Hill Creep Stress Update

This class uses the stress update material in a generalized radial return anisotropic power law creep model. This class can be used in conjunction with other creep and plasticity materials for more complex simulations.

Description

This class computes a creep strain rate based on an equivalent deviatoric stress function () that is calculated as a function of Hill's function anisotropy parameters , , , , , and : (1)

where and are the stress tensor and its component, respectively. The Eq. (1) is also called Hill stress function and accounts for anisotropy through the anisotropy parameters. The equivalent creep strain rate function may then be obtained as (2)

where is a creep coefficient and the creep exponent.

The effective creep strain increment is obtained within the framework of a generalized (Hill plasticity) radial return mapping, see GeneralizedRadialReturnStressUpdate. This class computes the generalized radial return inelastic increment. More details on the Hill-type creep material model may be found in Stewart et al. (2011).

Creep strain integration scheme

Newton iteration is performed for computing the effective creep strain increment with increment in the (d) for each Newton iteration computed as:

(3)

where is the residual and is the derivative of residual with respect to the . The residual and its derivative are computed as:

(4)

(5)

Substituting Eq. (2) in Eq. (4) and Eq. (5), we obtain:

(6)

(7)

We need expressions for and in terms of trial stress and , which are then substituted in Eq. (6) and Eq. (7).

Isotropic Elasticity

(8)

(9)

where is the shear modulus. For details of Eq. (8) and Eq. (9) see Dunne and Petrinic (2005).

Anisotropic Elasticity

For cases with anisotropic elasticity Eq. (8) is not valid. The stress tensor after radial return for the case with anisotropic elasticity is expressed as:

(10)

where is the creep strain tensor and is the elasticity tensor. Rewriting Eq. (1):

(11)

(12)

Note that Eq. (12) uses chain rule. Normality hypothesis is expressed as:

(13)

and the last term of Eq. (12) is obtained by taking derivative of Eq. (13) as:

(14)

Numerical time integration error

The return mapping algorithm used to solve for elastic and inelastic strains relies on an additive decomposition. The stress increment can be determined, assuming a one-dimensional problem, as , where is a representative value of the Young's modulus. One way of limiting the error incurred in the numerical time integration is to compare it with the elastic strain increment during such an increment. Namely, we want to ensure that . Estimating the creep numerical integration error as proportional to the increment of creep strain rates: , the recommended time step is

(15)

where is the computed time step limit, is the current time step, denotes a stress time increment scalar, and is the maximum numerical time integration error selected by the user. As Eq. (1) suggests, the creep error depends on the material stiffness and the given stress increment. For complex simulation scenarios, controlling this error by only prescribing a maximum inelastic strain increment may not be sufficient to limit creep error. Furthermore, too conservative selection of the maximum inelastic strain may lead to a large increase in the number of time steps required to finish the simulation.

warningwarning:Selection of time step increments with creep

It is recommended to choose a max_inelastic_increment that guarantees that creep strain increments are well within the small strain increment assumption. Complementarily, max_integration_error must be selected such that the numerical time integration will not significantly affect the creep results. Usually, for most applications, values on the order of - will suffice. For better results, these time integration limits may be combined with a soft Terminator.

For three-dimensional problems, a norm of the stress difference and a representative value for the Young's modulus is used internally.

Example Input File Syntax

[Materials]
  [trial_creep_two]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    # Force it to not use integration error
    max_integration_error = 0.000001
  []
[]
(moose/modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_y_3d.i)

Input Parameters

  • activation_energyActivation energy

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Activation energy

  • coefficientLeading coefficient in power-law equation

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Leading coefficient in power-law equation

  • effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain

    Default:effective_creep_strain

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the material property that stores the effective inelastic strain

  • inelastic_strain_rate_namecreep_strain_rateName of the material property that stores the inelastic strain rate

    Default:creep_strain_rate

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Name of the material property that stores the inelastic strain rate

  • n_exponentExponent on effective stress in power-law equation

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Exponent on effective stress in power-law equation

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

  • anisotropic_elasticityFalseEnable using anisotropic elasticity

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Enable using anisotropic elasticity

  • base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.

  • 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

  • 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

  • creep_prefactorOptional function to use as a scalar prefactor on the creep strain.

    C++ Type:FunctionName

    Unit:(no unit assumed)

    Controllable:No

    Description:Optional function to use as a scalar prefactor on the creep strain.

  • 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.

  • gas_constant8.3143Universal gas constant

    Default:8.3143

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Universal gas constant

  • m_exponent0Exponent on time in power-law equation

    Default:0

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Exponent on time in power-law equation

  • max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step

    Default:0.0001

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The maximum inelastic strain increment allowed in a time step

  • max_integration_error0.0005The maximum inelastic strain increment integration error allowed

    Default:0.0005

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:The maximum inelastic strain increment integration error allowed

  • 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

  • start_time0Start time (if not zero)

    Default:0

    C++ Type:double

    Unit:(no unit assumed)

    Controllable:No

    Description:Start time (if not zero)

  • temperatureCoupled temperature

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

    Unit:(no unit assumed)

    Controllable:No

    Description:Coupled temperature

  • 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.

  • use_transformationTrueWhether to employ updated Hill's tensor due to rigid body or large deformation kinematic rotations. If an initial rigid body rotation is provided by the user in increments of 90 degrees (e.g. 90, 180, 270), this option can be set to false, in which case the Hill's coefficients are extracted from the transformed Hill's tensor.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Whether to employ updated Hill's tensor due to rigid body or large deformation kinematic rotations. If an initial rigid body rotation is provided by the user in increments of 90 degrees (e.g. 90, 180, 270), this option can be set to false, in which case the Hill's coefficients are extracted from the transformed Hill's tensor.

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. Fionn Dunne and Nik Petrinic. Introduction to Computational Plasticity. Oxford University Press on Demand, 2005.[BibTeX]
  2. Calvin M Stewart, Ali P Gordon, Young Wha Ma, and Richard W Neu. An anisotropic tertiary creep damage constitutive model for anisotropic materials. International Journal of Pressure Vessels and Piping, 88(8-9):356–364, 2011.[BibTeX]