Self-stabilized Non-ordinary State-based Peridynamic Small Strain Mechanics Kernel

Description

Kernel SmallStrainMechanicsNOSPD calculates the residual and jacobian entries of the force density integral for self-stabilized non-ordinary state-based models under infinitesimal strain assumptions.

Force state

The force state for each Edge2 element, i.e., bond, is

$var element = document.getElementById("moose-equation-c31f2c66-2e02-4a3a-9231-f008763330d1");katex.render(" \\mathbf{f}\\left(\\mathbf{X},\\mathbf{X}^{\\prime},t\\right) = \\underline{\\mathbf{T}}\\left[\\mathbf{X},t\\right]\\left\\langle \\mathbf{X}^{\\prime}-\\mathbf{X} \\right\\rangle - \\underline{\\mathbf{T}}\\left[\\mathbf{X}^{\\prime},t\\right]\\left\\langle \\mathbf{X}-\\mathbf{X}^{\\prime} \\right\\rangle", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ with $var element = document.getElementById("moose-equation-581be7c3-8c40-491b-9e55-3a08a8fdf98c");katex.render(" \\underline{\\mathbf{T}}\\left[\\mathbf{X},t\\right]\\left\\langle \\mathbf{X}^{\\prime}-\\mathbf{X} \\right\\rangle = \\frac{\\int_{\\mathcal{H}_{\\mathbf{X}} \\cap h_{\\mathbf{X},\\boldsymbol{\\xi}}}1dV_{\\mathbf{X}^{\\prime}}}{\\int_{\\mathcal{H}_{\\mathbf{X}}}1 dV_{\\mathbf{X}^{\\prime}}} \\underline{\\omega}\\left\\langle \\boldsymbol{\\xi} \\right\\rangle \\mathbf{P}_{\\mathbf{X,\\boldsymbol{\\xi}}} \\mathbf{K}_{\\mathbf{X,\\boldsymbol{\\xi}}}^{-1} \\boldsymbol{\\xi}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

$var element = document.getElementById("moose-equation-7836d241-1ace-4b24-b005-1e781f4e23e2");katex.render(" \\underline{\\mathbf{T}}\\left[\\mathbf{X}^{\\prime},t\\right]\\left\\langle \\mathbf{X}-\\mathbf{X}^{\\prime} \\right\\rangle = - \\frac{\\int_{\\mathcal{H}_{\\mathbf{X}^{\\prime}} \\cap h_{\\mathbf{X}^{\\prime},-\\boldsymbol{\\xi}}}1dV_{\\mathbf{X}}}{\\int_{\\mathcal{H}_{\\mathbf{X}^{\\prime}}}1 dV_{\\mathbf{X}}} \\underline{\\omega}\\left\\langle \\boldsymbol{\\xi} \\right\\rangle \\mathbf{P}_{\\mathbf{X}^{\\prime},-\\boldsymbol{\\xi}} \\mathbf{K}_{\\mathbf{X}^{\\prime},-\\boldsymbol{\\xi}}^{-1} \\boldsymbol{\\xi}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

We don't distinguish Cauchy stress with the first Piola-Kichhoff stress under infinitesimal strain assumptions. The stress retrieved from ComputeLinearElasticStress is directly used in the force state calculation.

$var element = document.getElementById("moose-equation-611df9e4-ccc1-4605-a860-b22946cda7b1");katex.render(" \\mathbf{P} = \\boldsymbol{\\sigma}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

Input Parameters

componentAn integer corresponding to the variable this kernel acts on (0 for x, 1 for y, 2 for z)
C++ Type:unsigned int
Options:
Description:An integer corresponding to the variable this kernel acts on (0 for x, 1 for y, 2 for z)
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
eigenstrain_namesList of eigenstrains to be coupled in non-ordinary state-based mechanics kernels
C++ Type:std::vector
Options:
Description:List of eigenstrains to be coupled in non-ordinary state-based mechanics kernels
full_jacobianFalseWhether to include coupling terms with nodes connected to neighbors in the Jacobian matrix for state based formulations
Default:False
C++ Type:bool
Options:
Description:Whether to include coupling terms with nodes connected to neighbors in the Jacobian matrix for state based formulations
out_of_plane_strainNonlinear variable name for the out_of_plane strain for plane stress analysis using SNOSPD formulation
C++ Type:std::vector
Options:
Description:Nonlinear variable name for the out_of_plane strain for plane stress analysis using SNOSPD formulation
temperatureNonlinear variable name for the temperature
C++ Type:std::vector
Options:
Description:Nonlinear variable name for the temperature

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

Description
Force state
Input Parameters

Application Usage

Physics and Syntax

Application Development

Framework Development

MOOSEDocs

Infrastructure

Questions

Information and Tools