Stretch-based Failure Criterion AuxKernel

Description

AuxKernel StretchBasedFailureCriterionPD is to determine the status $var element = document.getElementById("moose-equation-795235f1-2722-4c4f-8e74-cc8a3d8f5fa9");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ of each individual bond using critical stretch failure criterion. For critical stretch failure criterion, if the bond's mechanical stretch $var element = document.getElementById("moose-equation-7a49cfd5-0bf6-41ab-9340-6389bf71a93d");katex.render("s", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ less than its critical value $var element = document.getElementById("moose-equation-920911e5-0453-47b1-8511-7d120ba20b6a");katex.render("s_{0}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and intact in previous simulation step, the bond is considered as intact and a value of 1 is returned, otherwise, the bond is broken and a value of 0 is returned.

Critical stretch failure criterion

$var element = document.getElementById("moose-equation-203d7dd5-135f-459a-89eb-f4c1a4e8edf7");katex.render(" \\mu \\left( \\mathbf{X}^{\\prime} - \\mathbf{X}, t \\right) = \\left\\{\\begin{matrix} 1 & s < s_{0} \\\\ 0 & s > s_{0} \\end{matrix}\\right.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The bond critical stretch value can be calculated for the bond-based models from the critical energy release rate $var element = document.getElementById("moose-equation-97faa74c-ca3f-4c38-af1e-043d5a7122d2");katex.render("G_c", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ as

$var element = document.getElementById("moose-equation-622d27f9-ce37-43bc-bf1e-d0f239c4b0cb");katex.render(" s_{0} = \\left\\{\\begin{matrix} \\sqrt{\\frac{\\pi G_{c}}{3K \\delta}} & \\text{two dimensional} \\\\ \\sqrt{\\frac{5 G_{c}}{9K \\delta}} & \\text{three dimensional} \\end{matrix}\\right.", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-a5d69756-d0e6-463e-b2f1-c9b4afa7614e");katex.render("K", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the bulk modulus and $var element = document.getElementById("moose-equation-85585d32-2efc-4ebf-8f16-63522dfe6a25");katex.render("\\delta", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the horizon size.

Derivation of above relationships can be found in Ref. citep:.

Input Parameters

critical_variableName of critical AuxVariable
C++ Type:std::vector
Options:
Description:Name of critical AuxVariable
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Options:
Description:The name of the variable that this object applies to

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
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
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM PRE_DISPLACE
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.

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.
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

Input Files

modules/peridynamics/test/tests/failure_tests/2D_stretch_failure_BPD.i

modules/peridynamics/test/tests/failure_tests/2D_stretch_failure_BPD.i


[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3
  cracks_start = '0.25 0.5 0'
  cracks_end = '0.75 0.5 0'

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 8
    ny = 8
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./damage]
  [../]
  [./intact_bonds_num]
  [../]
  [./critical_stretch]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[AuxKernels]
  [./bond_status]
    type = StretchBasedFailureCriterionPD
    critical_variable = critical_stretch
    variable = bond_status
  [../]
[]

[UserObjects]
  [./damage]
    type = NodalDamageIndexPD
    variable = damage
  [../]
  [./intact_bonds]
    type = NodalNumIntactBondsPD
    variable = intact_bonds_num
  [../]
[]

[ICs]
  [./critical_stretch]
    type = ConstantIC
    variable = critical_stretch
    value = 0.001
  [../]
[]

[BCs]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1003
    value = 0.0
  [../]
  [./top_y]
    type = DirichletBC
    variable = disp_y
    boundary = 1002
    value = 0.0
  [../]
  [./bottom_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 1000
    function = '-0.001*t'
  [../]

  [./rbm_x]
    type = RBMPresetOldValuePD
    variable = disp_x
    boundary = 999
  [../]
  [./rbm_y]
    type = RBMPresetOldValuePD
    variable = disp_y
    boundary = 999
  [../]
[]

[Modules/Peridynamics/Mechanics/Master]
  [./all]
    formulation = BOND
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2e5
    poissons_ratio = 0.33
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialBPD
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  line_search = none
  start_time = 0
  dt = 0.5
  end_time = 1
[]

[Outputs]
  file_base = 2D_stretch_failure_BPD
  exodus = true
[]

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Input Parameters
Input Files

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