PowerLawInelasticity¶

Overview¶

This class implements isotropic power-law perfect viscoplasticity with the form:

$\mathbf{D}^p = A \sigma_{eq}^{n-1} \mathbf{s} \mathbf{W}^p = \mathbf{0}$

where

$\sigma_{eq} = \sqrt{\frac{3}{2} \mathbf{s} : \mathbf{s}}, \mathbf{s} = \bm{\sigma} - \frac{1}{3} \operatorname{tr}\left( \bm{\sigma} \right) \mathbf{I},$

and $A$ and $n$ are parameters. Note this is then the standard $J_2$ flow rule.

The implementation does not require any internal variables.

Parameters¶

Parameter	Object type	Description	Default
`A`	`neml::Interpolate`	Prefactor as a function of temperature	No
`n`	`neml::Interpolate`	Rate sensitivity as a function of temperature	No

Class description¶

class PowerLawInelasticity : public neml::InelasticModel ¶

An isotropic power law creep model, typically combined with slip system models to represent diffusion

Public Functions

PowerLawInelasticity(ParameterSet &params)¶

virtual void populate_hist(History &history) const¶: Setup history variables (none used in this implementation)

virtual void init_hist(History &history) const¶: Initialize the history variables (n/a)

virtual double strength(const History &history, Lattice &L, double T, const History &fixed) const¶: Helper for external models that want an average strength.

virtual Symmetric d_p(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Symmetric part of the deformation rate.

virtual SymSymR4 d_d_p_d_stress(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Derivative of the symmetric part with respect to the stress.

virtual History d_d_p_d_history(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Derivative of the symmetric part with respect to the history (null here)

virtual History history_rate(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: History rate (null)

virtual History d_history_rate_d_stress(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Derivative of the history with respect to the stress (null here)

virtual History d_history_rate_d_history(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Derivative of the history rate with respect to the history (null here)

virtual Skew w_p(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Skew part of the deformation rate (zero here)

virtual SkewSymR4 d_w_p_d_stress(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Derivative of the skew part with respect to stress (=0)

virtual History d_w_p_d_history(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: Derivative of the skew part with respect to the history (null here)

Public Static Functions

static std::string type()¶: String type for the object system.

static std::unique_ptr<NEMLObject> initialize(ParameterSet &params)¶: Initialize from parameter set.

static ParameterSet parameters()¶: Default parameters.