KKSPhaseConcentrationMultiPhaseDerivatives

Kim-Kim-Suzuki (KKS) nested solve material for multiphase models (part 2 of 2). KKSPhaseConcentrationMultiPhaseDerivatives computes the partial derivatives of phase concentrations w.r.t global concentrations and phase parameters, for example, , where is the global concentration and is the phase concentration of species in phase . Another example is where is a phase parameter in the model. These partial derivatives are used in KKS kernels as chain rule terms in the residual and Jacobian. The expressions for the derivatives were presented in Kim et al. (1999).

Example input:

[Materials]
  # simple toy free energies
  [F1]
    type = DerivativeParsedMaterial
    property_name = F1
    expression = '20*(c1-0.2)^2'
    material_property_names = 'c1'
    additional_derivative_symbols = 'c1'
    compute = false
  []
  [F2]
    type = DerivativeParsedMaterial
    property_name = F2
    expression = '20*(c2-0.5)^2'
    material_property_names = 'c2'
    additional_derivative_symbols = 'c2'
    compute = false
  []
  [F3]
    type = DerivativeParsedMaterial
    property_name = F3
    expression = '20*(c3-0.8)^2'
    material_property_names = 'c3'
    additional_derivative_symbols = 'c3'
    compute = false
  []
  [KKSPhaseConcentrationMultiPhaseMaterial]
    type = KKSPhaseConcentrationMultiPhaseMaterial
    global_cs = 'c'
    all_etas = 'eta1 eta2 eta3'
    hj_names = 'h1 h2 h3'
    ci_names = 'c1 c2 c3'
    ci_IC = '0.2 0.5 0.8'
    Fj_names = 'F1 F2 F3'
    min_iterations = 1
    max_iterations = 1000
    absolute_tolerance = 1e-11
    relative_tolerance = 1e-10
  []
  [KKSPhaseConcentrationMultiPhaseDerivatives]
    type = KKSPhaseConcentrationMultiPhaseDerivatives
    global_cs = 'c'
    all_etas = 'eta1 eta2 eta3'
    Fj_names = 'F1 F2 F3'
    hj_names = 'h1 h2 h3'
    ci_names = 'c1 c2 c3'
  []

  # Switching functions for each phase
  # h1(eta1, eta2, eta3)
  [h1]
    type = SwitchingFunction3PhaseMaterial
    eta_i = eta1
    eta_j = eta2
    eta_k = eta3
    property_name = h1
  []
  # h2(eta1, eta2, eta3)
  [h2]
    type = SwitchingFunction3PhaseMaterial
    eta_i = eta2
    eta_j = eta3
    eta_k = eta1
    property_name = h2
  []
  # h3(eta1, eta2, eta3)
  [h3]
    type = SwitchingFunction3PhaseMaterial
    eta_i = eta3
    eta_j = eta1
    eta_k = eta2
    property_name = h3
  []

  # Barrier functions for each phase
  [g1]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta1
    function_name = g1
  []
  [g2]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta2
    function_name = g2
  []
  [g3]
    type = BarrierFunctionMaterial
    g_order = SIMPLE
    eta = eta3
    function_name = g3
  []

  # constant properties
  [constants]
    type = GenericConstantMaterial
    prop_names = 'L   kappa  M'
    prop_values = '0.7 1.0    0.025'
  []
[]
(moose/modules/phase_field/test/tests/KKS_system/kks_example_multiphase_nested.i)

Class Description

Computes the KKS phase concentration derivatives wrt global concentrations and order parameters, which are used for the chain rule in the KKS kernels. This class is intended to be used with KKSPhaseConcentrationMultiPhaseMaterial.

Input Parameters

  • Fj_namesFree energy material objects in the same order as all_etas.

    C++ Type:std::vector<MaterialName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Free energy material objects in the same order as all_etas.

  • all_etasOrder parameters.

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Order parameters.

  • ci_namesPhase concentrations. They must have the same order as Fj_names and global_cs, for example, c1, c2, b1, b2.

    C++ Type:std::vector<MaterialPropertyName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Phase concentrations. They must have the same order as Fj_names and global_cs, for example, c1, c2, b1, b2.

  • global_csThe interpolated concentrations c, b, etc

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The interpolated concentrations c, b, etc

  • hj_nameswitching functions in the same order as all_etas.

    C++ Type:std::vector<MaterialPropertyName>

    Unit:(no unit assumed)

    Controllable:No

    Description:witching functions in the same order as all_etas.

Required Parameters

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • boundaryThe list of boundaries (ids or names) from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of boundaries (ids or names) from the mesh where this object 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

    Unit:(no unit assumed)

    Controllable:No

    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 computeQpProperties() 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

    Unit:(no unit assumed)

    Options:NONE, ELEMENT, SUBDOMAIN

    Controllable:No

    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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

  • declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

  • prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.

  • use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:Yes

    Description:Set the enabled status of the MooseObject.

  • implicitTrueDetermines whether this object is calculated using an implicit or explicit form

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

  • output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

  • outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object

    Default:none

    C++ Type:std::vector<OutputName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

References

  1. Seong Gyoon Kim, Won Tae Kim, and Toshio Suzuki. Phase-field model for binary alloys. Physical Review E, 60(6):7186–7197, December 1999. URL: http://link.aps.org/doi/10.1103/PhysRevE.60.7186 (visited on 2014-03-31), doi:10.1103/PhysRevE.60.7186.[BibTeX]