- cbPhase b concentration
C++ Type:std::vector
Description:Phase b concentration
- fa_nameBase name of the free energy function Fa (f_name in the corresponding derivative function material)
C++ Type:MaterialPropertyName
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
Description:Base name of the free energy function Fb (f_name in the corresponding derivative function material)
- variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Description:The name of the variable that this Kernel operates on
KKSPhaseChemicalPotential
KKS model kernel to enforce the pointwise equality of phase chemical potentials dFa/dca = dFb/dcb. The non-linear variable of this kernel is ca.
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
Options:
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
Options:
Description:Vector of further parameters to Fb (optional, to add in second cross derivatives of Fb)
- blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
- displacementsThe displacements
C++ Type:std::vector
Options:
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
Options:
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
Options:
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)
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
- 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
Options:
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
Options:
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
Options:
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
Options:
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
Options:
Description:The seed for the master random number generator
- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Advanced Parameters
- extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
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
Options:
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
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
Description:The tag for the vectors this Kernel should fill
Tagging Parameters
Input Files
- modules/combined/test/tests/surface_tension_KKS/surface_tension_VDWgas.i
- modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i
- modules/phase_field/test/tests/KKS_system/kks_example.i
- modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i
- modules/combined/test/tests/surface_tension_KKS/surface_tension_KKS.i
- modules/phase_field/test/tests/KKS_system/kks_example_offset.i
- modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i
- modules/phase_field/test/tests/KKS_system/kks_phase_concentration.i
- modules/phase_field/test/tests/KKS_system/kks_multiphase.i
- modules/phase_field/test/tests/KKS_system/kks_example_split.i
- modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i
- modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i
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
value = 'r:=sqrt(x^2+y^2+z^2);0.5*(1.0-tanh((r-r0)/delta_eta/sqrt(2.0)))'
vars = 'delta_eta r0'
vals = '0.321 15'
[../]
[./ic_func_cv]
type = ParsedFunction
value = '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))'
vars = 'delta r0 cvbubinit cvmatrixinit'
vals = '0.321 15 0.7286 2.25e-11'
[../]
[./ic_func_cg]
type = ParsedFunction
value = '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))'
vars = 'delta r0 cgbubinit cgmatrixinit'
vals = '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
f_name = fm
args = 'cvm cgm'
material_property_names = 'kvmatrix kgmatrix cvmatrixeq cgmatrixeq'
function = '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
f_name = f_total_matrix
sum_materials = 'fm fe_m'
args = 'cvm cgm'
[../]
# Free energy of the bubble phase
[./fb]
type = DerivativeParsedMaterial
f_name = fb
args = 'cvb cgb'
material_property_names = 'kToverV nQ Va b f0 kpen kgbub kvbub cvbubeq cgbubeq'
function = '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
f_name = f_total_bub
sum_materials = 'fb fe_b'
# sum_materials = 'fb'
args = '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
f_name = cvmatrixeq
material_property_names = 'T'
constant_names = 'kB Efv'
constant_expressions = '8.6173324e-5 1.69'
function = 'exp(-Efv/(kB*T))'
[../]
[./cgmatrixeq]
type = ParsedMaterial
f_name = cgmatrixeq
material_property_names = 'T'
constant_names = 'kB Efg'
constant_expressions = '8.6173324e-5 4.92'
function = 'exp(-Efg/(kB*T))'
[../]
[./kToverV]
type = ParsedMaterial
f_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'
function = 'k*T*1e27/Va/C44dim'
[../]
[./nQ]
type = ParsedMaterial
f_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'
function = '(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/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
value = '0.5*(1.0+tanh((x)/delta_eta/sqrt(2.0)))'
vars = 'delta_eta'
vals = '0.8034'
[../]
[./ic_func_c]
type = ParsedFunction
value = '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))'
vars = 'delta'
vals = '0.8034'
[../]
[./psi_eq_int]
type = ParsedFunction
value = 'volume*psi_alpha'
vars = 'volume psi_alpha'
vals = 'volume psi_alpha'
[../]
[./gamma]
type = ParsedFunction
value = '(psi_int - psi_eq_int) / dy / dz'
vars = 'psi_int psi_eq_int dy dz'
vals = '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
args = 'Fglobal w c f_el sigma11 e11'
function = '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
f_name = fm
args = 'cm'
function = '6.55*(cm-0.13)^2'
[../]
# Chemical Free energy of the precipitate phase
[./fp]
type = DerivativeParsedMaterial
f_name = fp
args = 'cp'
function = '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
f_name = one_minus_h_explicit
args = eta
function = 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
interval = 20
[../]
checkpoint = true
[./csv]
type = CSV
execute_on = 'final'
[../]
[]
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
f_name = fm
args = 'cm'
function = '(0.1-cm)^2'
outputs = oversampling
[../]
# Free energy of the delta phase
[./fd]
type = DerivativeParsedMaterial
f_name = fd
args = 'cd'
function = '(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
args = '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/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
value = '0.5*(1.0+tanh((x)/delta_eta/sqrt(2.0)))'
vars = 'delta_eta'
vals = '0.8034'
[../]
[./ic_func_c]
type = ParsedFunction
value = '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))'
vars = 'delta'
vals = '0.8034'
[../]
[./psi_eq_int]
type = ParsedFunction
value = 'volume*psi_alpha'
vars = 'volume psi_alpha'
vals = 'volume psi_alpha'
[../]
[./gamma]
type = ParsedFunction
value = '(psi_int - psi_eq_int) / dy / dz'
vars = 'psi_int psi_eq_int dy dz'
vals = '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
args = 'Fglobal w c f_el sigma11 e11'
function = '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
f_name = fm
args = 'cm'
function = '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
f_name = f_total_matrix
sum_materials = 'fm fe_m'
args = 'cm'
[../]
# Free energy of the precipitate phase
[./fp]
type = DerivativeParsedMaterial
f_name = fp
args = 'cp'
function = '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
f_name = f_total_ppt
sum_materials = 'fp fe_p'
args = '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
interval = 20
[../]
[./csv]
type = CSV
execute_on = 'final'
[../]
#[./console]
# type = Console
# output_file = true
# [../]
[]
modules/combined/test/tests/surface_tension_KKS/surface_tension_KKS.i
#
# KKS coupled with elasticity. Physical parameters for matrix and precipitate phases
# are gamma and gamma-prime phases, respectively, in the Ni-Al system.
# Parameterization is as described in L.K. Aagesen et al., Computational Materials
# Science, 140, 10-21 (2017), with isotropic elastic properties in both phases
# and without eigenstrain.
#
[Mesh]
type = GeneratedMesh
dim = 1
nx = 200
xmax = 200
[]
[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
value = 'r:=sqrt(x^2+y^2+z^2);0.5*(1.0-tanh((r-r0)/delta_eta/sqrt(2.0)))'
vars = 'delta_eta r0'
vals = '6.431 100'
[../]
[./ic_func_c]
type = ParsedFunction
value = '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))'
vars = 'delta r0'
vals = '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
f_name = fm
args = 'cm'
function = '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
f_name = f_total_matrix
sum_materials = 'fm fe_m'
args = 'cm'
[../]
# Free energy of the precipitate phase
[./fp]
type = DerivativeParsedMaterial
f_name = fp
args = 'cp'
function = '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
f_name = f_total_ppt
sum_materials = 'fp fe_p'
args = '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/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
f_name = fm
args = 'cm'
function = '(0.1-cm)^2'
[../]
# Free energy of the delta phase
[./fd]
type = DerivativeParsedMaterial
f_name = fd
args = 'cd'
function = '(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
args = '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/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
value = '0.5*(1.0-tanh((x)/sqrt(2.0)))'
[../]
[./ic_func_c]
type = ParsedFunction
value = '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
f_name = fl
args = 'cl'
function = '(0.1-cl)^2'
[../]
# Free energy of the solid
[./fs]
type = DerivativeParsedMaterial
f_name = fs
args = 'cs'
function = '(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
args = 'cl cs'
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cl
cb = cs
fa_name = fl
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = eps_sq
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fl
fb_name = fs
w = 1.0
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 50
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[VectorPostprocessors]
[./c]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = c
num_points = 151
sort_by = id
execute_on = timestep_end
[../]
[./eta]
type = LineValueSampler
start_point = '-25 0 0'
end_point = '25 0 0'
variable = eta
num_points = 151
sort_by = id
execute_on = timestep_end
[../]
[]
[Outputs]
exodus = true
[./csv]
type = CSV
execute_on = final
[../]
[]
modules/phase_field/test/tests/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
f_name = Fa
args = 'ca'
function = 'ca^2'
[../]
[./fb]
type = DerivativeParsedMaterial
f_name = Fb
args = 'cb'
function = '(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/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
f_name = F1
args = 'c1'
function = '20*(c1-0.2)^2'
[../]
[./f2]
type = DerivativeParsedMaterial
f_name = F2
args = 'c2'
function = '20*(c2-0.5)^2'
[../]
[./f3]
type = DerivativeParsedMaterial
f_name = F3
args = 'c3'
function = '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'
function = D*h1
f_name = Dh1
[../]
[./Dh2]
type = DerivativeParsedMaterial
material_property_names = 'D h2'
function = D*h2
f_name = Dh2
[../]
[./Dh3]
type = DerivativeParsedMaterial
material_property_names = 'D h3'
function = D*h3
f_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
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
[../]
[]
[AuxKernels]
[./Energy_total]
type = KKSMultiFreeEnergy
Fj_names = 'F1 F2 F3'
hj_names = 'h1 h2 h3'
gj_names = 'g1 g2 g3'
variable = Energy
w = 1
interfacial_vars = 'eta1 eta2 eta3'
kappa_names = 'kappa kappa kappa'
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type'
petsc_options_value = 'asm ilu nonzero'
l_max_its = 30
nl_max_its = 10
l_tol = 1.0e-4
nl_rel_tol = 1.0e-10
nl_abs_tol = 1.0e-11
num_steps = 2
dt = 0.5
[]
[Preconditioning]
active = 'full'
[./full]
type = SMP
full = true
[../]
[./mydebug]
type = FDP
full = true
[../]
[]
[Outputs]
exodus = true
[]
modules/phase_field/test/tests/KKS_system/kks_example_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
f_name = fm
args = 'cm'
function = '(0.1-cm)^2'
[../]
# Free energy of the delta phase
[./fd]
type = DerivativeParsedMaterial
f_name = fd
args = 'cd'
function = '(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
args = 'cm cd'
w = 0.4
[../]
[./ACBulkC]
type = KKSACBulkC
variable = eta
ca = cm
cb = cd
fa_name = fm
[../]
[./ACInterface]
type = ACInterface
variable = eta
kappa_name = kappa
[../]
[./detadt]
type = TimeDerivative
variable = eta
[../]
[]
[AuxKernels]
[./GlobalFreeEnergy]
variable = Fglobal
type = KKSGlobalFreeEnergy
fa_name = fm
fb_name = fd
w = 0.4
[../]
[]
[Executioner]
type = Transient
solve_type = 'PJFNK'
petsc_options_iname = '-pctype -sub_pc_type -sub_pc_factor_shift_type -pc_factor_shift_type'
petsc_options_value = ' asm lu nonzero nonzero'
l_max_its = 100
nl_max_its = 100
num_steps = 3
dt = 0.1
[]
#
# Precondition using handcoded off-diagonal terms
#
[Preconditioning]
[./full]
type = SMP
full = true
[../]
[]
[Outputs]
file_base = kks_example_split
exodus = true
[]
modules/phase_field/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
value = 0.5*(1.0-tanh((x)/sqrt(2.0)))
[../]
[./ic_func_c]
type = ParsedFunction
value = '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
f_name = fl
args = 'cl'
function = '(0.1-cl)^2'
[../]
# Free energy of the solid
[./fs]
type = DerivativeParsedMaterial
f_name = fs
args = 'cs'
function = '(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
args = '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/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
value = '0.5*(1.0-tanh((x)/sqrt(2.0)))'
[../]
[./ic_func_c1]
type = ParsedFunction
value = '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
value = '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
f_name = fl
args = 'c1l c2l'
function = '(0.1-c1l)^2+(0.05-c2l)^2'
[../]
# Free energy of the solid
[./fs]
type = DerivativeParsedMaterial
f_name = fs
args = 'c1s c2s'
function = '(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
args = 'c1l c1s c2l c2s'
[../]
[./ACBulkC1]
type = KKSACBulkC
variable = eta
ca = c1l
cb = c1s
fa_name = fl
args = 'c2l'
[../]
[./ACBulkC2]
type = KKSACBulkC
variable = eta
ca = c2l
cb = c2s
fa_name = fl
args = '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
[]