XFEM

Description

The XFEM block must be supplied to run any MOOSE simulations using XFEM. The XFEMAction is associated with this block and performs the key model setup tasks. The XFEM input syntax block provides an interface to specify parameters related to XFEM. Including this block in the input file serves several functions:

Causes an algorithm to be run at defined intervals to split the mesh based on a set of evolving defined interfaces.
Causes a modified quadrature rule to be used to correctly integrate elements split by these interfaces.
Creates objects to generate output related to the XFEM algorithm.
Provides a syntax block where various parameters controlling the behavior of XFEM can be specified by the user, including:
- Provide qrule variable to XFEM to determine which quadrature weighting rule to use.
- Specify output_cut_plane variable to output cut elements to the exodus mesh.
- Optional: Provide parameter values for prescribed, incremental crack growth.
- Optional: Setup of near tip enrichment parameters.
- Optional: Allow users to control the amount of debugging information printed during a simulation.

Constructed Objects

Three of the above user-settable parameters pass parameters to the XFEM object for use in setting up relevant options: the qrule variable, incremental crack growth, and debug_output_level. The remaining parameters result in the creation of various objects, which allows for input files to be more concise. The following table details the types of classes created by utilizing the output_cut_plane option in the XFEMAction.

Table 1: Correspondence Among Action Functionality and MooseObjects for XFEMAction when output_cut_plane = true.

Functionality	Replaced Classes	Associated Parameters
Add `AuxVariables` for various cut parameters and volume fraction calculations	AuxVariables
Add `AuxKernels` for various cut parameters and volume fraction calculations	XFEMVolFracAux XFEMCutPlaneAux

Several objects are instantiated when using the output_cut_plane option. These AuxVariables and AuxKernels store data defining the XFEM cut: element volume fraction as well as definitions for two planes (their x, y, z origins and normals). This allows the cut location to be tracked throughout the simulation and saves the user from having to manually set up each AuxVariable and its associated AuxKernel (XFEMVolFracAux for the volume fraction and XFEMCutPlaneAux for cut plane AuxVariables).

Next, the class types created when using crack tip enrichment are detailed:

Table 2: Correspondence Among Action Functionality and MooseObjects for XFEMAction when use_crack_tip_enrichment = true.

Functionality	Replaced Classes	Associated Parameters
Add enrichment displacement variables	Variables	`enrichment_displacements`: vector of enrichment displacement names
Add stress divergence tensor kernels for crack tip enrichment	CrackTipEnrichmentStressDivergenceTensors	`crack_front_definition`, `enrichment_displacements`, `displacements`
Add crack tip enrichment boundary conditions	CrackTipEnrichmentCutOffBC	`cut_off_boundary`, `cut_off_radius`, `crack_front_definition`

When crack tip enrichment is used, enrichment_displacements are added as first-order, Lagrange Variables. Next, a CrackTipEnrichmentStressDivergenceTensors kernel is added for each enrichment displacement variable. Each kernel uses the crack_front_definition, enrichment_displacements, and displacements provided in the XFEM Action. All enrichment displacement variables also have an associated CrackTipEnrichmentCutOffBC object added by the action from user specified parameters (UserObject crack_front_definition, the vector of BoundaryName variables cut_off_boundary, and respective Real value cut_off_radius).

Example Input File Syntax

Many input files only utilize the qrule and output_cut_plane variables:

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

However, options exist for specifying cracks growing in a prescribed fashion:

[XFEM]
  qrule = volfrac
  output_cut_plane = true
  use_crack_growth_increment = true
  crack_growth_increment = 0.2
[]

Additionally, the XFEM Action contains variables used to employ near tip enrichment; of use when a propagating crack's tip ends within an element:

[XFEM]
  qrule = volfrac
  output_cut_plane = true
  use_crack_tip_enrichment = true
  crack_front_definition = crack_tip
  enrichment_displacements = 'enrich1_x enrich2_x enrich3_x enrich4_x enrich1_y enrich2_y enrich3_y enrich4_y'
  displacements = 'disp_x disp_y'
  cut_off_boundary = all
  cut_off_radius = 0.2
[]

Any use of the XFEM action can output varying levels of problem solution detail by changing the value of the debug_output_level variable. By default it is set to 1, but XFEM output can be either turned off (debug_output_level=0) or greater detail can be added to the output by setting the variable to 2 or 3.

Input Parameters

active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
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.
crack_front_definitionThe CrackFrontDefinition user object name (only needed if 'use_crack_tip_enrichment=true')
C++ Type:UserObjectName
Controllable:No
Description:The CrackFrontDefinition user object name (only needed if 'use_crack_tip_enrichment=true')
crack_growth_increment0.1Crack growth increment
Default:0.1
C++ Type:double
Controllable:No
Description:Crack growth increment
cut_off_boundaryBoundary that contains all nodes for which enrichment DOFs should be fixed away from crack tip (only needed if 'use_crack_tip_enrichment=true')
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:Boundary that contains all nodes for which enrichment DOFs should be fixed away from crack tip (only needed if 'use_crack_tip_enrichment=true')
cut_off_radiusThe cut off radius of crack tip enrichment functions (only needed if 'use_crack_tip_enrichment=true')
C++ Type:double
Controllable:No
Description:The cut off radius of crack tip enrichment functions (only needed if 'use_crack_tip_enrichment=true')
debug_output_level1Controls the amount of debug output from XFEM. 0: None, 1: Summary, 2: Details on modifications to mesh, 3: Full dump of element fragment algorithm mesh
Default:1
C++ Type:unsigned int
Controllable:No
Description:Controls the amount of debug output from XFEM. 0: None, 1: Summary, 2: Details on modifications to mesh, 3: Full dump of element fragment algorithm mesh
displacementsNames of displacement variables (only needed if 'use_crack_tip_enrichment=true')
C++ Type:std::vector<VariableName>
Controllable:No
Description:Names of displacement variables (only needed if 'use_crack_tip_enrichment=true')
enrichment_displacementsNames of enrichment displacement variables (only needed if 'use_crack_tip_enrichment=true')
C++ Type:std::vector<VariableName>
Controllable:No
Description:Names of enrichment displacement variables (only needed if 'use_crack_tip_enrichment=true')
geometric_cut_userobjectsList of names of GeometricCutUserObjects with cut info and methods
C++ Type:std::vector<UserObjectName>
Controllable:No
Description:List of names of GeometricCutUserObjects with cut info and methods
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.
output_cut_planeFalseOutput the XFEM cut plane and volume fraction
Default:False
C++ Type:bool
Controllable:No
Description:Output the XFEM cut plane and volume fraction
qrulevolfracXFEM quadrature rule to use
Default:volfrac
C++ Type:std::string
Controllable:No
Description:XFEM quadrature rule to use
use_crack_growth_incrementFalseUse fixed crack growth increment
Default:False
C++ Type:bool
Controllable:No
Description:Use fixed crack growth increment
use_crack_tip_enrichmentFalseUse crack tip enrichment functions
Default:False
C++ Type:bool
Controllable:No
Description:Use crack tip enrichment functions

Available Actions

XFEMApp
XFEMActionAction to input general parameters and simulation options for use in XFEM.

(modules/xfem/test/tests/bimaterials/glued_bimaterials_2d.i)

# This test is for two layer materials with different youngs modulus
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
  [../]
[]

[Mesh]
  displacements = 'disp_x disp_y'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = 0.0
    xmax = 5.
    ymin = 0.0
    ymax = 5.
    elem_type = QUAD4
  []
  [./left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0.0 0.0'
    input = gen
  [../]
  [./left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0.0 5.'
    input = left_bottom
  [../]
[]

[AuxVariables]
  [./ls]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  [../]
[]

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

[Functions]
  [./ls_func]
    type = ParsedFunction
    expression = 'y-2.5'
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  [../]
  [./a_strain_xx]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
    variable = a_strain_xx
  [../]
  [./a_strain_yy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
    variable = a_strain_yy
  [../]
  [./a_strain_xy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
    variable = a_strain_xy
  [../]
  [./b_strain_xx]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
    variable = b_strain_xx
  [../]
  [./b_strain_yy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
    variable = b_strain_yy
  [../]
  [./b_strain_xy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
    variable = b_strain_xy
  [../]
[]

[Constraints]
  [./dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
  [./dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
[]

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  [../]
  [./topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  [../]
  [./strain_A]
    type = ComputeSmallStrain
    base_name = A
  [../]
  [./stress_A]
    type = ComputeLinearElasticStress
    base_name = A
  [../]
  [./elasticity_tensor_B]
    type = ComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e5
    poissons_ratio = 0.3
  [../]
  [./strain_B]
    type = ComputeSmallStrain
    base_name = B
  [../]
  [./stress_B]
    type = ComputeLinearElasticStress
    base_name = B
  [../]
  [./combined_stress]
    type = LevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  [../]
  [./combined_dstressdstrain]
    type = LevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = Jacobian_mult
  [../]
[]

[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 = 'bt'

# controls for linear iterations
  l_max_its = 20
  l_tol = 1e-3

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-7

# time control
  start_time = 0.0
  dt = 0.1
  num_steps = 2

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/xfem/test/tests/solid_mechanics_basic/crack_propagation_2d.i)

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

[XFEM]
  qrule = volfrac
  output_cut_plane = true
  use_crack_growth_increment = true
  crack_growth_increment = 0.2
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 11
  ny = 11
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  elem_type = QUAD4
[]

[UserObjects]
  [./line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '1.0  0.5  0.7  0.5'
    time_start_cut = 0.0
    time_end_cut = 0.0
  [../]
  [./xfem_marker_uo]
    type = XFEMRankTwoTensorMarkerUserObject
    execute_on = timestep_end
    tensor = stress
    scalar_type = MaxPrincipal
    threshold = 5e+1
    average = true
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    strain = FINITE
    planar_formulation = plane_strain
    add_variables = true
  [../]
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x='0  50   100'
    y='0  0.02 0.1'
  [../]
[]

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = DirichletBC
    boundary = top
    variable = disp_x
    value = 0.0
  [../]
  [./topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = pull
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.3
    block = 0
  [../]

  [./_elastic_strain]
    type = ComputeFiniteStrainElasticStress
    block = 0
  [../]
[]

[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
  [../]

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

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-9

# time control
  start_time = 0.0
  dt = 1.0
  end_time = 2.0
  num_steps = 5000

  max_xfem_update = 1
[]

[Outputs]
  file_base = crack_propagation_2d_out
  exodus = true
  execute_on = timestep_end
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/xfem/test/tests/crack_tip_enrichment/edge_crack_2d.i)

[XFEM]
  qrule = volfrac
  output_cut_plane = true
  use_crack_tip_enrichment = true
  crack_front_definition = crack_tip
  enrichment_displacements = 'enrich1_x enrich2_x enrich3_x enrich4_x enrich1_y enrich2_y enrich3_y enrich4_y'
  displacements = 'disp_x disp_y'
  cut_off_boundary = all
  cut_off_radius = 0.2
[]

[UserObjects]
  [./line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '0.0 1.0 0.5 1.0'
    time_start_cut = 0.0
    time_end_cut = 0.0
  [../]
  [./crack_tip]
    type = CrackFrontDefinition
    crack_direction_method = CrackDirectionVector
    crack_front_points = '0.5 1.0 0'
    crack_direction_vector = '1 0 0'
    2d = true
    axis_2d = 2
  [../]
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 9
    xmin = 0.0
    xmax = 1.0
    ymin = 0.0
    ymax = 2.0
    elem_type = QUAD4
  []
  [./all_node]
    type = BoundingBoxNodeSetGenerator
    new_boundary = 'all'
    top_right = '1 2 0'
    bottom_left = '0 0 0'
    input = gen
  [../]
  [./right_bottom_node]
    type = ExtraNodesetGenerator
    new_boundary = 'right_bottom_node'
    coord = '1.0 0.0'
    input = all_node
  [../]
  [./right_top_node]
    type = ExtraNodesetGenerator
    new_boundary = 'right_top_node'
    coord = '1.0 2.0'
    input = right_bottom_node
  [../]
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
 [./saved_x]
  [../]
  [./saved_y]
  [../]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = vonmisesStress
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./top_y]
    type = Pressure
    variable = disp_y
    boundary = top
    factor = -1
    displacements = 'disp_x disp_y'
  [../]
  [./bottom_y]
    type = Pressure
    variable = disp_y
    boundary = bottom
    factor = -1
    displacements = 'disp_x disp_y'
  [../]
  [./fix_y]
    type = DirichletBC
    boundary = right_bottom_node
    variable = disp_y
    value = 0.0
  [../]
  [./fix_x]
    type = DirichletBC
    boundary = right_bottom_node
    variable = disp_x
    value =  0.0
  [../]
  [./fix_x2]
    type = DirichletBC
    boundary = right_top_node
    variable = disp_x
    value =  0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]
  [./strain]
    type = ComputeCrackTipEnrichmentSmallStrain
    displacements = 'disp_x disp_y'
    crack_front_definition = crack_tip
    enrichment_displacements = 'enrich1_x enrich2_x enrich3_x enrich4_x enrich1_y enrich2_y enrich3_y enrich4_y'
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  line_search = 'none'

  # Since we do not sub-triangularize the tip element,
  # we need to use higher order quadrature rule to improve
  # integration accuracy.
  # Here second = SECOND is for regression test only.
  # However, order = SIXTH is recommended.
  [./Quadrature]
    type = GAUSS
    order = SECOND
  [../]

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

  # controls for linear iterations
  l_max_its = 10
  l_tol = 1e-4

  # controls for nonlinear iterations
  nl_max_its = 100
  nl_rel_tol = 1e-12 #11
  nl_abs_tol = 1e-12 #12

  # time control
  start_time = 0.0
  dt = 1.0
  end_time = 1.0
  dtmin = 1.0
[]

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


[Outputs]
  file_base = edge_crack_2d_out
  exodus = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

Description
Constructed Objects
Example Input File Syntax
Input Parameters
Available Actions