ADGrainGrowth

Grain-Boundary model poly-crystalline interface Allen-Cahn Kernel

ADGrainGrowth is the automatic differentiation version of the ACGrGrPoly Kernel and can be activated in the GrainGrowthAction through the use_automatic_differentiation parameter.

The Kernel implements the bulk part of the grain growth model Moelans et al. (2008) Allen-Cahn equation $var element = document.getElementById("moose-equation-4e6e9ce4-79e3-4554-b2f8-9abb9eecefca");katex.render("\\left(L\\mu(\\eta_i^3-\\eta_i+2\\gamma\\eta_i\\sum_{j\\neq i}\\eta_j^2),\\psi\\right),", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-2afea1b5-8fa0-4c98-aa8a-3332fc00ceef");katex.render("L", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the mobility, $var element = document.getElementById("moose-equation-f6c5f5f4-4820-45f3-838c-21433111e725");katex.render("\\eta_i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the kernel variable, and $var element = document.getElementById("moose-equation-3cbf1d81-233c-4b55-9c35-68236ffc06d1");katex.render("\\eta_j", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are the other order parameters. $var element = document.getElementById("moose-equation-970a8a12-5b1e-4a27-8fa7-a179c882d474");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-ce150044-8f00-4b7c-834d-bc11a590e734");katex.render("\\gamma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are model parameters contributing to the grain boundary energy $var element = document.getElementById("moose-equation-0fc0a07c-c563-40ff-bdff-077b30a2bb14");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ as $var element = document.getElementById("moose-equation-c115d614-a216-4cb6-a00e-bdbde44ecede");katex.render("\\sigma = g(\\gamma)\\sqrt{\\kappa\\mu},", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-0ecf177a-2742-435e-9cda-936f94788eb4");katex.render("\\kappa", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the gradient energy coefficient from ADACInterface and $var element = document.getElementById("moose-equation-327f96bb-b01f-440b-b617-2d0d89868dce");katex.render("g", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a function that needs to be numerically determined (see Moelans et al. (2008) for details).

$var element = document.getElementById("moose-equation-0f2e2221-9069-4f70-95ce-c890d0d549e0");katex.render("\\kappa_{i,j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-09743596-ef9a-4718-85d6-69a7628af15f");katex.render("\\gamma_{i,j}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ could be defined for specific grain boundaries (grain pairs). This is provided by the GBAnisotropy material.

Input Parameters

vArray of coupled order parameter names for other order parameters
C++ Type:std::vector
Options:
Description:Array of coupled order parameter names for other order 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

Required Parameters

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
displacementsThe displacements
C++ Type:std::vector
Options:
Description:The displacements
mob_nameLThe mobility used with the kernel
Default:L
C++ Type:MaterialPropertyName
Options:
Description:The mobility used with the kernel

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.
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.)
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
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.)
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

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
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
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

Tagging Parameters

References

N. Moelans, B. Blanpain, and P. Wollants. Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems. Physical Review B, 78(2):024113, Jul 2008. URL: http://link.aps.org/doi/10.1103/PhysRevB.78.024113, doi:10.1103/PhysRevB.78.024113.

@article{moelans_quantitative_2008,
    author = "Moelans, N. and Blanpain, B. and Wollants, P.",
    title = "Quantitative analysis of grain boundary properties in a generalized phase field model for grain growth in anisotropic systems",
    volume = "78",
    url = "http://link.aps.org/doi/10.1103/PhysRevB.78.024113",
    doi = "10.1103/PhysRevB.78.024113",
    number = "2",
    urldate = "2016-06-02",
    journal = "Physical Review B",
    month = "Jul",
    year = "2008",
    pages = "024113",
    file = "APS Snapshot:/Users/i.greenquist/Zotero/storage/Q8854BXX/PhysRevB.78.html:text/html;PhysRevB.78.024113.pdf:/Users/i.greenquist/Zotero/storage/VSMEC28A/PhysRevB.78.024113.pdf:application/pdf;PhysRevB.78.pdf:/Users/i.greenquist/Zotero/storage/VEU7AATJ/PhysRevB.78.pdf:application/pdf"
}

Input Parameters
References

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