KKSPhaseConcentrationMultiPhaseDerivatives

Example input:

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  # simple toy free energies
  [F1]
    type = DerivativeParsedMaterial<<<{"description": "Parsed Function Material with automatic derivatives.", "href": "DerivativeParsedMaterial.html"}>>>
    property_name<<<{"description": "Name of the parsed material property"}>>> = F1
    expression<<<{"description": "Parsed function (see FParser) expression for the parsed material"}>>> = '20*(c1-0.2)^2'
    material_property_names<<<{"description": "Vector of material properties used in the parsed function"}>>> = 'c1'
    additional_derivative_symbols<<<{"description": "A list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t."}>>> = 'c1'
    compute<<<{"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."}>>> = false
  []
  [F2]
    type = DerivativeParsedMaterial<<<{"description": "Parsed Function Material with automatic derivatives.", "href": "DerivativeParsedMaterial.html"}>>>
    property_name<<<{"description": "Name of the parsed material property"}>>> = F2
    expression<<<{"description": "Parsed function (see FParser) expression for the parsed material"}>>> = '20*(c2-0.5)^2'
    material_property_names<<<{"description": "Vector of material properties used in the parsed function"}>>> = 'c2'
    additional_derivative_symbols<<<{"description": "A list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t."}>>> = 'c2'
    compute<<<{"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."}>>> = false
  []
  [F3]
    type = DerivativeParsedMaterial<<<{"description": "Parsed Function Material with automatic derivatives.", "href": "DerivativeParsedMaterial.html"}>>>
    property_name<<<{"description": "Name of the parsed material property"}>>> = F3
    expression<<<{"description": "Parsed function (see FParser) expression for the parsed material"}>>> = '20*(c3-0.8)^2'
    material_property_names<<<{"description": "Vector of material properties used in the parsed function"}>>> = 'c3'
    additional_derivative_symbols<<<{"description": "A list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t."}>>> = 'c3'
    compute<<<{"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."}>>> = false
  []
  [KKSPhaseConcentrationMultiPhaseMaterial]
    type = KKSPhaseConcentrationMultiPhaseMaterial<<<{"description": "Computes the KKS phase concentrations by using a nested Newton iteration to solve the equal chemical potential and concentration conservation equations for multiphase systems. This class is intented to be used with KKSPhaseConcentrationMultiPhaseDerivatives.", "href": "KKSPhaseConcentrationMultiPhaseMaterial.html"}>>>
    global_cs<<<{"description": "The interpolated concentrations c, b, etc."}>>> = 'c'
    all_etas<<<{"description": "Order parameters."}>>> = 'eta1 eta2 eta3'
    hj_names<<<{"description": "Switching functions in the same order as all_etas."}>>> = 'h1 h2 h3'
    ci_names<<<{"description": "Phase concentrations. They must have the same order as Fj_names and global_cs, for example, c1, c2, b1, b2."}>>> = 'c1 c2 c3'
    ci_IC<<<{"description": "Initial values of ci in the same order of ci_names"}>>> = '0.2 0.5 0.8'
    Fj_names<<<{"description": "Free energy material objects in the same order as all_etas."}>>> = 'F1 F2 F3'
    min_iterations<<<{"description": "Minimum number of nonlinear iterations to execute before accepting convergence"}>>> = 1
    max_iterations<<<{"description": "Maximum number of nonlinear iterations"}>>> = 1000
    absolute_tolerance<<<{"description": "Absolute convergence tolerance for Newton iteration"}>>> = 1e-11
    relative_tolerance<<<{"description": "Relative convergence tolerance for Newton iteration"}>>> = 1e-10
  []
  [KKSPhaseConcentrationMultiPhaseDerivatives]
    type = KKSPhaseConcentrationMultiPhaseDerivatives<<<{"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.", "href": "KKSPhaseConcentrationMultiPhaseDerivatives.html"}>>>
    global_cs<<<{"description": "The interpolated concentrations c, b, etc"}>>> = 'c'
    all_etas<<<{"description": "Order parameters."}>>> = 'eta1 eta2 eta3'
    Fj_names<<<{"description": "Free energy material objects in the same order as all_etas."}>>> = 'F1 F2 F3'
    hj_names<<<{"description": "witching functions in the same order as all_etas."}>>> = 'h1 h2 h3'
    ci_names<<<{"description": "Phase concentrations. They must have the same order as Fj_names and global_cs, for example, c1, c2, b1, b2."}>>> = 'c1 c2 c3'
  []

  # Switching functions for each phase
  # h1(eta1, eta2, eta3)
  [h1]
    type = SwitchingFunction3PhaseMaterial<<<{"description": "Material for switching function that prevents formation of a third phase at a two-phase interface: $h_i = \\eta_i^2/4 [15 (1-\\eta_i) [1 + \\eta_i - (\\eta_k - \\eta_j)^2] + \\eta_i (9\\eta_i^2 - 5)]$", "href": "SwitchingFunction3PhaseMaterial.html"}>>>
    eta_i<<<{"description": "Order parameter i"}>>> = eta1
    eta_j<<<{"description": "Order parameter j"}>>> = eta2
    eta_k<<<{"description": "Order parameter k"}>>> = eta3
    property_name<<<{"description": "Name of the parsed material property"}>>> = h1
  []
  # h2(eta1, eta2, eta3)
  [h2]
    type = SwitchingFunction3PhaseMaterial<<<{"description": "Material for switching function that prevents formation of a third phase at a two-phase interface: $h_i = \\eta_i^2/4 [15 (1-\\eta_i) [1 + \\eta_i - (\\eta_k - \\eta_j)^2] + \\eta_i (9\\eta_i^2 - 5)]$", "href": "SwitchingFunction3PhaseMaterial.html"}>>>
    eta_i<<<{"description": "Order parameter i"}>>> = eta2
    eta_j<<<{"description": "Order parameter j"}>>> = eta3
    eta_k<<<{"description": "Order parameter k"}>>> = eta1
    property_name<<<{"description": "Name of the parsed material property"}>>> = h2
  []
  # h3(eta1, eta2, eta3)
  [h3]
    type = SwitchingFunction3PhaseMaterial<<<{"description": "Material for switching function that prevents formation of a third phase at a two-phase interface: $h_i = \\eta_i^2/4 [15 (1-\\eta_i) [1 + \\eta_i - (\\eta_k - \\eta_j)^2] + \\eta_i (9\\eta_i^2 - 5)]$", "href": "SwitchingFunction3PhaseMaterial.html"}>>>
    eta_i<<<{"description": "Order parameter i"}>>> = eta3
    eta_j<<<{"description": "Order parameter j"}>>> = eta1
    eta_k<<<{"description": "Order parameter k"}>>> = eta2
    property_name<<<{"description": "Name of the parsed material property"}>>> = h3
  []

  # Barrier functions for each phase
  [g1]
    type = BarrierFunctionMaterial<<<{"description": "Helper material to provide $g(\\eta)$ and its derivative in a polynomial.\nSIMPLE: $\\eta^2(1-\\eta)^2$\nLOW: $\\eta(1-\\eta)$\nHIGH: $\\eta^2(1-\\eta^2)^2$", "href": "BarrierFunctionMaterial.html"}>>>
    g_order<<<{"description": "Polynomial order of the barrier function g(eta)"}>>> = SIMPLE
    eta<<<{"description": "Order parameter variable"}>>> = eta1
    function_name<<<{"description": "actual name for f(eta), i.e. 'h' or 'g'"}>>> = g1
  []
  [g2]
    type = BarrierFunctionMaterial<<<{"description": "Helper material to provide $g(\\eta)$ and its derivative in a polynomial.\nSIMPLE: $\\eta^2(1-\\eta)^2$\nLOW: $\\eta(1-\\eta)$\nHIGH: $\\eta^2(1-\\eta^2)^2$", "href": "BarrierFunctionMaterial.html"}>>>
    g_order<<<{"description": "Polynomial order of the barrier function g(eta)"}>>> = SIMPLE
    eta<<<{"description": "Order parameter variable"}>>> = eta2
    function_name<<<{"description": "actual name for f(eta), i.e. 'h' or 'g'"}>>> = g2
  []
  [g3]
    type = BarrierFunctionMaterial<<<{"description": "Helper material to provide $g(\\eta)$ and its derivative in a polynomial.\nSIMPLE: $\\eta^2(1-\\eta)^2$\nLOW: $\\eta(1-\\eta)$\nHIGH: $\\eta^2(1-\\eta^2)^2$", "href": "BarrierFunctionMaterial.html"}>>>
    g_order<<<{"description": "Polynomial order of the barrier function g(eta)"}>>> = SIMPLE
    eta<<<{"description": "Order parameter variable"}>>> = eta3
    function_name<<<{"description": "actual name for f(eta), i.e. 'h' or 'g'"}>>> = g3
  []

  # constant properties
  [constants]
    type = GenericConstantMaterial<<<{"description": "Declares material properties based on names and values prescribed by input parameters.", "href": "GenericConstantMaterial.html"}>>>
    prop_names<<<{"description": "The names of the properties this material will have"}>>> = 'L   kappa  M'
    prop_values<<<{"description": "The values associated with the named properties"}>>> = '0.7 1.0    0.025'
  []
[]

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

References