Two-phase models

MOOSE provides capabilities that enable the easy development of multiphase field model. A free energy expression has to be provided for each individual phase. Two different systems exist to combine those phase free energies into a global free energy.

Material objects that internally derive from DerivativeFunctionMaterialBase (Doxygen), like the materials for the Parsed Function Kernels are used to provide the free energy expressions for each phase.

The simplified two-phase model uses a single order parameter to switch between the two phases. A global free energy is constructed using a meta material class that combines the phase free energies.

For two phase models the DerivativeTwoPhaseMaterial (Doxygen) can be used to combine two phase free energies into a global free energy (which the Allen-Cahn and Cahn-Hilliard kernels use to evolve the system) as

Input Parameters

  • etaOrder parameter

    C++ Type:std::vector

    Options:

    Description:Order parameter

  • fa_namePhase A material (at eta=0)

    C++ Type:MaterialPropertyName

    Options:

    Description:Phase A material (at eta=0)

  • fb_namePhase A material (at eta=1)

    C++ Type:MaterialPropertyName

    Options:

    Description:Phase A material (at eta=1)

Required Parameters

  • W0Energy barrier for the phase transformation from A to B

    Default:0

    C++ Type:double

    Options:

    Description:Energy barrier for the phase transformation from A to B

  • argsArguments of fa and fb - use vector coupling

    C++ Type:std::vector

    Options:

    Description:Arguments of fa and fb - use vector coupling

  • 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 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

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

  • derivative_order3Maximum order of derivatives taken (2 or 3)

    Default:3

    C++ Type:unsigned int

    Options:

    Description:Maximum order of derivatives taken (2 or 3)

  • displacement_gradientsVector of displacement gradient variables (see Modules/PhaseField/DisplacementGradients action)

    C++ Type:std::vector

    Options:

    Description:Vector of displacement gradient variables (see Modules/PhaseField/DisplacementGradients action)

  • f_nameFBase name of the free energy function (used to name the material properties)

    Default:F

    C++ Type:std::string

    Options:

    Description:Base name of the free energy function (used to name the material properties)

  • ggBarrier Function Material that provides g(eta)

    Default:g

    C++ Type:MaterialPropertyName

    Options:

    Description:Barrier Function Material that provides g(eta)

  • hhSwitching Function Material that provides h(eta)

    Default:h

    C++ Type:MaterialPropertyName

    Options:

    Description:Switching Function Material that provides h(eta)

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

Check out the example input at modules/phase_field/tests/MultiPhase/derivativetwophasematerial.i to see it in action.

Outputs Parameters

Example

An example material block looks like this (materials for phase field mobilities omitted for clarity).


[Materials]
# Free energy for phase A

[./free_energy_A]
  type = DerivativeParsedMaterial
  block = 0
  f_name = Fa
  args = 'c'
  function = '(c-0.1)^2'
  third_derivatives = false
  enable_jit = true
[../]

# Free energy for phase B

[./free_energy_B]
  type = DerivativeParsedMaterial
  block = 0
  f_name = Fb
  args = 'c'
  function = '(c-0.9)^2'
  third_derivatives = false
  enable_jit = true
[../]

[./switching]
  type = SwitchingFunctionMaterial
  block = 0
  eta = eta
  h_order = SIMPLE
[../]

[./barrier]
  type = BarrierFunctionMaterial
  block = 0
  eta = eta
  g_order = SIMPLE
[../]

# Total free energy F = h(phi)*Fb + (1-h(phi))*Fa

[./free_energy]
  type = DerivativeTwoPhaseMaterial
  block = 0
  f_name = F    # Name of the global free energy function (use this in the Parsed Function Kernels)
  fa_name = Fa  # f_name of the phase A free energy function
  fb_name = Fb  # f_name of the phase B free energy function
  args = 'c'
  eta = eta     # order parameter that switches between A and B phase
  third_derivatives = false
  outputs = exodus
[../]
[]

Note that the phase free energies are single wells. The global free energy landscape will however have a double well character in this example.