- hardening_functionsList of functions of true stress as function of plastic strain at different temperatures
C++ Type:std::vector

Description:List of functions of true stress as function of plastic strain at different temperatures

- temperaturesList of temperatures corresponding to the functions listed in 'hardening_functions'
C++ Type:std::vector

Description:List of temperatures corresponding to the functions listed in 'hardening_functions'

# Temperature Dependent Hardening Stress Update

Computes the stress as a function of temperature and plastic strain from user-supplied hardening functions. 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:

(1)

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.

(2)

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.

## Isotropic Plasticity

`TemperatureDependentHardeningStressUpdate`

is formulated in the same manner as IsotropicPlasticityStressUpdate such that the effective plastic strain increment has the form (3) where is the isotropic shear modulus, is the scalar von Mises trial stress, is the yield stress, is the hardening function, and is the derivative of the hardening function with respect to the trial stress.

### Temperature Dependent Hardening

The temperature dependence in Eq. (3) is captured in the hardening function and the hardening function derivative. (4) where is the relative temperature fraction within the lower and upper temperature bounds of the current piecewise function section, is the index of the lower temperature bound and its corresponding hardening function, and is the upper temperature bound and hardening function index, and and are the current and old effective strain increments, respectively. The relative temperature fraction is defined as (5) where is the current temperature, and and are the same indices as defined for Eq. (4). The value is used in Eq. (4) to interpolate the hardening values.

This class, `TemperatureDependentHardeningStressUpdate`

, calculates an effective trial stress, an effective scalar plastic strain increment, and the derivative of the scalar effective plastic strain increment; these values are passed to the RadialReturnStressUpdate to compute the radial return stress increment. The plastic strain as a stateful material property.

## Example Input File

```
[./temp_dep_hardening]
type = TemperatureDependentHardeningStressUpdate
hardening_functions = 'hf1 hf2'
temperatures = '300.0 800.0'
relative_tolerance = 1e-25
absolute_tolerance = 1e-5
temperature = temp
[../]
```

(modules/tensor_mechanics/test/tests/temperature_dependent_hardening/temp_dep_hardening.i)where the arguments for the `hardening_functions`

parameter are defined in the `Functions`

block of the input file:

```
[./hf1]
type = PiecewiseLinear
x = '0.0 0.01 0.02 0.03 0.1'
y = '5000 5030 5060 5090 5300'
[../]
```

(modules/tensor_mechanics/test/tests/temperature_dependent_hardening/temp_dep_hardening.i)```
[./hf2]
type = PiecewiseLinear
x = '0.0 0.01 0.02 0.03 0.1'
y = '4000 4020 4040 4060 4200'
[../]
```

(modules/tensor_mechanics/test/tests/temperature_dependent_hardening/temp_dep_hardening.i)`TemperatureDependentHardeningStressUpdate`

must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:

```
[./radial_return_stress]
type = ComputeMultipleInelasticStress
tangent_operator = elastic
inelastic_models = 'temp_dep_hardening'
[../]
```

(modules/tensor_mechanics/test/tests/temperature_dependent_hardening/temp_dep_hardening.i)## Input Parameters

- max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001

C++ Type:double

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

- temperatureCoupled Temperature
C++ Type:std::vector

Description:Coupled Temperature

- 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

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.

- acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10

C++ Type:double

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

- absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11

C++ Type:double

Description:Absolute convergence tolerance for Newton iteration

- boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector

Description:The list of boundary IDs from the mesh where this boundary condition applies

- relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08

C++ Type:double

Description:Relative convergence tolerance for Newton iteration

- blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector

Description:The list of block ids (SubdomainID) that this object will be applied

### Optional Parameters

- effective_inelastic_strain_nameeffective_plastic_strainName of the material property that stores the effective inelastic strain
Default:effective_plastic_strain

C++ Type:std::string

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

- enableTrueSet the enabled status of the MooseObject.
Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

- 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

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.

- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector

Description:Adds user-defined labels for accessing object parameters via control logic.

- seed0The seed for the master random number generator
Default:0

C++ Type:unsigned int

Description:The seed for the master random number generator

- implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True

C++ Type:bool

Description:Determines whether this object is calculated using an implicit or explicit form

- 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 computeSubdomainProperties() 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

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 computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

### Advanced Parameters

- internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error

C++ Type:MooseEnum

Description:When to output internal Newton solve information

- 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

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.

### 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

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

- outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none

C++ Type:std::vector

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