Cohesive Zone Master Action System

Action to create an instance of the cohesive zone model kernel for each displacement component

Description

The TensorMechanics 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.

commentnote

The provided CZMInterfaceKernel assume the ComputeLocalTraction is only function of the displacement . If one wants to implement a traction separation law depending upon other variables, such as bulk stress or temperature, it is responsibility of the user to implement the proper Jacobian terms.

The CohesiveZoneMaster 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 CohesizeZoneMaster action.

commentnote

Even when using the CohesiveZoneMaster action it is the responsibility of the user to add the appropriate ComputeLocalTraction constitutive model and BreakMeshByBlockGenrator in the input file.

Supported Kinematic Formulations

The system supports two different kinematic formulations:

  1. Small Strain

  2. Total Lagrangian

Each type of formulations requires adding a different ComputeDisplacementJump, ComputeGlobalTraction, CZMInterfaceKernel.

The Small Strain formulations requires adding:

  1. CZMComputeDisplacementJumpSmallStrain

  2. CZMComputeGlobalTractionSmallStrain

  3. CZMInterfaceKernelSmallStrain

The Total Lagrangian formulations requires adding:

  1. CZMComputeDisplacementJumpTotalLagrangian

  2. CZMComputeGlobalTractionTotalLagrangian

  3. CZMInterfaceKernelTotalLagrangian

As mentioned in previous section, the CohesiveZoneMaster action adds the appropriate objects depending on the selected kinematic formulation.

warningwarning

To obtain a traction consistent with the bulk stress, the Small Strain kinematic should be used together with a bulk Small Strain formulation, and the Total Lagrangian kinematics should be used together with a Finite Strain formulation.

Cohesive Zone Constitutive Models

The implemented framework allows to implement two different types of cohesive zone constitutive models (e.g. traction separation laws): i) path independent, and ii) path dependent. The first type of models assumes the traction is only function of the total interface displacement jump, i.e. . This kind of models do not have history variables and can be implemented overriding the ComputeLocalTractionTotalBase class. Instead, path dependent models have history variables and assume the traction increment is a function of the interface displacement jump increment, and its old value, . Path dependent models can be implemented overriding the ComputeLocalTractionIncrementalBase class. In both cases, the traction separation law should always be formulated in terms of the local interface response and assuming Small strain. Furthermore, all constitutive laws should be implemented for the 3D general case, even if used for 1D or 2D simulations. The kinematic is already embedded in the ComputeDisplacementJump and ComputeGlobalTraction objects. Both types of ComputeLocalTraction objects allow using either the Small Strain and the Total Lagrangian kinematics.

Input Examples

The following example show how to use the CohesiveZoneMaster action.

[Modules/TensorMechanics/CohesiveZoneMaster]
  [Modules/TensorMechanics/CohesiveZoneMaster]
    [Modules/TensorMechanics/CohesiveZoneMaster]
      [./czm_ik]
        boundary = 'interface'
        strain = FINITE
        generate_output = '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'
      [../]
    []
  []
[]
(moose/modules/tensor_mechanics/test/tests/cohesive_zone_model/stretch_rotate_large_deformation.i)

If necessary, multiple instances of the CohesiveZoneMaster 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 the first Piola-Kirchoff 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).

[Modules/TensorMechanics/CohesiveZoneMaster]
  [./czm_ik_012]
    boundary = 'Block0_Block1 Block1_Block2'
    base_name = 'czm_b012'
  [../]
  [./czm_ik_23]
    boundary = 'Block2_Block3'
    base_name = 'czm_b23'
  [../]
[]

[Materials]
  # cohesive materials
  [./czm_3dc]
    type = SalehaniIrani3DCTraction
    boundary = 'Block0_Block1 Block1_Block2'
    normal_gap_at_maximum_normal_traction = 1
    tangential_gap_at_maximum_shear_traction = 0.5
    maximum_normal_traction = 500
    maximum_shear_traction = 300
    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
  [../]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 200e4
    poissons_ratio = 0.3
  [../]
[]
(moose/modules/tensor_mechanics/test/tests/cohesive_zone_model/czm_multiple_action_and_materials.i)

Action to create an instance of the cohesive zone model kernel for each displacement component

Associated Actions

Available Actions