# Isotropic Plasticity Stress Update

This class uses the discrete material in a radial return isotropic plasticity model. This class is one of the basic radial return constitutive models, yet it 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.

In isotropic linear hardening plasticity, with the hardening function , the effective plastic strain increment has the form: (3) where is the isotropic shear modulus, and is the scalar von Mises trial stress.

This class 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. 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.

## Example Input File Syntax

[./isotropic_plasticity]
type = IsotropicPlasticityStressUpdate
yield_stress = 50.0
hardening_function = hf
[../]


IsotropicPlasticityStressUpdate 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 = 'isotropic_plasticity'
[../]


## Input Parameters

• hardening_functionTrue stress as a function of plastic strain

C++ Type:FunctionName

Options:

Description:True stress as a function of plastic strain

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

Default:0.0001

C++ Type:double

Options:

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

• temperatureCoupled Temperature

C++ Type:std::vector

Options:

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

Options:

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.

• yield_stress0The point at which plastic strain begins accumulating

Default:0

C++ Type:double

Options:

Description:The point at which plastic strain begins accumulating

• hardening_constant0Hardening slope

Default:0

C++ Type:double

Options:

Description:Hardening slope

• absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration

Default:1e-11

C++ Type:double

Options:

Description:Absolute convergence tolerance for Newton iteration

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Options:

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

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

Default:10

C++ Type:double

Options:

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

• yield_stress_functionYield stress as a function of temperature

C++ Type:FunctionName

Options:

Description:Yield stress as a function of temperature

• relative_tolerance1e-08Relative convergence tolerance for Newton iteration

Default:1e-08

C++ Type:double

Options:

Description:Relative convergence tolerance for Newton iteration

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Options:

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

Options:

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

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

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

Options:

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

Options:

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

Options:

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

Options:

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

Options:NONE ELEMENT SUBDOMAIN

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

• internal_solve_output_onon_errorWhen to output internal Newton solve information

Default:on_error

C++ Type:MooseEnum

Options:never on_error always

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

Options:

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

Options:

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

Options:

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

## References

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