A self-consistent Eulerian rate type model for finite deformation elastoplasticity with isotropic damage

Continuum models for coupled behaviour of elastoplasticity and isotropic da mage at finite deformation are usually formulated by first postulating the additive decomposition of the stretching tensor D into the elastic and the plastic part and then relating each part to an objective rate of the effect ive stress, etc. It is pointed out that, according to the existing models w ith several widely used objective stress rates, none of the rate equations intended for characterizing the damaged elastic response is exactly integra ble to really deliver a damaged elastic relation between the effective stre ss and an elastic strain measure, The existing models are thus self-inconsi stent in the sense of formulating the damaged elastic response, By consiste ntly combining additive and multiplicative decomposition of the stretching D and the deformation gradient F and adopting the logarithmic stress rate, in this article, we propose a general Eulerian rate type model for finite d eformation elastoplasticity coupled with isotropic damage. The new model is shown to be self-consistent in the sense that the incorporated rate equati on for the damaged elastic response is exactly integrable to yield a damage d elastic relation between the effective Kirchhoff stress and the elastic l ogarithmic strain. The rate form of the new model in a rotating frame in wh ich the foregoing logarithmic rate is defined, is derived and from it an in tegral form is obtained. The former is found to have the same structure as the counterpart of the small deformation theory and may be appropriate for numerical integration. The latter indicates, in a clear and direct manner, the effect of finite rotation and deformation history on the current stress and the hardening and damage behaviours. Further, it is pointed out that i n the foregoing self-consistency sense of formulating the damaged elastic r esponse, the suggested model is unique among all objective Eulerian rate ty pe models of its kind with infinitely many objective stress rates to be cho sen. In particular, it is indicated that, within the context of the propose d theory, a natural combination of the two widely used decompositions conce rning D and F can consistently and uniquely determine the elastic and the p lastic parts in the two decompositions as well as all their related kinemat ical quantities, without recourse to any ad hoc assumption concerning a spe cial form of the elastic part F-e in the decomposition F = (FFp)-F-e or a r elated relaxed intermediate configuration. As an application, the proposed general model is applied to derive a self-consistent Eulerian rate type mod el for void growth and nucleation in metals experiencing finite elastic-pla stic deformation by incorporating a modified Gurson's yield function and an associated flow rule, etc. Two issues involved in previous relevant litera ture are detected and raised for consideration. As a test problem, the fini te simple shear response of the just-mentioned model is studied by means of numerical integration. (C) 2000 Elsevier Science Ltd. All rights reserved.