InterfaceOrientationMultiphaseMaterial

This Material accounts for the the orientation dependence of interfacial energy for multi-phase multi-order parameter phase-field model.

This Material accounts for the the orientation dependence of interfacial energy for multi-phase multi-order parameter phase-field model. It is assumed interface parameter $var element = document.getElementById("moose-equation-442cd822-6a88-489e-9e77-bc601930b5d6");katex.render("\\kappa", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a function of gradients of order parameters.

Input Parameters

d2kappadgrad_etaa_nameName of the second derivative of kappa w.r.t. the gradient of eta
C++ Type:MaterialPropertyName
Options:
Description:Name of the second derivative of kappa w.r.t. the gradient of eta
dkappadgrad_etaa_nameName of the derivative of kappa w.r.t. the gradient of eta
C++ Type:MaterialPropertyName
Options:
Description:Name of the derivative of kappa w.r.t. the gradient of eta
etaaOrder parameter for the current phase alpha
C++ Type:std::vector
Options:
Description:Order parameter for the current phase alpha
etabOrder parameter for the neighboring phase beta
C++ Type:std::vector
Options:
Description:Order parameter for the neighboring phase beta
kappa_nameName of the kappa for the given phase
C++ Type:MaterialPropertyName
Options:
Description:Name of the kappa for the given phase

Required Parameters

anisotropy_strength0.04Strength of the anisotropy (typically < 0.05)
Default:0.04
C++ Type:double
Options:
Description:Strength of the anisotropy (typically < 0.05)
blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Options:
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE ELEMENT SUBDOMAIN
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
kappa_bar0.1125Average value of the interface parameter kappa
Default:0.1125
C++ Type:double
Options:
Description:Average value of the interface parameter kappa
mode_number4Mode number for anisotropy
Default:4
C++ Type:unsigned int
Options:
Description:Mode number for anisotropy
reference_angle90Reference angle for defining anisotropy in degrees
Default:90
C++ Type:double
Options:
Description:Reference angle for defining anisotropy in degrees

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
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
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

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Options:
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

modules/phase_field/examples/anisotropic_interfaces/GrandPotentialTwophaseAnisotropy.i
modules/phase_field/examples/anisotropic_interfaces/GrandPotentialPlanarGrowth.i
modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialAnisotropyAntitrap.i
modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialAnisotropy.i
modules/phase_field/examples/anisotropic_interfaces/GrandPotentialSolidification.i

modules/phase_field/examples/anisotropic_interfaces/GrandPotentialTwophaseAnisotropy.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmin = -4
  xmax = 4
  ymin = -4
  ymax = 4
  uniform_refine = 2
[]

[GlobalParams]
  radius = 0.5
  int_width = 0.3
  x1 = 0
  y1 = 0
  derivative_order = 2
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
[]

[AuxVariables]
  [./bnds]
  [../]
[]

[AuxKernels]
  [./bnds]
    type = BndsCalcAux
    variable = bnds
    v = 'etaa0 etab0'
  [../]
[]

[ICs]
  [./w]
    type = SmoothCircleIC
    variable = w
    # note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
    outvalue = -4.0
    invalue = 0.0
  [../]
  [./etaa0]
    type = SmoothCircleIC
    variable = etaa0
    #Solid phase
    outvalue = 0.0
    invalue = 1.0
  [../]
  [./etab0]
    type = SmoothCircleIC
    variable = etab0
    #Liquid phase
    outvalue = 1.0
    invalue = 0.0
  [../]
[]

[BCs]
  [./Periodic]
    [./w]
      variable = w
      auto_direction = 'x y'
    [../]
    [./etaa0]
      variable = etaa0
      auto_direction = 'x y'
    [../]
    [./etab0]
      variable = etab0
      auto_direction = 'x y'
    [../]
  [../]
[]

[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0'
    gamma_names = 'gab'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etab0 w'
  [../]
  [./ACa0_int1]
    type = ACInterface2DMultiPhase1
    variable = etaa0
    etas = 'etab0'
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
  [../]
  [./ACa0_int2]
    type = ACInterface2DMultiPhase2
    variable = etaa0
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0'
    gamma_names = 'gab'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 w'
  [../]
  [./ACb0_int1]
    type = ACInterface2DMultiPhase1
    variable = etab0
    etas = 'etaa0'
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
  [../]
  [./ACb0_int2]
    type = ACInterface2DMultiPhase2
    variable = etab0
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
[]

[Materials]
  [./ha]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0'
    phase_etas = 'etaa0'
  [../]
  [./hb]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0'
    phase_etas = 'etab0'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegab
    material_property_names = 'Vm kb cbeq'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
  [../]
  [./kappaa]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
    etaa = etaa0
    etab = etab0
    outputs = exodus
    output_properties = 'kappaa'
  [../]
  [./kappab]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
    etaa = etab0
    etab = etaa0
    outputs = exodus
    output_properties = 'kappab'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'L   D    chi  Vm   ka    caeq kb    cbeq  gab mu'
    prop_values = '1.0 1.0  0.1  1.0  10.0  0.1  10.0  0.9   4.5 10.0'
  [../]
  [./Mobility]
    type = ParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg      31'
  l_tol = 1.0e-3
  l_max_its = 30
  nl_max_its = 15
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1e-8
  end_time = 10.0
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.0005
    cutback_factor = 0.7
    growth_factor = 1.2
  [../]
[]

[Adaptivity]
 initial_steps = 5
 max_h_level = 3
 initial_marker = err_eta
 marker = err_bnds
[./Markers]
   [./err_eta]
     type = ErrorFractionMarker
     coarsen = 0.3
     refine = 0.95
     indicator = ind_eta
   [../]
   [./err_bnds]
     type = ErrorFractionMarker
     coarsen = 0.3
     refine = 0.95
     indicator = ind_bnds
   [../]
 [../]
 [./Indicators]
   [./ind_eta]
     type = GradientJumpIndicator
     variable = etaa0
    [../]
    [./ind_bnds]
      type = GradientJumpIndicator
      variable = bnds
   [../]
 [../]
[]

[Outputs]
  interval = 10
  exodus = true
[]

modules/phase_field/examples/anisotropic_interfaces/GrandPotentialPlanarGrowth.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 10
  ny = 10
  xmin = -2
  xmax = 2
  ymin = -2
  ymax = 2
  uniform_refine = 2
[]

[GlobalParams]
  x1 = -2
  y1 = -2
  x2 = 2
  y2 = -1.5
  derivative_order = 2
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
[]

[AuxVariables]
  [./bnds]
  [../]
  #Temperature
  [./T]
  [../]
[]

[AuxKernels]
  [./bnds]
    type = BndsCalcAux
    variable = bnds
    v = 'etaa0 etab0'
  [../]
  [./T]
    type = FunctionAux
    function = 95.0+2.0*(y-1.0*t)
    variable = T
    execute_on = 'initial timestep_begin'
  [../]
[]

[ICs]
  [./w]
    type = BoundingBoxIC
    variable = w
    # note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
    outside = -4.0
    inside = 0.0
  [../]
  [./etaa0]
    type = BoundingBoxIC
    variable = etaa0
    #Solid phase
    outside = 0.0
    inside = 1.0
  [../]
  [./etab0]
    type = BoundingBoxIC
    variable = etab0
    #Liquid phase
    outside = 1.0
    inside = 0.0
  [../]
[]


[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0'
    gamma_names = 'gab'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etab0 w'
  [../]
  [./ACa0_int1]
    type = ACInterface2DMultiPhase1
    variable = etaa0
    etas = 'etab0'
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
  [../]
  [./ACa0_int2]
    type = ACInterface2DMultiPhase2
    variable = etaa0
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0'
    gamma_names = 'gab'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 w'
  [../]
  [./ACb0_int1]
    type = ACInterface2DMultiPhase1
    variable = etab0
    etas = 'etaa0'
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
  [../]
  [./ACb0_int2]
    type = ACInterface2DMultiPhase2
    variable = etab0
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
[]


[Materials]
  [./ha]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0'
    phase_etas = 'etaa0'
  [../]
  [./hb]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0'
    phase_etas = 'etab0'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w T'
    f_name = omegab
    material_property_names = 'Vm kb cbeq S Tm'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq-S*(T-Tm)'
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
  [../]
  [./kappaa]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
    etaa = etaa0
    etab = etab0
    outputs = exodus
    output_properties = 'kappaa'
  [../]
  [./kappab]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
    etaa = etab0
    etab = etaa0
    outputs = exodus
    output_properties = 'kappab'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'L   D    chi  Vm   ka    caeq kb    cbeq  gab mu   S   Tm'
    prop_values = '1.0 1.0  0.1  1.0  10.0  0.1  10.0  0.9   4.5 10.0 1.0 100.0'
  [../]
  [./Mobility]
    type = ParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg      31'
  l_tol = 1.0e-3
  l_max_its = 30
  nl_max_its = 15
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1e-8
  end_time = 2.0
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.0005
    cutback_factor = 0.7
    growth_factor = 1.2
  [../]
[]

[Adaptivity]
 initial_steps = 3
 max_h_level = 3
 initial_marker = err_eta
 marker = err_bnds
[./Markers]
   [./err_eta]
     type = ErrorFractionMarker
     coarsen = 0.3
     refine = 0.95
     indicator = ind_eta
   [../]
   [./err_bnds]
     type = ErrorFractionMarker
     coarsen = 0.3
     refine = 0.95
     indicator = ind_bnds
   [../]
 [../]
 [./Indicators]
   [./ind_eta]
     type = GradientJumpIndicator
     variable = etaa0
    [../]
    [./ind_bnds]
      type = GradientJumpIndicator
      variable = bnds
   [../]
 [../]
[]

[Outputs]
  interval = 10
  exodus = true
[]

modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialAnisotropyAntitrap.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -2
  xmax = 2
  ymin = -2
  ymax = 2
[]

[GlobalParams]
  radius = 1.0
  int_width = 0.8
  x1 = 0
  y1 = 0
  enable_jit = true
  derivative_order = 2
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
[]

[AuxVariables]
  [./bnds]
  [../]
[]

[AuxKernels]
  [./bnds]
    type = BndsCalcAux
    variable = bnds
    v = 'etaa0 etab0'
  [../]
[]

[ICs]
  [./w]
    type = SmoothCircleIC
    variable = w
    outvalue = -4.0
    invalue = 0.0
  [../]
  [./etaa0]
    type = SmoothCircleIC
    variable = etaa0
    #Solid phase
    outvalue = 0.0
    invalue = 1.0
  [../]
  [./etab0]
    type = SmoothCircleIC
    variable = etab0
    #Liquid phase
    outvalue = 1.0
    invalue = 0.0
  [../]
[]

[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0'
    gamma_names = 'gab'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etab0 w'
  [../]
  [./ACa0_int1]
    type = ACInterface2DMultiPhase1
    variable = etaa0
    etas = 'etab0'
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
  [../]
  [./ACa0_int2]
    type = ACInterface2DMultiPhase2
    variable = etaa0
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0'
    gamma_names = 'gab'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 w'
  [../]
  [./ACb0_int1]
    type = ACInterface2DMultiPhase1
    variable = etab0
    etas = 'etaa0'
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
  [../]
  [./ACb0_int2]
    type = ACInterface2DMultiPhase2
    variable = etab0
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
    args = '' # in this case chi (the susceptibility) is simply a constant
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
    args = ''
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./coupled_etaa0dot_int]
    type = AntitrappingCurrent
    variable = w
    v = etaa0
    f_name = rhodiff
  [../]
  [./coupled_etab0dot_int]
    type = AntitrappingCurrent
    variable = w
    v = etab0
    f_name = rhodiff
  [../]
[]

[Materials]
  [./ha]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0'
    phase_etas = 'etaa0'
  [../]
  [./hb]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0'
    phase_etas = 'etab0'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegab
    material_property_names = 'Vm kb cbeq'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
  [../]
  [./int]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhodiff
    material_property_names = 'rhoa rhob'
    constant_names = 'int_width'
    constant_expressions = '0.8'
    function = 'int_width*(rhob-rhoa)'
  [../]
  [./kappaa]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
    etaa = etaa0
    etab = etab0
  [../]
  [./kappab]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
    etaa = etab0
    etab = etaa0
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'L   D    chi  Vm   ka    caeq kb    cbeq  gab mu'
    prop_values = '1.0 1.0  0.1  1.0  10.0  0.1  10.0  0.9   4.5 10.0'
  [../]
  [./Mobility]
    type = ParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm      31                  lu           1'
  l_tol = 1.0e-3
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1e-8
  num_steps = 3
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.001
  [../]
[]

[Outputs]
  exodus = true
[]

modules/phase_field/test/tests/GrandPotentialPFM/GrandPotentialAnisotropy.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 15
  ny = 15
  xmin = -2
  xmax = 2
  ymin = -2
  ymax = 2
[]

# enable_jit set to false in many materials to make this test start up faster.
# It is recommended to set enable_jit = true or just remove these lines for
# production runs with this model
[GlobalParams]
  radius = 1.0
  int_width = 0.8
  x1 = 0
  y1 = 0
  derivative_order = 2
  enable_jit = false
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
[]

[AuxVariables]
  [./bnds]
  [../]
[]

[AuxKernels]
  [./bnds]
    type = BndsCalcAux
    variable = bnds
    v = 'etaa0 etab0'
  [../]
[]

[ICs]
  [./w]
    type = SmoothCircleIC
    variable = w
    # note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
    outvalue = -4.0
    invalue = 0.0
  [../]
  [./etaa0]
    type = SmoothCircleIC
    variable = etaa0
    #Solid phase
    outvalue = 0.0
    invalue = 1.0
  [../]
  [./etab0]
    type = SmoothCircleIC
    variable = etab0
    #Liquid phase
    outvalue = 1.0
    invalue = 0.0
  [../]
[]

[BCs]
  [./Periodic]
    [./w]
      variable = w
      auto_direction = 'x y'
    [../]
    [./etaa0]
      variable = etaa0
      auto_direction = 'x y'
    [../]
    [./etab0]
      variable = etab0
      auto_direction = 'x y'
    [../]
  [../]
[]

[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0'
    gamma_names = 'gab'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etab0 w'
  [../]
  [./ACa0_int1]
    type = ACInterface2DMultiPhase1
    variable = etaa0
    etas = 'etab0'
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
  [../]
  [./ACa0_int2]
    type = ACInterface2DMultiPhase2
    variable = etaa0
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0'
    gamma_names = 'gab'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 w'
  [../]
  [./ACb0_int1]
    type = ACInterface2DMultiPhase1
    variable = etab0
    etas = 'etaa0'
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
  [../]
  [./ACb0_int2]
    type = ACInterface2DMultiPhase2
    variable = etab0
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
[]

[Materials]
  [./ha]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0'
    phase_etas = 'etaa0'
  [../]
  [./hb]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0'
    phase_etas = 'etab0'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegab
    material_property_names = 'Vm kb cbeq'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq'
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
  [../]
  [./kappaa]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
    etaa = etaa0
    etab = etab0
    outputs = exodus
    output_properties = 'kappaa dkappadgrad_etaa'
  [../]
  [./kappab]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
    etaa = etab0
    etab = etaa0
    outputs = exodus
    output_properties = 'kappab dkappadgrad_etab'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'L   D    chi  Vm   ka    caeq kb    cbeq  gab mu'
    prop_values = '1.0 1.0  0.1  1.0  10.0  0.1  10.0  0.9   4.5 10.0'
  [../]
  [./Mobility]
    type = ParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  l_tol = 1.0e-5
  nl_rel_tol = 1.0e-10
  nl_abs_tol = 1e-12
  num_steps = 2
  dt = 0.001
[]

[Outputs]
  exodus = true
[]

modules/phase_field/examples/anisotropic_interfaces/GrandPotentialSolidification.i

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 28
  ny = 28
  xmin = -7
  xmax = 7
  ymin = -7
  ymax = 7
  uniform_refine = 2
[]

[GlobalParams]
  radius = 0.2
  int_width = 0.1
  x1 = 0.0
  y1 = 0.0
  derivative_order = 2
[]

[Variables]
  [./w]
  [../]
  [./etaa0]
  [../]
  [./etab0]
  [../]
  [./T]
  [../]
[]

[AuxVariables]
  [./bnds]
  [../]
[]

[AuxKernels]
  [./bnds]
    type = BndsCalcAux
    variable = bnds
    v = 'etaa0 etab0'
  [../]
[]

[ICs]
  [./w]
    type = SmoothCircleIC
    variable = w
    # note w = A*(c-cleq), A = 1.0, cleq = 0.0 ,i.e., w = c (in the matrix/liquid phase)
    outvalue = -4.0
    invalue = 0.0
  [../]
  [./etaa0]
    type = SmoothCircleIC
    variable = etaa0
    #Solid phase
    outvalue = 0.0
    invalue = 1.0
  [../]
  [./etab0]
    type = SmoothCircleIC
    variable = etab0
    #Liquid phase
    outvalue = 1.0
    invalue = 0.0
  [../]
[]

[Kernels]
# Order parameter eta_alpha0
  [./ACa0_bulk]
    type = ACGrGrMulti
    variable = etaa0
    v =           'etab0'
    gamma_names = 'gab'
  [../]
  [./ACa0_sw]
    type = ACSwitching
    variable = etaa0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etab0 w T'
  [../]
  [./ACa0_int1]
    type = ACInterface2DMultiPhase1
    variable = etaa0
    etas = 'etab0'
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
  [../]
  [./ACa0_int2]
    type = ACInterface2DMultiPhase2
    variable = etaa0
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
  [../]
  [./ea0_dot]
    type = TimeDerivative
    variable = etaa0
  [../]
# Order parameter eta_beta0
  [./ACb0_bulk]
    type = ACGrGrMulti
    variable = etab0
    v =           'etaa0'
    gamma_names = 'gab'
  [../]
  [./ACb0_sw]
    type = ACSwitching
    variable = etab0
    Fj_names  = 'omegaa omegab'
    hj_names  = 'ha     hb'
    args = 'etaa0 w T'
  [../]
  [./ACb0_int1]
    type = ACInterface2DMultiPhase1
    variable = etab0
    etas = 'etaa0'
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
  [../]
  [./ACb0_int2]
    type = ACInterface2DMultiPhase2
    variable = etab0
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
  [../]
  [./eb0_dot]
    type = TimeDerivative
    variable = etab0
  [../]
#Chemical potential
  [./w_dot]
    type = SusceptibilityTimeDerivative
    variable = w
    f_name = chi
  [../]
  [./Diffusion]
    type = MatDiffusion
    variable = w
    diffusivity = Dchi
  [../]
  [./coupled_etaa0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etaa0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./coupled_etab0dot]
    type = CoupledSwitchingTimeDerivative
    variable = w
    v = etab0
    Fj_names = 'rhoa rhob'
    hj_names = 'ha   hb'
    args = 'etaa0 etab0'
  [../]
  [./T_dot]
    type = TimeDerivative
    variable = T
  [../]
  [./CoefDiffusion]
    type = Diffusion
    variable = T
  [../]
  [./etaa0_dot_T]
    type = CoefCoupledTimeDerivative
    variable = T
    v = etaa0
    coef = -5.0
  [../]
[]

[Materials]
  [./ha]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = ha
    all_etas = 'etaa0 etab0'
    phase_etas = 'etaa0'
  [../]
  [./hb]
    type = SwitchingFunctionMultiPhaseMaterial
    h_name = hb
    all_etas = 'etaa0 etab0'
    phase_etas = 'etab0'
  [../]
  [./omegaa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = omegaa
    material_property_names = 'Vm ka caeq'
    function = '-0.5*w^2/Vm^2/ka-w/Vm*caeq'
  [../]
  [./omegab]
    type = DerivativeParsedMaterial
    args = 'w T'
    f_name = omegab
    material_property_names = 'Vm kb cbeq S Tm'
    function = '-0.5*w^2/Vm^2/kb-w/Vm*cbeq-S*(T-Tm)'
  [../]
  [./rhoa]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhoa
    material_property_names = 'Vm ka caeq'
    function = 'w/Vm^2/ka + caeq/Vm'
  [../]
  [./rhob]
    type = DerivativeParsedMaterial
    args = 'w'
    f_name = rhob
    material_property_names = 'Vm kb cbeq'
    function = 'w/Vm^2/kb + cbeq/Vm'
  [../]
  [./kappaa]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappaa
    dkappadgrad_etaa_name = dkappadgrad_etaa
    d2kappadgrad_etaa_name = d2kappadgrad_etaa
    etaa = etaa0
    etab = etab0
    anisotropy_strength = 0.05
    kappa_bar = 0.05
    outputs = exodus
    output_properties = 'kappaa'
  [../]
  [./kappab]
    type = InterfaceOrientationMultiphaseMaterial
    kappa_name = kappab
    dkappadgrad_etaa_name = dkappadgrad_etab
    d2kappadgrad_etaa_name = d2kappadgrad_etab
    etaa = etab0
    etab = etaa0
    anisotropy_strength = 0.05
    kappa_bar = 0.05
    outputs = exodus
    output_properties = 'kappab'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'L     D    chi  Vm   ka    caeq kb    cbeq  gab mu   S   Tm'
    prop_values = '33.33 1.0  0.1  1.0  10.0  0.1  10.0  0.9   4.5 10.0 1.0 5.0'
  [../]
  [./Mobility]
    type = ParsedMaterial
    f_name = Dchi
    material_property_names = 'D chi'
    function = 'D*chi'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre    boomeramg      31'
   l_tol = 1.0e-3
  l_max_its = 30
  nl_max_its = 15
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1e-10
  end_time = 2.0
  dtmax = 0.05
  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.0005
    cutback_factor = 0.7
    growth_factor = 1.2
  [../]
[]

[Adaptivity]
 initial_steps = 5
 max_h_level = 3
 initial_marker = err_eta
 marker = err_bnds
[./Markers]
   [./err_eta]
     type = ErrorFractionMarker
     coarsen = 0.3
     refine = 0.95
     indicator = ind_eta
   [../]
   [./err_bnds]
     type = ErrorFractionMarker
     coarsen = 0.3
     refine = 0.95
     indicator = ind_bnds
   [../]
 [../]
 [./Indicators]
   [./ind_eta]
     type = GradientJumpIndicator
     variable = etaa0
    [../]
    [./ind_bnds]
      type = GradientJumpIndicator
      variable = bnds
   [../]
 [../]
[]

[Outputs]
  interval = 5
  exodus = true
[]

Input Parameters
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