Eulerian Framework for Inelasticity Based on the Jaumann Rate and a Hyperelastic Constitutive Relation—Part II: Finite Strain Elastoplasticity

Abstract

An Eulerian rate formulation of finite strain elastoplasticity is developed based on a fully integrable rate form of hyperelasticity proposed in Part I of this work. A flow rule is proposed in the Eulerian framework, based on the principle of maximum plastic dissipation in sixdimensional stress space for the case of J2 isotropic plasticity. The proposed flow rule bypasses the need for additional evolution laws and/or simplifying assumptions for the skewsymmetric part of the plastic velocity gradient, known as the material plastic spin. Kinematic hardening is modeled with an evolution equation for the backstress tensor considering Prager’s yieldingstationarity criterion. Nonlinear evolution equations for the backstress and flow stress are proposed for an extension of the model to mixed nonlinear hardening. Furthermore, exact deviatoric/volumetric decoupled forms for kinematic and kinetic variables are obtained. The proposed model is implemented with the Zaremba–Jaumann rate and is used to solve the problem of rectilinear shear for a perfectly plastic and for a linear kinematic hardening material. Neither solution produces oscillatory stress or backstress components. The model is then used to predict the nonlinear hardening behavior of SUS 304 stainless steel under fixedend finite torsion. Results obtained are in good agreement with reported experimental data. The Swift effect under finite torsion is well predicted by the proposed model.