MeshCut2DFractureUserObject

XFEM mesh cutter for 2D models that defines cuts with amesh and uses fracture integrals to determine growth

Overview

This class is used to define an evolving cutting plane for 2D XFEM simulations based on a mesh that defines the initial crack and uses fracture integrals or maximum stress to grow that crack. It (1) reads in a mesh describing the crack surface or uses nucleated cracks, (2) uses the mesh to do initial cutting of 2D elements, and (3) grows the mesh incrementally based on fracture domain integrals to allow nonplanar crack growth based on propagation directions determined by fracture integrals. A maximum stress criterion can also be used to drive crack growth.

The crack propagates if the failure criterion is met, given by:

$var element = document.getElementById("moose-equation-f56e3c34-76eb-4857-bd6c-44480199f3c0");katex.render("K_c \\le \\sqrt{K^2_I+K^2_{II}}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-c01da33e-a896-4ace-bbe3-a881bf05ac9f");katex.render("K_I", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-4a8b4fd6-bcac-4448-af0f-518c18b77db9");katex.render("K_{II}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are the mode I and II stress intensity factors provided by the fracture integral and the material property $var element = document.getElementById("moose-equation-c5f3142f-5a00-4635-892c-272cf5841b7e");katex.render("K_c", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is given defined in the input file by "k_critical". The crack growth direction is given by the direction the maximized the crack-tip hoop stress, given by Equation 5 in Jiang et al. (2020). The growth increment is a user provided input given in the defined by "growth_increment". The fracture integrals $var element = document.getElementById("moose-equation-db383e21-cc7b-4786-8fab-1501645cc867");katex.render("K_I", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ and $var element = document.getElementById("moose-equation-3d4b8382-60fc-4d72-8bce-22bc90e2c095");katex.render("K_{II}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ are obtained from the Interaction Integral vectorpostprocessor specified in the input file by "ki_vectorpostprocessor" and "kii_vectorpostprocessor". Defaults for "ki_vectorpostprocessor" and "kii_vectorpostprocessor" use the names produced by the DomainIntegralAction which is the standard way to set-up the Interaction Integral.

Near a free surface, the integration volumes of the rings used to compute the InteractionIntegral will intersect the surface, leading to a reduction in the fracture integral values. This can lead to cracks becoming unable to farther propagate as they approach free surfaces. For these cases, a maximum stress criterion computed using CrackFrontNonlocalStress vectorpostprocessor can be used for crack growth using an additional failure criterion given by:

$var element = document.getElementById("moose-equation-9fa28fc6-c684-4677-9af1-d168c2795eaa");katex.render("\\sigma_c \\le \\sigma_{nn}", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where $var element = document.getElementById("moose-equation-e065b412-ffff-40ba-92c5-0e1be8e7afc7");katex.render("\\sigma_c", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is a critcal stress normal to the crack face specified by "stress_threshold" and $var element = document.getElementById("moose-equation-cc868e50-7a55-4349-a1ae-823d7f92e73e");katex.render("\\sigma_{nn}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the average scalar stress measure normal to the crack face specified by "stress_vectorpostprocessor". The crack front normal stress will only extend the crack in the direction it is already going and will not cause the crack to curve.

Quasistatic behavior is assumed, and an iterative approach is taken to repeatedly solve the equilibrium equations, evaluate the fracture integrals, and as indicated by the failure criterion, incrementally advance the crack until the failure criterion is no longer met. To iteratively repeat the solution in this manner for each step, "max_xfem_update" must be set in the Executioner block, and should be large enough to allow a sufficient number of iterations for crack growth to cease during each timestep.

Example Input Syntax

The following input file provides an example of a MeshCut2DFractureUserObject that uses fracture integrals to propagate the crack. In this example, crack growth stops before the crack grows through the right boundary due to the fracture integral q-function intersecting the boundary. A stress based crack growth criterion is used in conjunction with the fracture integrals by uncommenting the two lines containing stress_vectorpostprocessor and stress_threshold in the MeshCut2DFractureUserObject. The stress based growth criterion causes the crack to continue to grow through the right boundary, as expected.

[UserObjects]
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    growth_increment = 0.05
    ki_vectorpostprocessor = "II_KI_1"
    kii_vectorpostprocessor = "II_KII_1"
    k_critical = 100
    # stress_vectorpostprocessor = "CrackFrontNonlocalStressVpp"
    # stress_threshold = 120
  []
[]

Input Parameters

growth_incrementLength to grow crack if k>k_critical or stress>stress_threshold
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Length to grow crack if k>k_critical or stress>stress_threshold
mesh_fileMesh file for the XFEM geometric cut; currently only the Exodus type is supported
C++ Type:MeshFileName
Unit:(no unit assumed)
Controllable:No
Description:Mesh file for the XFEM geometric cut; currently only the Exodus type is supported

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Unit:(no unit assumed)
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
crack_front_definitioncrackFrontDefinitionThe CrackFrontDefinition user object name
Default:crackFrontDefinition
C++ Type:UserObjectName
Unit:(no unit assumed)
Controllable:No
Description:The CrackFrontDefinition user object name
execute_onXFEM_MARKThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:XFEM_MARK
C++ Type:ExecFlagEnum
Unit:(no unit assumed)
Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
heal_alwaysFalseHeal previous cuts at every time step
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Heal previous cuts at every time step
k_criticalCritical fracture toughness.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Critical fracture toughness.
ki_vectorpostprocessorII_KI_1The name of the vectorpostprocessor that contains KI
Default:II_KI_1
C++ Type:VectorPostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the vectorpostprocessor that contains KI
kii_vectorpostprocessorII_KII_1The name of the vectorpostprocessor that contains KII
Default:II_KII_1
C++ Type:VectorPostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the vectorpostprocessor that contains KII
nucleate_uoThe MeshCutNucleation UO for nucleating cracks.
C++ Type:UserObjectName
Unit:(no unit assumed)
Controllable:No
Description:The MeshCutNucleation UO for nucleating cracks.
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
Unit:(no unit assumed)
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.
stress_thresholdStress threshold for growing crack
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Stress threshold for growing crack
stress_vectorpostprocessorThe name of the vectorpostprocessor that contains crack front stress
C++ Type:VectorPostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:The name of the vectorpostprocessor that contains crack front stress
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
Unit:(no unit assumed)
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

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:Yes
Description:Set the enabled status of the MooseObject.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Unit:(no unit assumed)
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Unit:(no unit assumed)
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Unit:(no unit assumed)
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
Unit:(no unit assumed)
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/xfem/test/tests/nucleation_uo/nucleate_bulkCrack.i)
(modules/xfem/test/tests/mesh_cut_2D_fracture/edge_crack_2d_propagation.i)
(modules/xfem/test/tests/nucleation_uo/nucleate_AllEdgeCracks.i)
(modules/xfem/test/tests/nucleation_uo/nucleate_edge_bulk_crack_2d.i)

References

Wen Jiang, Benjamin W. Spencer, and John E. Dolbow. Ceramic nuclear fuel fracture modeling with the extended finite element method. Engineering Fracture Mechanics, 223:106713, 2020. URL: http://www.sciencedirect.com/science/article/pii/S0013794419307568, doi:https://doi.org/10.1016/j.engfracmech.2019.106713.

@article{jiang2020,
    author = "Jiang, Wen and Spencer, Benjamin W. and Dolbow, John E.",
    title = "Ceramic nuclear fuel fracture modeling with the extended finite element method",
    journal = "Engineering Fracture Mechanics",
    volume = "223",
    pages = "106713",
    year = "2020",
    issn = "0013-7944",
    doi = "https://doi.org/10.1016/j.engfracmech.2019.106713",
    url = "http://www.sciencedirect.com/science/article/pii/S0013794419307568"
}

(modules/xfem/test/tests/mesh_cut_2D_fracture/edge_crack_2d_propagation.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[XFEM]
  geometric_cut_userobjects = 'cut_mesh2'
  qrule = volfrac
  output_cut_plane = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 45
    ny = 15
    xmin = -1
    xmax = 0.49
    ymin = 0.0
    ymax = 1.0
    elem_type = QUAD4
  []
  [dispBlock]
    type = BoundingBoxNodeSetGenerator
    new_boundary = pull_set
    bottom_left = '-0.1 0.99 0'
    top_right = '0.1 1.01 0'
    input = gen
  []
[]

[DomainIntegral]
  integrals = 'Jintegral InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh2
  2d = true
  number_points_from_provider = 2
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = true
  used_by_xfem_to_grow_crack = true
[]

[VectorPostprocessors]
  [CrackFrontNonlocalStressVpp]
    type = CrackFrontNonlocalStress
    crack_front_definition = crackFrontDefinition
    box_length = 0.05
    box_height = 0.1
    execute_on = NONLINEAR
  []
[]
[UserObjects]
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    growth_increment = 0.05
    ki_vectorpostprocessor = "II_KI_1"
    kii_vectorpostprocessor = "II_KII_1"
    k_critical = 100
    # stress_vectorpostprocessor = "CrackFrontNonlocalStressVpp"
    # stress_threshold = 120
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    incremental = true
    planar_formulation = plane_strain
    add_variables = true
    generate_output = 'stress_xx stress_yy'
  []
[]

[Functions]
  [pull_func]
    type = ParsedFunction
    expression = 0.00025*(1+t)
  []
[]

[BCs]
  [top_y]
    type = FunctionDirichletBC
    boundary = pull_set
    variable = disp_y
    function = pull_func
  []
  [bottom_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 207000
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                 NONZERO               1e-20'
  line_search = 'none'
  [Predictor]
    type = SimplePredictor
    scale = 1.0
  []
  # time control
  start_time = 0.0
  dt = 1.0
  end_time = 3
  max_xfem_update = 100
[]

[Outputs]
  exodus = true
  [xfemcutter]
    type = XFEMCutMeshOutput
    xfem_cutter_uo = cut_mesh2
  []
  [console]
    type = Console
    output_linear = false
    output_nonlinear = false
  []
[]

(modules/xfem/test/tests/nucleation_uo/nucleate_bulkCrack.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[XFEM]
  geometric_cut_userobjects = 'cut_mesh2'
  qrule = volfrac
  output_cut_plane = true
[]

[Mesh]
[gen]
  type = GeneratedMeshGenerator
  dim = 2
  nx = 10
  ny = 20
  xmin = 0
  xmax = 1.0
  ymin = 0.0
  ymax = 2.0
  elem_type = QUAD4
[]

[]

[DomainIntegral]
  integrals = 'InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh2
  2d=true
  number_points_from_provider = 0
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.0
  youngs_modulus = 207000
  block = 0
  incremental = true
  used_by_xfem_to_grow_crack = true
[]

[AuxVariables]
[strength]
  order = CONSTANT
  family = MONOMIAL
[]
[]

[ICs]
[strength]
  type = VolumeWeightedWeibull
  variable = strength
  reference_volume = 1e-2
  weibull_modulus = 1
  median = 5000
[]
[]

[UserObjects]
  [nucleate]
    type = MeshCut2DRankTwoTensorNucleation
    tensor = stress
    scalar_type = MaxPrincipal
    nucleation_threshold = strength
    nucleation_radius = .21
    edge_extension_factor = .1
  []
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    k_critical=500000 #Large so that cracks will not grow
    growth_increment = 0.11
    nucleate_uo = nucleate
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    planar_formulation = plane_strain
    add_variables = true
    generate_output = 'stress_xx stress_yy vonmises_stress max_principal_stress'
  []
[]

[Functions]
  [bc_pull_top]
    type = ParsedFunction
    expression = 0.0005*t
  []
[]

[BCs]
  [top_edges]
      type = FunctionDirichletBC
      boundary = 'top'
      variable = disp_y
      function = bc_pull_top
  []
  [bottom_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 207000
    poissons_ratio = 0.0
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'none'

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]

  l_max_its = 100
  l_tol = 1e-2

  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9

  start_time = 0.0
  dt = 1.0
  end_time = 5
  max_xfem_update = 1
[]

[Outputs]
  csv=true
  execute_on = final
  # exodus=true
  # [xfemcutter]
  #   type=XFEMCutMeshOutput
  #   xfem_cutter_uo=cut_mesh2
  # []
[]

(modules/xfem/test/tests/mesh_cut_2D_fracture/edge_crack_2d_propagation.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[XFEM]
  geometric_cut_userobjects = 'cut_mesh2'
  qrule = volfrac
  output_cut_plane = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 45
    ny = 15
    xmin = -1
    xmax = 0.49
    ymin = 0.0
    ymax = 1.0
    elem_type = QUAD4
  []
  [dispBlock]
    type = BoundingBoxNodeSetGenerator
    new_boundary = pull_set
    bottom_left = '-0.1 0.99 0'
    top_right = '0.1 1.01 0'
    input = gen
  []
[]

[DomainIntegral]
  integrals = 'Jintegral InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh2
  2d = true
  number_points_from_provider = 2
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = true
  used_by_xfem_to_grow_crack = true
[]

[VectorPostprocessors]
  [CrackFrontNonlocalStressVpp]
    type = CrackFrontNonlocalStress
    crack_front_definition = crackFrontDefinition
    box_length = 0.05
    box_height = 0.1
    execute_on = NONLINEAR
  []
[]
[UserObjects]
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    growth_increment = 0.05
    ki_vectorpostprocessor = "II_KI_1"
    kii_vectorpostprocessor = "II_KII_1"
    k_critical = 100
    # stress_vectorpostprocessor = "CrackFrontNonlocalStressVpp"
    # stress_threshold = 120
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    incremental = true
    planar_formulation = plane_strain
    add_variables = true
    generate_output = 'stress_xx stress_yy'
  []
[]

[Functions]
  [pull_func]
    type = ParsedFunction
    expression = 0.00025*(1+t)
  []
[]

[BCs]
  [top_y]
    type = FunctionDirichletBC
    boundary = pull_set
    variable = disp_y
    function = pull_func
  []
  [bottom_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 207000
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                 NONZERO               1e-20'
  line_search = 'none'
  [Predictor]
    type = SimplePredictor
    scale = 1.0
  []
  # time control
  start_time = 0.0
  dt = 1.0
  end_time = 3
  max_xfem_update = 100
[]

[Outputs]
  exodus = true
  [xfemcutter]
    type = XFEMCutMeshOutput
    xfem_cutter_uo = cut_mesh2
  []
  [console]
    type = Console
    output_linear = false
    output_nonlinear = false
  []
[]

(modules/xfem/test/tests/nucleation_uo/nucleate_AllEdgeCracks.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[XFEM]
  geometric_cut_userobjects = 'cut_mesh2'
  qrule = volfrac
  output_cut_plane = true
[]

[Mesh]
[gen]
  type = GeneratedMeshGenerator
  dim = 2
  nx = 10
  ny = 20
  xmin = 0
  xmax = 1.0
  ymin = 0.0
  ymax = 2.0
  elem_type = QUAD4
[]
[top_left]
  type = BoundingBoxNodeSetGenerator
  new_boundary = pull_top_left
  bottom_left = '-0.01 1.99 0'
  top_right = '0.11 2.01 0'
  input = gen
[]
[]

[DomainIntegral]
  integrals = 'InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh2
  2d=true
  number_points_from_provider = 0
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = true
  used_by_xfem_to_grow_crack = true
[]

[UserObjects]
  [nucleate]
    type = MeshCut2DRankTwoTensorNucleation
    tensor = stress
    scalar_type = MaxPrincipal
    nucleation_threshold = 180
    initiate_on_boundary = 'left'
    nucleation_radius = .21
    edge_extension_factor = 2e-5
    nucleation_length = 0.11
  []
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    k_critical=500000 #Large so that cracks will not grow
    growth_increment = 0.11
    nucleate_uo = nucleate
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    planar_formulation = plane_strain
    add_variables = true
    generate_output = 'stress_xx stress_yy vonmises_stress max_principal_stress'
  []
[]

[Functions]
  [bc_pull_top]
    type = ParsedFunction
    expression = 0.0005*t
  []
[]

[BCs]
  [top_edges]
      type = FunctionDirichletBC
      boundary = 'pull_top_left'
      variable = disp_y
      function = bc_pull_top
  []
  [bottom_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 207000
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'none'

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]

  l_max_its = 100
  l_tol = 1e-2

  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9

  start_time = 0.0
  dt = 1.0
  end_time = 5
  max_xfem_update = 100
[]

[Outputs]
  csv=true
  execute_on = TIMESTEP_END
[]

(modules/xfem/test/tests/nucleation_uo/nucleate_edge_bulk_crack_2d.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[XFEM]
  geometric_cut_userobjects = 'cut_mesh2'
  qrule = volfrac
  output_cut_plane = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 60
    ny = 10
    xmin = -3
    xmax = 3
    ymin = 0.0
    ymax = 1.0
    elem_type = QUAD4
  []
  [top_left]
    type = BoundingBoxNodeSetGenerator
    new_boundary = pull_top_left
    bottom_left = '-3.01 0.99 0'
    top_right = '-2.99 1.01 0'
    input = gen
  []
  [top_mid_left]
    type = BoundingBoxNodeSetGenerator
    new_boundary = pull_mid_left
    bottom_left = '-1.01 0.99 0'
    top_right = '-0.99 1.01 0'
    input = top_left
  []
  [top_mid_right]
    type = BoundingBoxNodeSetGenerator
    new_boundary = pull_mid_right
    bottom_left = '0.99 0.99 0'
    top_right = '1.01 1.01 0'
    input = top_mid_left
  []
  [top_right]
    type = BoundingBoxNodeSetGenerator
    new_boundary = pull_top_right
    bottom_left = '2.99 0.99 0'
    top_right = '3.01 1.01 0'
    input = top_mid_right
  []

  [top_mid_left_ss]
    type = SideSetsFromBoundingBoxGenerator
    input = top_right
    bottom_left = '-2.21 0.89 0'
    top_right = '-1.79 1.01 0'
    boundary_new = top_mid_left_ss
    boundaries_old = top
  []
  [top_mid_ss]
    type = SideSetsFromBoundingBoxGenerator
    input = top_mid_left_ss
    bottom_left = '-0.21 0.89 0'
    top_right = '0.21 1.01 0'
    boundary_new = top_mid_ss
    boundaries_old = top
  []
  [top_mid_right_ss]
    type = SideSetsFromBoundingBoxGenerator
    input = top_mid_ss
    bottom_left = '1.79 0.89 0'
    top_right = '2.21 1.01 0'
    boundary_new = top_mid_right_ss
    boundaries_old = top
  []

  [nucleation_strip]
    # strip in middle of domain where cracks can nucleate
    type = ParsedSubdomainMeshGenerator
    input = top_mid_right_ss
    combinatorial_geometry = 'y > 0.39 & y < 0.51'
    block_id = 10
  []
[]

[DomainIntegral]
  integrals = 'InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh2
  2d = true
  number_points_from_provider = 0
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.15'
  radius_outer = '0.45'
  poissons_ratio = 0.3
  youngs_modulus = 207000
  block = 0
  incremental = false
  used_by_xfem_to_grow_crack = true
[]

[UserObjects]
  [nucleate]
    type = MeshCut2DRankTwoTensorNucleation
    tensor = stress
    scalar_type = MaxPrincipal
    nucleation_threshold = nucleation_threshold
    # initiate_on_boundary = 'left right'
    nucleation_radius = .41
    nucleation_length = 0.21
  []
  [cut_mesh2]
    type = MeshCut2DFractureUserObject
    mesh_file = make_edge_crack_in.e
    k_critical = 230
    growth_increment = 0.11
    nucleate_uo = nucleate
    execute_on = 'XFEM_MARK'
  []
[]
[AuxVariables]
  [nucleation_threshold]
    order = CONSTANT
    family = MONOMIAL
  []
[]
[ICs]
  [nucleation_bulk]
    type = ConstantIC
    value = 10000
    variable = nucleation_threshold
    block = 0
  []
  [nucleation_weak]
    type = FunctionIC
    function = nucleation_x
    variable = nucleation_threshold
    block = 10
  []
[]

[Functions]
  [nucleation_x]
    type = ParsedFunction
    expression = 'A*cos(pi*x)+D'
    symbol_names = 'A D'
    symbol_values = '100 200'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    planar_formulation = PLANE_STRAIN
    add_variables = true
  []
[]

[Functions]
  [bc_pull_edge]
    type = ParsedFunction
    expression = 0.0004*t
  []
  [bc_pull_mid]
    type = ParsedFunction
    expression = 0.0005*t
  []
[]

[BCs]
  [top_edge_nodes]
    type = FunctionDirichletBC
    boundary = 'pull_top_left pull_top_right'
    variable = disp_y
    function = bc_pull_edge
  []
  [top_mid_nodes]
    type = FunctionDirichletBC
    boundary = 'pull_mid_left pull_mid_right'
    variable = disp_y
    function = bc_pull_mid
  []
  # [top_middle]
  #   type = NeumannBC
  #   boundary = 'top_mid_left_ss top_mid_ss top_mid_right_ss'
  #   variable = disp_y
  #   value = -2000
  # []
  [top_middle]
    type = DirichletBC
    boundary = 'top_mid_left_ss top_mid_ss top_mid_right_ss'
    variable = disp_y
    value = 0
  []
  [bottom_x]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 207000
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  petsc_options_iname = '-ksp_type -pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'gmres lu superlu_dist'

  line_search = 'none'

  [Predictor]
    type = SimplePredictor
    scale = 1.0
  []

  reuse_preconditioner = true
  reuse_preconditioner_max_linear_its = 25

  # controls for linear iterations
  l_max_its = 100
  l_tol = 1e-2

  # controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-9

  # time control
  start_time = 0.0
  dt = 1.0
  end_time = 10
  max_xfem_update = 100
[]

[Outputs]
  csv = true
  execute_on = FINAL
  # exodus = true
  # [xfemcutter]
  #   type = XFEMCutMeshOutput
  #   xfem_cutter_uo = cut_mesh2
  # []
  [console]
    type = Console
    output_linear = false
    output_nonlinear = false
  []
[]

Overview
Example Input Syntax
Input Parameters
Input Files
References