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

$(1)var element = document.getElementById("moose-equation-2e08dd51-0da3-4eeb-a094-1c6b0b3341ea");katex.render("\\frac{dF_a}{dc_a}=\\frac{dF_b}{dc_b}.", element, {displayMode:true,throwOnError:false});$

The non-linear variable of this Kernel is $var element = document.getElementById("moose-equation-069b6302-2b4b-49e0-a8d0-26452152984e");katex.render("c_a", element, {displayMode:false,throwOnError:false});$ .

Residual

$(2)var element = document.getElementById("moose-equation-a137374c-6223-4063-a76a-a37536d42cbd");katex.render("R=\\frac{dF_a}{dc_a} - \\frac{dF_b}{dc_b}", element, {displayMode:true,throwOnError:false});$

Jacobian

For the Jacobian we need to calculate

$(3)var element = document.getElementById("moose-equation-108a7c4e-db96-4462-8af0-63a225889e72");katex.render("J=\\frac \\partial{\\partial u_j}\\left( \\frac{dF_a}{dc_a} - \\frac{dF_b}{dc_b} \\right).", element, {displayMode:true,throwOnError:false});$

On-Diagonal

$(4)var element = document.getElementById("moose-equation-d5e89cef-0a2e-458d-a8fc-4ef3713c75f8");katex.render("J = \\phi_j \\left( \\frac{\\partial^2 F_a}{\\partial c_a^2} - \\frac{\\partial^2 F_b}{\\partial c_a \\partial c_b} \\right)", element, {displayMode:true,throwOnError:false});$

Off-Diagonal

With $var element = document.getElementById("moose-equation-e70e6202-6d75-4f6f-9cdd-d85d4b6eb1da");katex.render("q", element, {displayMode:false,throwOnError:false});$ the union of the argument vectors of $var element = document.getElementById("moose-equation-3706b7b6-7d95-4468-a734-02bf363112c0");katex.render("F_a", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-e39cc8a4-8b4e-413c-8cc4-791245dfb953");katex.render("F_b", element, {displayMode:false,throwOnError:false});$ (represented in the code by _coupled_moose_vars[]) we get

$(5)var element = document.getElementById("moose-equation-286f3ae0-f46f-4e01-8307-c31df94d9d5b");katex.render("\\sum_i \\left( \\frac{\\partial^2 F_a}{\\partial c_a \\partial q_i}\\frac{\\partial q_i}{\\partial u_j} - \\frac{\\partial^2 F_b}{\\partial c_b \\partial q_i}\\frac{\\partial q_i}{\\partial u_j} \\right).", element, {displayMode:true,throwOnError:false});$

Again the $var element = document.getElementById("moose-equation-32c99918-edef-4fc1-bb45-4f996c76ad0a");katex.render("\\frac{\\partial q_i}{\\partial u_j}", element, {displayMode:false,throwOnError:false});$ is non-zero only if $var element = document.getElementById("moose-equation-1ae78331-6439-4c1f-8e24-b75171de356d");katex.render("u\\equiv q_i", element, {displayMode:false,throwOnError:false});$ , which is the case if $var element = document.getElementById("moose-equation-33571a72-0e0d-4006-b636-cc50926ec0c7");katex.render("q_i", element, {displayMode:false,throwOnError:false});$ is the argument selected through jvar.

$(6)var element = document.getElementById("moose-equation-99695a8a-8e17-485d-a733-c61614da2725");katex.render("J = \\frac{\\partial^2 F_a}{\\partial c_a \\partial q_\\text{jvar}}\\phi_j - \\frac{\\partial^2 F_b}{\\partial c_b \\partial q_\\text{jvar}}\\phi_j.", element, {displayMode:true,throwOnError:false});$

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

variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this Kernel operates on
cbPhase b concentration
C++ Type:std::vector
Options:
Description:Phase b concentration
fa_nameBase name of the free energy function Fa (f_name in the corresponding derivative function material)
C++ Type:MaterialPropertyName
Options:
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
Options:
Description:Base name of the free energy function Fb (f_name in the corresponding derivative function material)

Required 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

Optional Parameters

enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
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.)
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.
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.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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.)
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

Advanced Parameters

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
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
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

Tagging Parameters

Input Files

modules/phase_field/test/tests/KKS_system/kks_example.i
modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i
modules/phase_field/test/tests/KKS_system/kks_example_split.i
modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i
modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i
modules/phase_field/test/tests/KKS_system/kks_example_offset.i
modules/phase_field/test/tests/KKS_system/kks_multiphase.i
modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i
modules/phase_field/test/tests/KKS_system/kks_phase_concentration.i
modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i

Input Parameters
Input Files

Application Usage

Physics and Syntax

Application Development

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MOOSEDocs

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Questions

Information and Tools

KKSPhaseChemicalPotential

Residual

Jacobian

On-Diagonal

Off-Diagonal

Input Parameters

Required Parameters

Optional Parameters

Advanced Parameters

Tagging Parameters

Input Files

KKSPhaseChemicalPotential

Residual

Jacobian

On-Diagonal

Off-Diagonal

Input Parameters

Required Parameters

Optional Parameters

Advanced Parameters

Tagging Parameters

Input Files

modules/phase_field/test/tests/KKS_system/kks_example.i

modules/phase_field/examples/kim-kim-suzuki/kks_example_noflux.i

modules/phase_field/test/tests/KKS_system/kks_example_split.i

modules/combined/examples/phase_field-mechanics/kks_mechanics_KHS.i

modules/combined/examples/phase_field-mechanics/kks_mechanics_VTS.i

modules/phase_field/test/tests/KKS_system/kks_example_offset.i

modules/phase_field/test/tests/KKS_system/kks_multiphase.i

modules/phase_field/examples/kim-kim-suzuki/kks_example_dirichlet.i

modules/phase_field/test/tests/KKS_system/kks_phase_concentration.i

modules/phase_field/examples/kim-kim-suzuki/kks_example_ternary.i