ComputeSimoHughesJ2PlasticityStress

The Simo-Hughes style J2 plasticity.

Overview

This class provides a hyperelastic Neo-Hookean stress update with J2 plasticity Simo and Hughes (2006), Borden et al. (2016).

Following a multiplicative decomposition of the deformation gradient and a yield surface with associated flow rule the stress-strain relation is defined as

In the above definitions, Einstein notation is used. is the deformation gradient, is the elastic deformation gradient, is the plastic deformation gradient, is the elastic counterpart of the left Cauchy-Green strain, is the yield surface (yield function), is the Kirchhoff stress, is the direction of plastic flow, is the hardening function, is the effective (equivalent) plastic strain, is the deviatoric part of the Kirchhoff stress, is the first Piola-Kirchhoff stress, and and bulk and shear moduli, and is the determinant of the deformation gradient.

Several remarks:

  • The flow rule is consistent with the principal of maximum dissipation.

  • The flow rule determines the strain up to a spin. It is normalized by the constraint under uniaxial assumptions.

  • The plastic flow is purely isochoric, i.e. , .

Algorithm

First, the incremental deformation gradient and its volume-preserving counterpart are computed as Assuming an elastic step, i.e. Then, for each iteration in the return mapping, we do Then we update the current configuration

Example Input File Syntax

The follow example configures a large deformation Neo-Hookean model with J2 plasticity and linear hardening.

[Materials]
  [elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = ${E}
    poissons_ratio = ${nu}
  []
  [compute_strain]
    type = ComputeLagrangianStrain
    displacements = 'disp_x disp_y disp_z'
  []
  [flow_stress]
    type = DerivativeParsedMaterial
    property_name = flow_stress
    expression = '320+688*effective_plastic_strain'
    material_property_names = 'effective_plastic_strain'
    additional_derivative_symbols = 'effective_plastic_strain'
    derivative_order = 2
    compute = false
  []
  [compute_stress]
    type = ComputeSimoHughesJ2PlasticityStress
    flow_stress_material = flow_stress
  []
[]
(moose/modules/solid_mechanics/test/tests/lagrangian/materials/correctness/hyperelastic_J2_plastic.i)

Input Parameters

  • flow_stress_materialThe material defining the flow stress

    C++ Type:MaterialName

    Unit:(no unit assumed)

    Controllable:No

    Description:The material defining the flow stress

Required Parameters

  • absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

    Default:1e-11

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Absolute convergence tolerance for Newton iteration

  • acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

    Default:10

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress

  • automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to use automatic differentiation to compute the derivative.

  • base_nameMaterial property base name

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Material property base name

  • 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

  • boundaryThe list of boundaries (ids or names) from the mesh where this object applies

    C++ Type:std::vector<BoundaryName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of boundaries (ids or names) from the mesh where this object applies

  • computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.

  • constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

    Default:NONE

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:NONE, ELEMENT, SUBDOMAIN

    Controllable:No

    Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

  • declare_suffixAn optional suffix parameter that can be appended to any declared 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 declared properties. The suffix will be prepended with a '_' character.

  • elasticity_tensorelasticity_tensorThe name of the elasticity tensor.

    Default:elasticity_tensor

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the elasticity tensor.

  • large_kinematicsFalseUse a large displacement stress update.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Use a large displacement stress update.

  • 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.

  • relative_tolerance1e-08Relative convergence tolerance for Newton iteration

    Default:1e-08

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Relative convergence tolerance for Newton iteration

  • 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

  • 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.

  • 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

  • internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Set true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.

  • internal_solve_output_onon_errorWhen to output internal Newton solve information

    Default:on_error

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:never, on_error, always

    Controllable:No

    Description:When to output internal Newton solve information

Debug Parameters

  • output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

  • outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object

    Default:none

    C++ Type:std::vector<OutputName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

References

  1. Michael J Borden, Thomas JR Hughes, Chad M Landis, Amin Anvari, and Isaac J Lee. A phase-field formulation for fracture in ductile materials: finite deformation balance law derivation, plastic degradation, and stress triaxiality effects. Computer Methods in Applied Mechanics and Engineering, 312:130–166, 2016.[BibTeX]
  2. Juan C Simo and Thomas JR Hughes. Computational inelasticity. Volume 7. Springer Science & Business Media, 2006.[BibTeX]