Stretch-based Failure Criterion AuxKernel

Description

The StretchBasedFailureCriterionPD AuxKernel is to determine the status $var element = document.getElementById("moose-equation-1ab81db4-bba1-42d6-a052-33c9a1cf824e");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ of each individual bond using critical stretch failure criterion. For critical stretch failure criterion, if the bond's mechanical stretch $var element = document.getElementById("moose-equation-e244c5a0-4f72-4015-8062-6f97877d6073");katex.render("s", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ less than its critical value $var element = document.getElementById("moose-equation-76a23f17-f860-4148-b74f-27d020569cf2");katex.render("s_{0}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 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

$var element = document.getElementById("moose-equation-7f4bd0b0-61ec-438f-8fd3-e624dac271b4");katex.render(" \\mu \\left( \\mathbf{X}^{\\prime} - \\mathbf{X}, t \\right) = \\left\\{\\begin{matrix} 1 & s < s_{0} \\\\ 0 & s > s_{0} \\end{matrix}\\right.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

The bond critical stretch value can be calculated for the bond-based models from the critical energy release rate $var element = document.getElementById("moose-equation-9e280aa8-83f3-4e02-8f20-c26ef8af0782");katex.render("G_c", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ as

$var element = document.getElementById("moose-equation-058b9380-03d9-4705-b275-d5036da450c9");katex.render(" s_{0} = \\left\\{\\begin{matrix} \\sqrt{\\frac{\\pi G_{c}}{3K \\delta}} & \\text{two dimensional} \\\\ \\sqrt{\\frac{5 G_{c}}{9K \\delta}} & \\text{three dimensional} \\end{matrix}\\right.", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-1659a5d7-00eb-45d2-a650-9f298dc05773");katex.render("K", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the bulk modulus and $var element = document.getElementById("moose-equation-0ee14190-8014-45e9-9860-d78537351ae8");katex.render("\\delta", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the horizon size.

Derivation of above relationships can be found in Ref. (Silling and Askari, 2005).

Input Parameters

critical_variableName of critical AuxVariable
C++ Type:std::vector<VariableName>
Controllable:No
Description:Name of critical AuxVariable
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Controllable:No
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
Default:True
C++ Type:bool
Controllable:No
Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
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
Controllable:No
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_bond_status_convergence_BPD.i)
(modules/peridynamics/test/tests/failure_tests/2D_stretch_failure_BPD.i)

References

S.A. Silling and E. Askari. A meshfree method based on the peridynamic model of solid mechanics. Computers & Structures, 83(17):1526 – 1535, 2005. Advances in Meshfree Methods. URL: https://doi.org/10.1016/j.compstruc.2004.11.026, doi:10.1016/j.compstruc.2004.11.026.

@article{Silling2005meshfree,
    author = "Silling, S.A. and Askari, E.",
    title = "A Meshfree Method Based on the Peridynamic Model of Solid Mechanics",
    journal = "Computers \& Structures",
    volume = "83",
    number = "17",
    pages = "1526 - 1535",
    year = "2005",
    note = "Advances in Meshfree Methods",
    issn = "0045-7949",
    doi = "10.1016/j.compstruc.2004.11.026",
    url = "https://doi.org/10.1016/j.compstruc.2004.11.026"
}

(modules/peridynamics/test/tests/failure_tests/2D_bond_status_convergence_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]
  [./critical_stretch]
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

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

[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
  [../]
[]

[Postprocessors]
  [./bond_status_updated_times]
    type = BondStatusConvergedPostprocessorPD
  [../]
[]

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

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

  fixed_point_max_its = 5
  accept_on_max_fixed_point_iteration = true
  custom_pp = bond_status_updated_times
  custom_abs_tol = 2
  disable_fixed_point_residual_norm_check = true
[]

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

(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
[]

Description
Input Parameters
Input Files
References