Cohesive Zone QuasiStatic Physics System

Description

The SolidMechanics system provides a cohesive zone modeling capability that can be used to introduce traction-separation models running at the interfaces between regions modeled with continuum finite elements. The implemented cohesive zone model (CZM) is based on a Discrete Galerkin approach and therefore does not require cohesive elements. The CZM is formulated in terms of traction separation laws and requires five ingredients:

1. BreakMeshByBlockGenerator

2. ComputeDisplacementJump

3. ComputeLocalTraction

4. ComputeGlobalTraction

5. CZMInterfaceKernel

The BreakMeshByBlockGenerator is utilized to create the cohesive zone interface by splitting a monolithic mesh into blocks by adding the required nodes and boundaries between each block pair. The split mesh allows to compute a displacement jump at each quadrature point on the interface. The schematic below is an example of using BreakMeshByBlockGenerator on a 3-blocks, 2-dimensional mesh. The generated interfaces are highlighted in yellow.

The ComputeDisplacementJump object computes the displacement jump across the cohesive zone according to the selected formulation. The ComputeLocalTraction provides the cohesive zone response in the natural interface coordinate system. The ComputeGlobalTraction object computes the traction in global coordinates and its derivative w.r.t. the displacement jump in global coordinates, . The CZMInterfaceKernel imposes equilibrium by adding the proper residual to the system, and provides the analytic Jacobian.

The CohesiveZone action automatically adds the proper ComputeDisplacementJump, ComputeGlobalTraction, CZMInterfaceKernel based on the kinematic_type parameter value (see inputs). The flowchart below summarizes the flow of information of the cohesive zone modeling frameworks, and highlights the objects automatically added by the CohesiveZone action.

Input Examples

The following example show how to use the CohesiveZone action.

[Physics<<<{"href": "../../index.html"}>>>]
  [SolidMechanics<<<{"href": "../index.html"}>>>]
    [CohesiveZone<<<{"href": "index.html"}>>>]
      [./czm_ik]
        boundary<<<{"description": "The list of boundary IDs from the mesh where the cohesive zone will be applied"}>>> = 'interface'
        strain<<<{"description": "Strain formulation"}>>> = FINITE
        generate_output<<<{"description": "Add scalar quantity output for stress and/or strain"}>>> = 'traction_x traction_y traction_z jump_x jump_y jump_z normal_traction tangent_traction normal_jump tangent_jump pk1_traction_x pk1_traction_y pk1_traction_z'
      [../]
    []
  []
[]

If necessary, multiple instances of the CohesiveZone action can be added, for instance when different material properties base_name are needed for different boundaries. The base_name parameter used in the action should also be provided to the associated materials. The generate_output parameter adds scalar quantities of the traction and displacement jump to the outputs. Available options are: traction_x traction_y traction_z normal_traction tangent_traction jump_x jump_y jump_z normal_jump tangent_jump pk1_traction_x pk1_traction_y pk1_traction_z `. The name `traction refers to the Cauchy traction, pk1_traction refers to the first Piola-Kirchhoff traction, and jump refers to the displacement jump across the cohesive interface. All the above vectors are defined in the global coordinate system. The normal_traction and tangent_traction are scalar values compute using CZMRealVectorScalar (the same is true for the normal_jump and tangent_jump).

[Physics<<<{"href": "../../index.html"}>>>/SolidMechanics<<<{"href": "../index.html"}>>>/CohesiveZone<<<{"href": "index.html"}>>>]
  [./czm_ik_012]
    boundary<<<{"description": "The list of boundary IDs from the mesh where the cohesive zone will be applied"}>>> = 'Block0_Block1 Block1_Block2'
    base_name<<<{"description": "Material property base name"}>>> = 'czm_b012'
  [../]
  [./czm_ik_23]
    boundary<<<{"description": "The list of boundary IDs from the mesh where the cohesive zone will be applied"}>>> = 'Block2_Block3'
    base_name<<<{"description": "Material property base name"}>>> = 'czm_b23'
  [../]
[]

[Materials<<<{"href": "../../../Materials/index.html"}>>>]
  # cohesive materials
  [./czm_3dc]
    type = SalehaniIrani3DCTraction<<<{"description": "3D Coupled (3DC) cohesive law of Salehani and Irani with no damage", "href": "../../../../source/materials/cohesive_zone_model/SalehaniIrani3DCTraction.html"}>>>
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 'Block0_Block1 Block1_Block2'
    normal_gap_at_maximum_normal_traction<<<{"description": "The value of normal gap at which maximum normal traction is achieved"}>>> = 1
    tangential_gap_at_maximum_shear_traction<<<{"description": "The value of tangential gap at which maximum shear traction is achieved"}>>> = 0.5
    maximum_normal_traction<<<{"description": "The maximum normal traction the interface can sustain"}>>> = 500
    maximum_shear_traction<<<{"description": "The maximum shear traction the interface can sustain"}>>> = 300
    base_name<<<{"description": "Material property base name"}>>> = 'czm_b012'
  [../]
  [./czm_elastic_incremental]
    type = PureElasticTractionSeparationIncremental
    boundary = 'Block2_Block3'
    normal_stiffness = 500
    tangent_stiffness = 300
    base_name = 'czm_b23'
  [../]
  # bulk materials
  [./stress]
    type = ADComputeFiniteStrainElasticStress<<<{"description": "Compute stress using elasticity for finite strains", "href": "../../../../source/materials/ADComputeFiniteStrainElasticStress.html"}>>>
  [../]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor<<<{"description": "Compute a constant isotropic elasticity tensor.", "href": "../../../../source/materials/ComputeIsotropicElasticityTensor.html"}>>>
    youngs_modulus<<<{"description": "Young's modulus of the material."}>>> = 200e4
    poissons_ratio<<<{"description": "Poisson's ratio for the material."}>>> = 0.3
  [../]
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic<<<{"href": "../QuasiStatic/index.html"}>>>]
      [./all]
        strain<<<{"description": "Strain formulation"}>>> = FINITE
        add_variables<<<{"description": "Add the displacement variables"}>>> = true
        use_finite_deform_jacobian<<<{"description": "Jacobian for corrotational finite strain"}>>> = true
        use_automatic_differentiation<<<{"description": "Flag to use automatic differentiation (AD) objects when possible"}>>> = true
        generate_output<<<{"description": "Add scalar quantity output for stress and/or strain"}>>> = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_xz'
      [../]
    [../]
  [../]
[]

[Preconditioning<<<{"href": "../../../Preconditioning/index.html"}>>>]
  [./SMP]
    type = SMP<<<{"description": "Single matrix preconditioner (SMP) builds a preconditioner using user defined off-diagonal parts of the Jacobian.", "href": "../../../../source/preconditioners/SingleMatrixPreconditioner.html"}>>>
    full<<<{"description": "Set to true if you want the full set of couplings between variables simply for convenience so you don't have to set every off_diag_row and off_diag_column combination."}>>> = true
  [../]
[]

[Executioner<<<{"href": "../../../Executioner/index.html"}>>>]
  # Executioner
  type = Transient

  solve_type = 'NEWTON'
  line_search = none
  petsc_options_iname = '-pc_type '
  petsc_options_value = 'lu'
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-6
  l_max_its = 20
  start_time = 0.0
  dt = 0.25
  dtmin = 0.25
  num_steps =1
[]

[Outputs<<<{"href": "../../../Outputs/index.html"}>>>]
  exodus<<<{"description": "Output the results using the default settings for Exodus output."}>>> = true
[]

Input Parameters

Associated Actions

Available Actions

• Solid Mechanics App
• CommonCohesiveZoneActionStore common cohesive zone paramters
• CohesiveZoneActionAction to create an instance of the cohesive zone model kernel for each displacement component