
ymax = 35
elem_type = QUAD4
[]
[Variables]
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 25.0
y1 = 25.0
radius = 6.0
invalue = 0.9
outvalue = 0.1
int_width = 3.0
[../]
[../]
[./w]
order = FIRST
family = LAGRANGE
[../]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 30.0
y1 = 25.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'c eta2'
f_name = F
[../]
[./ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa_eta
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'c eta1'
f_name = F
[../]
[./ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa_eta
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2'
h_names = 'h1 h2'
epsilon = 0
[../]
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
kappa_name = kappa_c
w = w
coupled_variables = 'eta1 eta2'
[../]
[./w_res]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time1]
type = CoupledTimeDerivative
variable = w
v = c
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'L kappa_eta'
prop_values = '1 1 '
[../]
[./consts2]
type = GenericConstantMaterial
prop_names = 'M kappa_c'
prop_values = '1 1'
[../]
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
outputs = exodus
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
outputs = exodus
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2'
[../]
[./free_energy_A]
type = DerivativeParsedMaterial
property_name = Fa
coupled_variables = 'c'
expression = '(c-0.1)^2'
derivative_order = 2
enable_jit = true
[../]
[./free_energy_B]
type = DerivativeParsedMaterial
property_name = Fb
coupled_variables = 'c'
expression = '(c-0.9)^2'
derivative_order = 2
enable_jit = true
[../]
[./free_energy]
type = DerivativeMultiPhaseMaterial
property_name = F
fi_names = 'Fa Fb'
hi_names = 'h1 h2'
etas = 'eta1 eta2'
coupled_variables = 'c'
derivative_order = 2
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
#petsc_options = '-snes_ksp -snes_ksp_ew'
#petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
#petsc_options_iname = '-ksp_gmres_restart'
#petsc_options_value = '1000 '
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 1
dt = 0.01
dtmin = 0.01
[]
[Debug]
# show_var_residual_norms = true
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested_damped.i)
#
# This test is for the damped nested solve of 3-phase KKS model, and uses log-based free energies.
# The split-form of the Cahn-Hilliard equation instead of the Fick's diffusion equation is solved
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = 0
xmax = 40
ymin = 0
ymax = 40
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[BCs]
[Periodic]
[all]
auto_direction = 'x y'
[]
[]
[]
[AuxVariables]
[Energy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
[]
# order parameter 3
[eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# chemical potential
[mu]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# Lagrange multiplier
[lambda]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
[]
[ICs]
[eta1]
variable = eta1
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.9
outvalue = 0.1
int_width = 4
[]
[eta2]
variable = eta2
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.1
outvalue = 0.9
int_width = 4
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.2
outvalue = 0.5
int_width = 2
[]
[]
[Materials]
# simple toy free energies
[F1]
type = DerivativeParsedMaterial
property_name = F1
expression = 'c1*log(c1/1e-4) + (1-c1)*log((1-c1)/(1-1e-4))'
material_property_names = 'c1'
additional_derivative_symbols = 'c1'
compute = false
[]
[F2]
type = DerivativeParsedMaterial
property_name = F2
expression = 'c2*log(c2/0.5) + (1-c2)*log((1-c2)/(1-0.5))'
material_property_names = 'c2'
additional_derivative_symbols = 'c2'
compute = false
[]
[F3]
type = DerivativeParsedMaterial
property_name = F3
expression = 'c3*log(c3/0.9999) + (1-c3)*log((1-c3)/(1-0.9999))'
material_property_names = 'c3'
additional_derivative_symbols = 'c3'
compute = false
[]
[C]
type = DerivativeParsedMaterial
property_name = 'C'
material_property_names = 'c1 c2 c3'
expression = '(c1>0)&(c1<1)&(c2>0)&(c2<1)&(c3>0)&(c3<1)'
compute = false
[]
[KKSPhaseConcentrationMultiPhaseMaterial]
type = KKSPhaseConcentrationMultiPhaseMaterial
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
ci_IC = '0.2 0.5 0.8'
Fj_names = 'F1 F2 F3'
min_iterations = 1
max_iterations = 1000
absolute_tolerance = 1e-15
relative_tolerance = 1e-8
step_size_tolerance = 1e-05
damped_Newton = true
conditions = C
damping_factor = 0.8
[]
[KKSPhaseConcentrationMultiPhaseDerivatives]
type = KKSPhaseConcentrationMultiPhaseDerivatives
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
[]
# Switching functions for each phase
# h1(eta1, eta2, eta3)
[h1]
type = SwitchingFunction3PhaseMaterial
eta_i = eta1
eta_j = eta2
eta_k = eta3
property_name = h1
[]
# h2(eta1, eta2, eta3)
[h2]
type = SwitchingFunction3PhaseMaterial
eta_i = eta2
eta_j = eta3
eta_k = eta1
property_name = h2
[]
# h3(eta1, eta2, eta3)
[h3]
type = SwitchingFunction3PhaseMaterial
eta_i = eta3
eta_j = eta1
eta_k = eta2
property_name = h3
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
[g3]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta3
function_name = g3
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'L kappa M'
prop_values = '0.7 1.0 0.025'
[]
[]
[Kernels]
[lambda_lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-04
[]
[eta1_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2 eta3'
[]
[eta2_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1 eta3'
[]
[eta3_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
coupled_variables = 'eta1 eta2'
[]
#Kernels for Cahn-Hilliard equation
[diff_time]
type = CoupledTimeDerivative
variable = mu
v = c
[]
[CHBulk]
type = NestedKKSMultiSplitCHCRes
variable = c
all_etas = 'eta1 eta2 eta3'
global_cs = 'c'
w = mu
c1_names = 'c1'
F1_name = F1
coupled_variables = 'eta1 eta2 eta3 mu'
[]
[ckernel]
type = SplitCHWRes
variable = mu
mob_name = M
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = NestedKKSMultiACBulkF
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g1
mob_name = L
wi = 1.0
coupled_variables = 'c eta2 eta3'
[]
[ACBulkC1]
type = NestedKKSMultiACBulkC
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta2 eta3'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta2
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = NestedKKSMultiACBulkF
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g2
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta3'
[]
[ACBulkC2]
type = NestedKKSMultiACBulkC
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta3'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta3
[deta3dt]
type = TimeDerivative
variable = eta3
[]
[ACBulkF3]
type = NestedKKSMultiACBulkF
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g3
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta2'
[]
[ACBulkC3]
type = NestedKKSMultiACBulkC
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta2'
[]
[ACInterface3]
type = ACInterface
variable = eta3
kappa_name = kappa
[]
[]
[AuxKernels]
[Energy_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gj_names = 'g1 g2 g3'
variable = Energy
w = 1
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 2
dt = 0.01
[]
[Preconditioning]
active = 'full'
[full]
type = SMP
full = true
[]
[mydebug]
type = FDP
full = true
[]
[]
[Outputs]
file_base = kks_example_multiphase_nested_damped
exodus = true
[]
(modules/combined/examples/publications/rapid_dev/fig8.i)
#
# Fig. 8 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Two growing particles with differnet anisotropic Eigenstrains
#
[Mesh]
[./gen]
type = GeneratedMeshGenerator
dim = 2
nx = 80
ny = 40
xmin = -20
xmax = 20
ymin = 0
ymax = 20
elem_type = QUAD4
[../]
[./cnode]
type = ExtraNodesetGenerator
input = gen
coord = '0.0 0.0'
new_boundary = 100
tolerance = 0.1
[../]
[]
[GlobalParams]
# CahnHilliard needs the third derivatives
derivative_order = 3
enable_jit = true
displacements = 'disp_x disp_y'
int_width = 1
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
execute_on = 'INITIAL TIMESTEP_END'
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
# particle x positions and radius
P1X=8
P2X=-4
PR=2
[Variables]
# Solute concentration variable
[./c]
[./InitialCondition]
type = SpecifiedSmoothCircleIC
x_positions = '${P1X} ${P2X}'
y_positions = '0 0'
z_positions = '0 0'
radii = '${PR} ${PR}'
outvalue = 0.5
invalue = 0.9
[../]
[../]
[./w]
[../]
# Order parameter for the Matrix
[./eta1]
[./InitialCondition]
type = SpecifiedSmoothCircleIC
x_positions = '${P1X} ${P2X}'
y_positions = '0 0'
z_positions = '0 0'
radii = '${PR} ${PR}'
outvalue = 1.0
invalue = 0.0
[../]
[../]
# Order parameters for the 2 different inclusion orientations
[./eta2]
[./InitialCondition]
type = SmoothCircleIC
x1 = ${P2X}
y1 = 0
radius = ${PR}
invalue = 1.0
outvalue = 0.0
[../]
[../]
[./eta3]
[./InitialCondition]
type = SmoothCircleIC
x1 = ${P1X}
y1 = 0
radius = ${PR}
invalue = 1.0
outvalue = 0.0
[../]
[../]
# Lagrange-multiplier
[./lambda]
initial_condition = 1.0
[../]
[]
[Physics/SolidMechanics/QuasiStatic/all]
add_variables = true
strain = SMALL
eigenstrain_names = eigenstrain
[]
[Kernels]
# Split Cahn-Hilliard kernels
[./c_res]
type = SplitCHParsed
variable = c
f_name = F
coupled_variables = 'eta1 eta2 eta3'
kappa_name = kappa_c
w = w
[../]
[./wres]
type = SplitCHWRes
variable = w
mob_name = M
[../]
[./time]
type = CoupledTimeDerivative
variable = w
v = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
# Lagrange-multiplier constraint kernel for lambda
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-6
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
block = 0
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0.5 1 1 1 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 '
[../]
# We use this to output the level of constraint enforcement
# ideally it should be 0 everywhere, if the constraint is fully enforced
[./etasummat]
type = ParsedMaterial
property_name = etasum
coupled_variables = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
expression = 'h1+h2+h3-1'
outputs = exodus
[../]
# This parsed material creates a single property for visualization purposes.
# It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
[./phasemap]
type = ParsedMaterial
property_name = phase
coupled_variables = 'eta2 eta3'
expression = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
outputs = exodus
[../]
# global mechanical properties
[./elasticity_tensor]
type = ComputeElasticityTensor
C_ijkl = '400 400'
fill_method = symmetric_isotropic
[../]
[./stress]
type = ComputeLinearElasticStress
[../]
# eigenstrain
[./eigenstrain_2]
type = GenericConstantRankTwoTensor
tensor_name = s2
tensor_values = '0 -0.05 0 0 0 0'
[../]
[./eigenstrain_3]
type = GenericConstantRankTwoTensor
tensor_name = s3
tensor_values = '-0.05 0 0 0 0 0'
[../]
[./eigenstrain]
type = CompositeEigenstrain
weights = 'h2 h3'
tensors = 's2 s3'
coupled_variables = 'eta2 eta3'
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = '4*c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(c-0.9)^2-0.4'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_3]
type = DerivativeParsedMaterial
property_name = Fc3
expression = '(c-0.9)^2-0.5'
coupled_variables = 'c'
derivative_order = 2
[../]
# global chemical free energy
[./chemical_free_energy]
type = DerivativeMultiPhaseMaterial
f_name = Fc
fi_names = 'Fc1 Fc2 Fc3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
coupled_variables = 'c'
W = 3
[../]
# global elastic free energy
[./elastic_free_energy]
type = ElasticEnergyMaterial
f_name = Fe
coupled_variables = 'eta2 eta3'
outputs = exodus
output_properties = Fe
derivative_order = 2
[../]
# Penalize phase 2 and 3 coexistence
[./multi_phase_penalty]
type = DerivativeParsedMaterial
property_name = Fp
expression = '50*(eta2*eta3)^2'
coupled_variables = 'eta2 eta3'
derivative_order = 2
outputs = exodus
output_properties = Fp
[../]
# free energy
[./free_energy]
type = DerivativeSumMaterial
property_name = F
sum_materials = 'Fc Fe Fp'
coupled_variables = 'c eta1 eta2 eta3'
derivative_order = 2
[../]
[]
[BCs]
# fix center point location
[./centerfix_x]
type = DirichletBC
boundary = 100
variable = disp_x
value = 0
[../]
# fix side point x coordinate to inhibit rotation
[./angularfix]
type = DirichletBC
boundary = bottom
variable = disp_y
value = 0
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
execute_on = 'INITIAL TIMESTEP_END'
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
execute_on = 'INITIAL TIMESTEP_END'
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm lu'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
end_time = 12.0
[./TimeStepper]
type = IterationAdaptiveDT
optimal_iterations = 8
iteration_window = 1
dt = 0.01
[../]
[]
[Outputs]
print_linear_residuals = false
execute_on = 'INITIAL TIMESTEP_END'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
(modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested.i)
#
# This test is for the nested solve of 3-phase KKS model
# The split-form of the Cahn-Hilliard equation instead of the Fick's diffusion equation is solved
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 20
nz = 0
xmin = 0
xmax = 40
ymin = 0
ymax = 40
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[BCs]
[Periodic]
[all]
auto_direction = 'x y'
[]
[]
[]
[AuxVariables]
[Energy]
order = CONSTANT
family = MONOMIAL
[]
[]
[Variables]
# concentration
[c]
order = FIRST
family = LAGRANGE
[]
# order parameter 1
[eta1]
order = FIRST
family = LAGRANGE
[]
# order parameter 2
[eta2]
order = FIRST
family = LAGRANGE
[]
# order parameter 3
[eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# chemical potential
[mu]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
# Lagrange multiplier
[lambda]
order = FIRST
family = LAGRANGE
initial_condition = 0.0
[]
[]
[ICs]
[eta1]
variable = eta1
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.9
outvalue = 0.1
int_width = 4
[]
[eta2]
variable = eta2
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.1
outvalue = 0.9
int_width = 4
[]
[c]
variable = c
type = SmoothCircleIC
x1 = 20.0
y1 = 20.0
radius = 10
invalue = 0.2
outvalue = 0.5
int_width = 2
[]
[]
[Materials]
# simple toy free energies
[F1]
type = DerivativeParsedMaterial
property_name = F1
expression = '20*(c1-0.2)^2'
material_property_names = 'c1'
additional_derivative_symbols = 'c1'
compute = false
[]
[F2]
type = DerivativeParsedMaterial
property_name = F2
expression = '20*(c2-0.5)^2'
material_property_names = 'c2'
additional_derivative_symbols = 'c2'
compute = false
[]
[F3]
type = DerivativeParsedMaterial
property_name = F3
expression = '20*(c3-0.8)^2'
material_property_names = 'c3'
additional_derivative_symbols = 'c3'
compute = false
[]
[KKSPhaseConcentrationMultiPhaseMaterial]
type = KKSPhaseConcentrationMultiPhaseMaterial
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
ci_IC = '0.2 0.5 0.8'
Fj_names = 'F1 F2 F3'
min_iterations = 1
max_iterations = 1000
absolute_tolerance = 1e-11
relative_tolerance = 1e-10
[]
[KKSPhaseConcentrationMultiPhaseDerivatives]
type = KKSPhaseConcentrationMultiPhaseDerivatives
global_cs = 'c'
all_etas = 'eta1 eta2 eta3'
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
ci_names = 'c1 c2 c3'
[]
# Switching functions for each phase
# h1(eta1, eta2, eta3)
[h1]
type = SwitchingFunction3PhaseMaterial
eta_i = eta1
eta_j = eta2
eta_k = eta3
property_name = h1
[]
# h2(eta1, eta2, eta3)
[h2]
type = SwitchingFunction3PhaseMaterial
eta_i = eta2
eta_j = eta3
eta_k = eta1
property_name = h2
[]
# h3(eta1, eta2, eta3)
[h3]
type = SwitchingFunction3PhaseMaterial
eta_i = eta3
eta_j = eta1
eta_k = eta2
property_name = h3
[]
# Barrier functions for each phase
[g1]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta1
function_name = g1
[]
[g2]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta2
function_name = g2
[]
[g3]
type = BarrierFunctionMaterial
g_order = SIMPLE
eta = eta3
function_name = g3
[]
# constant properties
[constants]
type = GenericConstantMaterial
prop_names = 'L kappa M'
prop_values = '0.7 1.0 0.025'
[]
[]
[Kernels]
[lambda_lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-04
[]
[eta1_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
coupled_variables = 'eta2 eta3'
[]
[eta2_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
coupled_variables = 'eta1 eta3'
[]
[eta3_lagrange]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
coupled_variables = 'eta1 eta2'
[]
#Kernels for Cahn-Hilliard equation
[diff_time]
type = CoupledTimeDerivative
variable = mu
v = c
[]
[CHBulk]
type = NestedKKSMultiSplitCHCRes
variable = c
all_etas = 'eta1 eta2 eta3'
global_cs = 'c'
w = mu
c1_names = 'c1'
F1_name = F1
coupled_variables = 'eta1 eta2 eta3 mu'
[]
[ckernel]
type = SplitCHWRes
variable = mu
mob_name = M
[]
# Kernels for Allen-Cahn equation for eta1
[deta1dt]
type = TimeDerivative
variable = eta1
[]
[ACBulkF1]
type = NestedKKSMultiACBulkF
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g1
mob_name = L
wi = 1.0
coupled_variables = 'c eta2 eta3'
[]
[ACBulkC1]
type = NestedKKSMultiACBulkC
variable = eta1
global_cs = 'c'
eta_i = eta1
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta2 eta3'
[]
[ACInterface1]
type = ACInterface
variable = eta1
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta2
[deta2dt]
type = TimeDerivative
variable = eta2
[]
[ACBulkF2]
type = NestedKKSMultiACBulkF
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g2
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta3'
[]
[ACBulkC2]
type = NestedKKSMultiACBulkC
variable = eta2
global_cs = 'c'
eta_i = eta2
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta3'
[]
[ACInterface2]
type = ACInterface
variable = eta2
kappa_name = kappa
[]
# Kernels for Allen-Cahn equation for eta3
[deta3dt]
type = TimeDerivative
variable = eta3
[]
[ACBulkF3]
type = NestedKKSMultiACBulkF
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
gi_name = g3
mob_name = L
wi = 1.0
coupled_variables = 'c eta1 eta2'
[]
[ACBulkC3]
type = NestedKKSMultiACBulkC
variable = eta3
global_cs = 'c'
eta_i = eta3
all_etas = 'eta1 eta2 eta3'
ci_names = 'c1 c2 c3'
hj_names = 'h1 h2 h3'
Fj_names = 'F1 F2 F3'
coupled_variables = 'c eta1 eta2'
[]
[ACInterface3]
type = ACInterface
variable = eta3
kappa_name = kappa
[]
[]
[AuxKernels]
[Energy_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gj_names = 'g1 g2 g3'
variable = Energy
w = 1
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa kappa kappa'
[]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 2
dt = 0.5
[]
[Preconditioning]
active = 'full'
[full]
type = SMP
full = true
[]
[mydebug]
type = FDP
full = true
[]
[]
[Outputs]
file_base = kks_example_multiphase_nested
exodus = true
[]
(modules/phase_field/test/tests/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/phase_field-mechanics/Pattern1.i)
#
# Pattern example 1
#
# Phase changes driven by a combination mechanical (elastic) and chemical
# driving forces. In this three phase system a matrix phase, an oversized and
# an undersized precipitate phase compete. The chemical free energy favors a
# phase separation into either precipitate phase. A mix of both precipitate
# emerges to balance lattice expansion and contraction.
#
# This example demonstrates the use of
# * ACMultiInterface
# * SwitchingFunctionConstraintEta and SwitchingFunctionConstraintLagrange
# * DerivativeParsedMaterial
# * ElasticEnergyMaterial
# * DerivativeMultiPhaseMaterial
# * MultiPhaseStressMaterial
# which are the components to se up a phase field model with an arbitrary number
# of phases
#
[Mesh]
type = GeneratedMesh
dim = 2
nx = 80
ny = 80
nz = 0
xmin = -20
xmax = 20
ymin = -20
ymax = 20
zmin = 0
zmax = 0
elem_type = QUAD4
[]
[GlobalParams]
# CahnHilliard needs the third derivatives
derivative_order = 3
enable_jit = true
displacements = 'disp_x disp_y'
[]
# AuxVars to compute the free energy density for outputting
[AuxVariables]
[./local_energy]
order = CONSTANT
family = MONOMIAL
[../]
[./cross_energy]
order = CONSTANT
family = MONOMIAL
[../]
[]
[AuxKernels]
[./local_free_energy]
type = TotalFreeEnergy
variable = local_energy
interfacial_vars = 'c'
kappa_names = 'kappa_c'
additional_free_energy = cross_energy
[../]
[./cross_terms]
type = CrossTermGradientFreeEnergy
variable = cross_energy
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa11 kappa12 kappa13
kappa21 kappa22 kappa23
kappa31 kappa32 kappa33'
[../]
[]
[Variables]
# Solute concentration variable
[./c]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = RandomIC
min = 0
max = 0.8
seed = 1235
[../]
[../]
# Order parameter for the Matrix
[./eta1]
order = FIRST
family = LAGRANGE
initial_condition = 0.5
[../]
# Order parameters for the 2 different inclusion orientations
[./eta2]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
[./eta3]
order = FIRST
family = LAGRANGE
initial_condition = 0.1
[../]
# Mesh displacement
[./disp_x]
order = FIRST
family = LAGRANGE
[../]
[./disp_y]
order = FIRST
family = LAGRANGE
[../]
# Lagrange-multiplier
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
# Set up stress divergence kernels
[./TensorMechanics]
[../]
# Cahn-Hilliard kernels
[./c_res]
type = CahnHilliard
variable = c
f_name = F
coupled_variables = 'eta1 eta2 eta3'
[../]
[./time]
type = TimeDerivative
variable = c
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2 eta3 c'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3 c'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
# Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2 c'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
# Lagrange-multiplier constraint kernel for lambda
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 1e-6
[../]
[]
[Materials]
# declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
[./consts]
type = GenericConstantMaterial
prop_names = 'M kappa_c L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0.2 0 1 1 1 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 '
[../]
# We use this to output the level of constraint enforcement
# ideally it should be 0 everywhere, if the constraint is fully enforced
[./etasummat]
type = ParsedMaterial
property_name = etasum
coupled_variables = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
expression = 'h1+h2+h3-1'
outputs = exodus
[../]
# This parsed material creates a single property for visualization purposes.
# It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
[./phasemap]
type = ParsedMaterial
property_name = phase
coupled_variables = 'eta2 eta3'
expression = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
outputs = exodus
[../]
# matrix phase
[./elasticity_tensor_1]
type = ComputeElasticityTensor
base_name = phase1
C_ijkl = '3 3'
fill_method = symmetric_isotropic
[../]
[./strain_1]
type = ComputeSmallStrain
base_name = phase1
displacements = 'disp_x disp_y'
[../]
[./stress_1]
type = ComputeLinearElasticStress
base_name = phase1
[../]
# oversized phase
[./elasticity_tensor_2]
type = ComputeElasticityTensor
base_name = phase2
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_2]
type = ComputeSmallStrain
base_name = phase2
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./stress_2]
type = ComputeLinearElasticStress
base_name = phase2
[../]
[./eigenstrain_2]
type = ComputeEigenstrain
base_name = phase2
eigen_base = '0.02'
eigenstrain_name = eigenstrain
[../]
# undersized phase
[./elasticity_tensor_3]
type = ComputeElasticityTensor
base_name = phase3
C_ijkl = '7 7'
fill_method = symmetric_isotropic
[../]
[./strain_3]
type = ComputeSmallStrain
base_name = phase3
displacements = 'disp_x disp_y'
eigenstrain_names = eigenstrain
[../]
[./stress_3]
type = ComputeLinearElasticStress
base_name = phase3
[../]
[./eigenstrain_3]
type = ComputeEigenstrain
base_name = phase3
eigen_base = '-0.05'
eigenstrain_name = eigenstrain
[../]
# switching functions
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
# chemical free energies
[./chemical_free_energy_1]
type = DerivativeParsedMaterial
property_name = Fc1
expression = '4*c^2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_2]
type = DerivativeParsedMaterial
property_name = Fc2
expression = '(c-0.9)^2-0.4'
coupled_variables = 'c'
derivative_order = 2
[../]
[./chemical_free_energy_3]
type = DerivativeParsedMaterial
property_name = Fc3
expression = '(c-0.9)^2-0.5'
coupled_variables = 'c'
derivative_order = 2
[../]
# elastic free energies
[./elastic_free_energy_1]
type = ElasticEnergyMaterial
base_name = phase1
f_name = Fe1
derivative_order = 2
coupled_variables = 'c' # should be empty
[../]
[./elastic_free_energy_2]
type = ElasticEnergyMaterial
base_name = phase2
f_name = Fe2
derivative_order = 2
coupled_variables = 'c' # should be empty
[../]
[./elastic_free_energy_3]
type = ElasticEnergyMaterial
base_name = phase3
f_name = Fe3
derivative_order = 2
coupled_variables = 'c' # should be empty
[../]
# phase free energies (chemical + elastic)
[./phase_free_energy_1]
type = DerivativeSumMaterial
property_name = F1
sum_materials = 'Fc1 Fe1'
coupled_variables = 'c'
derivative_order = 2
[../]
[./phase_free_energy_2]
type = DerivativeSumMaterial
property_name = F2
sum_materials = 'Fc2 Fe2'
coupled_variables = 'c'
derivative_order = 2
[../]
[./phase_free_energy_3]
type = DerivativeSumMaterial
property_name = F3
sum_materials = 'Fc3 Fe3'
coupled_variables = 'c'
derivative_order = 2
[../]
# global free energy
[./free_energy]
type = DerivativeMultiPhaseMaterial
f_name = F
fi_names = 'F1 F2 F3'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
coupled_variables = 'c'
W = 3
[../]
# Generate the global stress from the phase stresses
[./global_stress]
type = MultiPhaseStressMaterial
phase_base = 'phase1 phase2 phase3'
h = 'h1 h2 h3'
[../]
[]
[BCs]
# the boundary conditions on the displacement enforce periodicity
# at zero total shear and constant volume
[./bottom_y]
type = DirichletBC
variable = disp_y
boundary = 'bottom'
value = 0
[../]
[./top_y]
type = DirichletBC
variable = disp_y
boundary = 'top'
value = 0
[../]
[./left_x]
type = DirichletBC
variable = disp_x
boundary = 'left'
value = 0
[../]
[./right_x]
type = DirichletBC
variable = disp_x
boundary = 'right'
value = 0
[../]
[./Periodic]
[./disp_x]
auto_direction = 'y'
[../]
[./disp_y]
auto_direction = 'x'
[../]
# all other phase field variables are fully periodic
[./c]
auto_direction = 'x y'
[../]
[./eta1]
auto_direction = 'x y'
[../]
[./eta2]
auto_direction = 'x y'
[../]
[./eta3]
auto_direction = 'x y'
[../]
[./lambda]
auto_direction = 'x y'
[../]
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
[./total_free_energy]
type = ElementIntegralVariablePostprocessor
variable = local_energy
[../]
[./total_solute]
type = ElementIntegralVariablePostprocessor
variable = c
[../]
[]
[Executioner]
type = Transient
scheme = bdf2
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type'
petsc_options_value = 'asm ilu'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 200
[./TimeStepper]
type = SolutionTimeAdaptiveDT
dt = 0.1
[../]
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[./table]
type = CSV
delimiter = ' '
[../]
[]
[Debug]
# show_var_residual_norms = true
[]
(modules/phase_field/test/tests/MultiPhase/acmultiinterface.i)
[Mesh]
type = GeneratedMesh
dim = 2
nx = 20
ny = 10
nz = 0
xmin = -10
xmax = 10
ymin = -5
ymax = 5
elem_type = QUAD4
[]
[Variables]
[./eta1]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = -3.5
y1 = 0.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[./eta2]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SmoothCircleIC
x1 = 3.5
y1 = 0.0
radius = 4.0
invalue = 0.9
outvalue = 0.1
int_width = 2.0
[../]
[../]
[./eta3]
order = FIRST
family = LAGRANGE
[./InitialCondition]
type = SpecifiedSmoothCircleIC
x_positions = '-4.0 4.0'
y_positions = ' 0.0 0.0'
z_positions = ' 0.0 0.0'
radii = '4.0 4.0'
invalue = 0.1
outvalue = 0.9
int_width = 2.0
[../]
[../]
[./lambda]
order = FIRST
family = LAGRANGE
initial_condition = 1.0
[../]
[]
[Kernels]
[./deta1dt]
type = TimeDerivative
variable = eta1
[../]
[./ACBulk1]
type = AllenCahn
variable = eta1
coupled_variables = 'eta2 eta3'
mob_name = L1
f_name = F
[../]
[./ACInterface1]
type = ACMultiInterface
variable = eta1
etas = 'eta1 eta2 eta3'
mob_name = L1
kappa_names = 'kappa11 kappa12 kappa13'
[../]
[./lagrange1]
type = SwitchingFunctionConstraintEta
variable = eta1
h_name = h1
lambda = lambda
[../]
[./deta2dt]
type = TimeDerivative
variable = eta2
[../]
[./ACBulk2]
type = AllenCahn
variable = eta2
coupled_variables = 'eta1 eta3'
mob_name = L2
f_name = F
[../]
[./ACInterface2]
type = ACMultiInterface
variable = eta2
etas = 'eta1 eta2 eta3'
mob_name = L2
kappa_names = 'kappa21 kappa22 kappa23'
[../]
[./lagrange2]
type = SwitchingFunctionConstraintEta
variable = eta2
h_name = h2
lambda = lambda
[../]
[./deta3dt]
type = TimeDerivative
variable = eta3
[../]
[./ACBulk3]
type = AllenCahn
variable = eta3
coupled_variables = 'eta1 eta2'
mob_name = L3
f_name = F
[../]
[./ACInterface3]
type = ACMultiInterface
variable = eta3
etas = 'eta1 eta2 eta3'
mob_name = L3
kappa_names = 'kappa31 kappa32 kappa33'
[../]
[./lagrange3]
type = SwitchingFunctionConstraintEta
variable = eta3
h_name = h3
lambda = lambda
[../]
[./lagrange]
type = SwitchingFunctionConstraintLagrange
variable = lambda
etas = 'eta1 eta2 eta3'
h_names = 'h1 h2 h3'
epsilon = 0
[../]
[]
[BCs]
[./Periodic]
[./All]
auto_direction = 'x y'
[../]
[../]
[]
[Materials]
[./consts]
type = GenericConstantMaterial
prop_names = 'Fx L1 L2 L3 kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
prop_values = '0 1 1 1 1 1 1 1 1 1 1 1 1 '
[../]
[./etasummat]
type = ParsedMaterial
property_name = etasum
coupled_variables = 'eta1 eta2 eta3'
material_property_names = 'h1 h2 h3'
expression = 'h1+h2+h3'
[../]
[./switching1]
type = SwitchingFunctionMaterial
function_name = h1
eta = eta1
h_order = SIMPLE
[../]
[./switching2]
type = SwitchingFunctionMaterial
function_name = h2
eta = eta2
h_order = SIMPLE
[../]
[./switching3]
type = SwitchingFunctionMaterial
function_name = h3
eta = eta3
h_order = SIMPLE
[../]
[./barrier]
type = MultiBarrierFunctionMaterial
etas = 'eta1 eta2 eta3'
[../]
[./free_energy]
type = DerivativeMultiPhaseMaterial
property_name = F
# we use a constant free energy (GeneriConstantmaterial property Fx)
fi_names = 'Fx Fx Fx'
hi_names = 'h1 h2 h3'
etas = 'eta1 eta2 eta3'
# the free energy is given by the MultiBarrierFunctionMaterial only
W = 1
derivative_order = 2
[../]
[]
[Preconditioning]
[./SMP]
type = SMP
full = true
[../]
[]
[Executioner]
type = Transient
scheme = 'bdf2'
solve_type = 'PJFNK'
#petsc_options = '-snes_ksp -snes_ksp_ew'
#petsc_options = '-ksp_monitor_snes_lg-snes_ksp_ew'
#petsc_options_iname = '-ksp_gmres_restart'
#petsc_options_value = '1000 '
l_max_its = 15
l_tol = 1.0e-6
nl_max_its = 50
nl_rel_tol = 1.0e-8
nl_abs_tol = 1.0e-10
start_time = 0.0
num_steps = 2
dt = 0.2
[]
[Outputs]
execute_on = 'timestep_end'
exodus = true
[]