Compute Creep and Plasticity Inelastic Stress

Compute state (stress and internal parameters such as inelastic strains and internal parameters) using an Newton process for one creep and one plasticity model

Description

ComputeCreepPlasticityStress computes the stress, the consistent tangent operator (or an approximation), and a decomposition of the strain into elastic and inelastic components for a pair inelastic material models, namely creep and plasticity. By default finite strains are assumed.

The elastic strain is calculated by subtracting the computed inelastic strain increment tensor from the mechanical strain increment tensor. (1) Mechanical strain, , is considered to be the sum of the elastic and inelastic (creep and plastic) strains.

commentnote:Default Finite Strain Formulation

This class uses the finite incremental strain formulation as a default. Users may elect to use a small incremental strain formulation and set perform_finite_strain_rotations = false if the simulation will only ever use small strains. This class is not intended for use with a total small linearize strain formulation.

ComputeCreepPlasticityStress requires one creep model and one plasticity model. These need to be "stress update" models that derive from the following base classes for creep and plasticity:

Combined Newton Iteration

The power law creep equation is where is the creep inelastic strain rate, is a prefactor that does not depend on stress, is the effective stress, is the trial effective stress, is the shear modulus, is the creep inelastic strain increment, is the plastic inelastic strain increment, and is the exponent. A residual is formed as

The isotropic plasticity residual is where is the hardening value and is the yield stress.

A Taylor expansion of with two terms is

By setting and to zero and using this two-term Taylor expansion, we obtain

where the subscript represents the current value. This leads to

The diagonal terms in the matrix are the derivative of the creep residual with respect to the inelastic creep increment and the derivative of the plasticity residual with respect to the inelastic plastic strain increment. These are available from the two inelastic models.

Jacobian Multiplier and the Consistent Tangent Operator

The Jacobian multiplier, which is used in the StressDivergenceTensors kernel to condition the Jacobian calculation, must be calculated from the combination of the two inelastic material models. There are three options used to calculate the combined Jacobian multiplier: Elastic, Partial, and Nonlinear, which are set by the individual elastic material models. (2) where is the Jacobian multiplier, is the elasticity tensor, is the Rank-4 identity tensor, and is the consistent tangent operator.

The consistent tangent operator, defined in Eq. (3) provides the information on how the stress changes with respect to changes in the displacement variables. (3) where is an arbitrary change in the total strain (which occurs because the displacements are changed) and is the resulting change in the stress. In a purely elastic situation (the elasticity tensor), but the inelastic mapping of changes in the stress as a result of changes in the displacement variables is more complicated. In a plastic material model, the proposed values of displacements for the current time step were used to calculate a trial inadmissible stress, , that was brought back to the yield surface through a radial return algorithm. A slight change in the proposed displacement variables will produce a slightly different trial stress and so on. Other inelastic material models follow a similar pattern.

The user can chose to force all of the inelastic material models to use the elasticity tensor as the consistent tangent operator by setting tangent_operator = elastic. This setting will reduce the computational load of the inelastic material models but may hamper the convergence of the simulation. By default, the inelastic material models are allowed to compute the consistent tangent operator implemented in each individual inelastic model with the tangent_operator = nonlinear option.

Material Time Step Size Limitations

Prior to calculating the final strain values, the algorithm checks the size of the current time step against any limitations on the size of the time step as optionally defined by the inelastic material models. As described in the Material Time Step Limiter section, the time step size involves a post processor to ensure that the current time step size is reasonable for each of the inelastic material models used in the simulation.

At the end of the algorithm, the final value of the elastic and inelastic strain tensors are calculated by adding the increments to the old values.

Other Calculations Performed by StressUpdate Materials

The ComputeCreepPlasticityStress material relies on two helper calculations to aid the simulation in converging. These helper computations are defined within the specific inelastic models, and only a brief overview is given here. For specific details of the implementations, see the documentation pages for the individual inelastic StressUpdate materials.

The first helper computation, the consistent tangent operator, is an optional feature which is implemented for only certain inelastic stress material models, and the material time step limiter is implemented in the models which use the Radial Return Stress Update algorithm.

Consistent Tangent Operator

The consistent tangent operator is used to improve the convergence of mechanics problems (see a reference such as Simo and Taylor (1985) for an introduction to consistent tangent operators). The Jacobian matrix, Eq. (2), is used to capture how the change in the residual calculation changes with respect to changes in the displacement variables. To calculate the Jacobian, MOOSE relies on knowing how the stress changes with respect to changes in the displacement variables.

Because the change of the stress with respect to the change in displacements is material specific, the value of the consistent tangent operator is computed in each inelastic material model. By default the consistent tangent operator is set equal to the elasticity tensor (the option Elastic in Eq. (2)). Inelastic material models which use either the Partial or Nonlinear options in Eq. (2) define a material specific consistent tangent operator.

Generally Partial consistent tangent operators should be implemented for non-yielding materials (e.g. volumetric swelling) and Full consistent tangent operators should be implemented for yielding material models (e.g. plasticity).

Include Damage Model

Optionally, the effect of damage on the stress calculation can be included in the model. Another material that defines the evolution of damage should be coupled using parameter damage_model. Here, first the inelastic strains and corresponding effective stresses are calculated based on the undamaged properties. Afterwards, the damage index is applied on the effective stress to calculate the damaged stress. This captures the effect of damage in a material undergoing creep or plastic deformation.

Material Time Step Limiter

In some cases, particularly in creep, limits on the time step are required by the material model formulation. Each inelastic material model is responsible for calculating the maximum time step allowable for that material model. The MaterialTimeStepPostprocessor finds the minimum time step size limits from the entire simulation domain. The postprocessor then interfaces with the IterationAdaptiveDT to restrict the time step size based on the limit calculated in the previous time step. When the damage model is included, the timestep is limited by the minimum timestep between the inelastic models and the damage model.

Example Input File

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 0
    youngs_modulus = 1e3
    poissons_ratio = 0.3
  []
  [creep_plas]
    type = ComputeCreepPlasticityStress
    block = 0
    tangent_operator = elastic
    creep_model = creep
    plasticity_model = plasticity
    max_iterations = 50
    relative_tolerance = 1e-8
    absolute_tolerance = 1e-8
  []
  [creep]
    type = PowerLawCreepStressUpdate
    block = 0
    coefficient = 0.5e-7
    n_exponent = 5
    m_exponent = -0.5
    activation_energy = 0
    temperature = 1
  []
  [plasticity]
    type = IsotropicPlasticityStressUpdate
    block = 0
    yield_stress = 20
    hardening_constant = 100
  []
[]
(moose/modules/solid_mechanics/test/tests/combined_creep_plasticity/creepWithPlasticity.i)

Input Parameters

  • creep_modelCreep model that derives from PowerLawCreepStressUpdate.

    C++ Type:MaterialName

    Unit:(no unit assumed)

    Controllable:No

    Description:Creep model that derives from PowerLawCreepStressUpdate.

  • plasticity_modelPlasticity model that derives from IsotropicPlasticityStressUpdate.

    C++ Type:MaterialName

    Unit:(no unit assumed)

    Controllable:No

    Description:Plasticity model that derives from IsotropicPlasticityStressUpdate.

Required Parameters

  • absolute_tolerance1e-05Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called

    Default:1e-05

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called

  • base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

  • 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

  • combined_inelastic_strain_weightsThe combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1

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

    Unit:(no unit assumed)

    Controllable:No

    Description:The combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1

  • 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

  • cycle_modelsFalseAt timestep N use only inelastic model N % num_models.

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:At timestep N use only inelastic model N % num_models.

  • damage_modelName of the damage model

    C++ Type:MaterialName

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the damage model

  • 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.

  • internal_solve_full_iteration_historyFalseSet to true to output stress update iteration information over the stress change

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Set to true to output stress update iteration information over the stress change

  • max_iterations30Maximum number of the stress update iterations over the stress change after all update materials are called

    Default:30

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:Maximum number of the stress update iterations over the stress change after all update materials are called

  • perform_finite_strain_rotationsTrueTensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Tensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains

  • 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-05Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called

    Default:1e-05

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called

  • tangent_operatornonlinearType of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.

    Default:nonlinear

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:elastic, nonlinear

    Controllable:No

    Description:Type of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.

  • 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

Advanced 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. Juan C Simo and Robert Leroy Taylor. Consistent tangent operators for rate-independent elastoplasticity. Computer Methods in Applied Mechanics and Engineering, 48(1):101–118, 1985.[BibTeX]