Power Law Creep Stress Update

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

Description

In this numerical approach, a trial stress is calculated at the start of each simulation time increment; the trial stress calculation assumed all of the new strain increment is elastic strain:

$var element = document.getElementById("moose-equation-fde092ca-6dac-47c3-9cf8-be64dd8f2ef5");katex.render("\\sigma_{trial} = C_{ijkl} \\left( \\Delta \\epsilon_{assumed-elastic} + \\epsilon_{elastic}^{old} \\right)", element, {displayMode:true,throwOnError:false});$

The algorithms checks to see if the trial stress state is outside of the yield surface, as shown in the figure to the right. If the stress state is outside of the yield surface, the algorithm recomputes the scalar effective inelastic strain required to return the stress state to the yield surface. This approach is given the name Radial Return because the yield surface used is the von Mises yield surface: in the devitoric stress space, this yield surface has the shape of a circle, and the scalar inelastic strain is assumed to always be directed at the circle center.

Recompute Iterations on the Effective Plastic Strain Increment

The recompute radial return materials each individually calculate, using the Newton Method, the amount of effective inelastic strain required to return the stress state to the yield surface.

$var element = document.getElementById("moose-equation-84062cfc-b77e-4264-b7fd-9663e6e57b38");katex.render("\\Delta p^{(t+1)} = \\Delta p^t + d \\Delta p", element, {displayMode:true,throwOnError:false});$

where the change in the iterative effective inelastic strain is defined as the yield surface over the derivative of the yield surface with respect to the inelastic strain increment.

The increment of inelastic strain is computed from the creep rate in this class.

$(1)var element = document.getElementById("moose-equation-f4afd616-2687-4a7c-89f4-f8c7de400c49");katex.render(" \\dot{\\epsilon} = \\left( \\sigma^{trial}_{effective} - 3 G \\Delta p \\right)^n exp \\left( \\frac{-Q}{RT} \\right) \\left(t - t_o \\right)^m", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-6718a1d0-9eba-4f28-8ad1-bb56c38d4446");katex.render("\\sigma^{trial}_{effective}", element, {displayMode:false,throwOnError:false});$ is the scalar von Mises trial stress, $var element = document.getElementById("moose-equation-263b31a5-1fe5-426d-b231-5e0685f59e21");katex.render("G", element, {displayMode:false,throwOnError:false});$ is the isotropic shear modulus, $var element = document.getElementById("moose-equation-375aa2aa-152a-49ce-b974-9ab4afb1e6c1");katex.render("Q", element, {displayMode:false,throwOnError:false});$ is the activation energy, $var element = document.getElementById("moose-equation-856c2f8d-69e0-46e1-b73f-c6f311a0d319");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the universal gas constant, $var element = document.getElementById("moose-equation-c519074e-6676-4423-8288-6364d0f0ef45");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature, $var element = document.getElementById("moose-equation-5a1bd24d-33bd-49a7-a19f-d7eb531d4c87");katex.render("t", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-d6eea748-0b79-42b9-a4b0-7d578c1b9910");katex.render("t_o", element, {displayMode:false,throwOnError:false});$ are the current and initial times, respectively, and $var element = document.getElementById("moose-equation-31ae6cd7-79ef-4c2e-ae48-cf2b33949893");katex.render("n", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-93e6572d-d30e-4845-a6d4-f4bd3916e201");katex.render("m", element, {displayMode:false,throwOnError:false});$ are exponent values.

This class calculates an effective trial stress, an effective creep strain rate increment and the derivative of the creep strain rate, and an effective scalar inelastic strain increment; these values are passed to the ADRadialReturnStressUpdate to compute the radial return stress increment. This isotropic plasticity class also computes the plastic strain as a stateful material property.

This class is based on the implicit integration algorithm in Dunne and Petrinic (2005) pg. 146 - 149.

PowerLawCreepStressUpdate must be run in conjunction with an inelastic strain return mapping stress calculator such as ADComputeMultipleInelasticStress

Input Parameters

activation_energyActivation energy
C++ Type:double
Controllable:No
Description:Activation energy
coefficientLeading coefficient in power-law equation
C++ Type:double
Controllable:No
Description:Leading coefficient in power-law equation
n_exponentExponent on effective stress in power-law equation
C++ Type:double
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
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
Controllable:No
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
Default:False
C++ Type:bool
Controllable:No
Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic differentiation to compute the derivative.
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
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>
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>
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
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
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
Controllable:No
Description:Universal gas constant
m_exponent0Exponent on time in power-law equation
Default:0
C++ Type:double
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
Controllable:No
Description:The maximum inelastic strain increment allowed in a time step
maximum_number_substeps25The maximum number of substeps allowed before cutting the time step.
Default:25
C++ Type:unsigned int
Controllable:No
Description:The maximum number of substeps allowed before cutting the time step.
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
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
Controllable:No
Description:Relative convergence tolerance for Newton iteration
start_time0Start time (if not zero)
Default:0
C++ Type:double
Controllable:No
Description:Start time (if not zero)
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Controllable:No
Description:Coupled temperature
use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
Default:False
C++ Type:bool
Controllable:No
Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
use_substeppingNONEWhether and how to use substepping
Default:NONE
C++ Type:MooseEnum
Options:NONE, ERROR_BASED, INCREMENT_BASED
Controllable:No
Description:Whether and how to use substepping

Optional Parameters

apply_strainTrueFlag to apply strain. Used for testing.
Default:True
C++ Type:bool
Controllable:No
Description:Flag to apply strain. Used for testing.
control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain
Default:effective_creep_strain
C++ Type:std::string
Controllable:No
Description:Name of the material property that stores the effective inelastic strain
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
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
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
Controllable:No
Description:The seed for the master random number generator
substep_strain_tolerance0.1Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
Default:0.1
C++ Type:double
Controllable:No
Description:Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
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
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
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
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>
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>
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

Fionn Dunne and Nik Petrinic. Introduction to Computational Plasticity. Oxford University Press on Demand, 2005.

@book{dunne2005introduction,
    author = "Dunne, Fionn and Petrinic, Nik",
    title = "Introduction to Computational Plasticity",
    year = "2005",
    publisher = "Oxford University Press on Demand"
}