AsaroInelasticity¶

Overview¶

This class implements the standard crystal plasticity plastic deformation rate presented in [A1983]. The plastic deformation rate is the sum of simple shear deformations on each individual slip direction and plane:

$\mathbf{L}^p = \sum_{g=1}^{n_{group}}\sum_{i=1}^{n_{slip}}\dot{\gamma}_{g,i}\left(\mathbf{d}_{g,i}\otimes\mathbf{n}_{g,i}\right)$

where $\mathbf{d}_{g,i}$ are the slip directions and $\mathbf{n}_{g,i}$ are the slip normals in the current frame $\Omega$ . $\mathbf{D}^p$ and $\mathbf{W}^p$ are the symmetric and skew parts of this definition.

The slip rate, $\dot{\gamma}_{g,i}$ , is a function of stress, temperature, and the internal variables. A separate class implements different models for the slip rate:

SlipRule

The implementation also defers the definition of the internal variables to the SlipRule object.

Parameters¶

Parameter	Object type	Description	Default
`rule`	`neml::SlipRule`	Slip rate and history definition	No

Class description¶

class AsaroInelasticity : public neml::InelasticModel ¶

The classic crystal plasticity inelastic model, as described in the manual.

Public Functions

AsaroInelasticity(ParameterSet &params)¶: Provide a SlipRule defining the slip rate/strength relations.

virtual ~AsaroInelasticity()¶: Destructor.

virtual void populate_hist(History &history) const¶: Populate the history, deferred to the SlipRule.

virtual void init_hist(History &history) const¶: Initialize the history with the starting values, deferred to the SlipRule.

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 plastic 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 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 history.

virtual History history_rate(const Symmetric &stress, const Orientation &Q, const History &history, Lattice &lattice, double T, const History &fixed) const¶: History rate, deferred to the SlipRule.

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 rate with respect to stress.

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 history.

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 plastic deformation rate.

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.

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 history.

virtual bool use_nye() const¶: Whether this model uses the Nye tensor.

inline const SlipRule &slip_rule() const¶: Access to the slip rule for other models to get detailed slip information.

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.