IsoKinJ2

Overview

This object implements standard $J_2$ plasticity. The yield function is

$f\left(\bm{\sigma}, \mathbf{q}, T\right) = J_2\left(\bm{\sigma} + \mathbf{X}\right) + \sqrt{\frac{2}{3}} Q J_2\left(\mathbf{Y}\right) = \sqrt{\frac{3}{2} \operatorname{dev}\left(\mathbf{Y}\right): \operatorname{dev}\left(\mathbf{Y}\right)}.$

It assumes a “stress-like” history vector of

$\mathbf{q}=\left[\begin{array}{cc}Q & \mathbf{X}\end{array}\right]$

where $Q$ is the isotropic hardening stress and $\mathbf{X}$ is the backstress.

Warning

All of the NEML yield surfaces assume the opposite of the standard sign convention for isotropic and kinematic hardening. The hardening model is expected to return a negative value of the isotropic hardening stress and a negative value of the backstress.

Parameters

None.

Class description

class IsoKinJ2 : public neml::YieldSurface 

Combined isotropic/kinematic hardening with a von Mises surface.

Public Functions

IsoKinJ2(ParameterSet &params): No actual parameters.

virtual size_t nhist() const: Expects 7 history variables [isotropic 6-Mandel-vector-backstress].

virtual void f(const double *const s, const double *const q, double T, double &fv) const: J2(stress + backstress) + sqrt(2/3) * isotropic.

virtual void df_ds(const double *const s, const double *const q, double T, double *const df) const: Gradient wrt stress.

virtual void df_dq(const double *const s, const double *const q, double T, double *const df) const: Gradient wrt history.

virtual void df_dsds(const double *const s, const double *const q, double T, double *const ddf) const: Hessian dsds.

virtual void df_dqdq(const double *const s, const double *const q, double T, double *const ddf) const: Hessian dqdq.

virtual void df_dsdq(const double *const s, const double *const q, double T, double *const ddf) const: Hessian dsdq.

virtual void df_dqds(const double *const s, const double *const q, double T, double *const ddf) const: Hessian dqds.

Public Static Functions

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

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

static ParameterSet parameters(): Default parameters.