A general framework for continuum damage models. II. Integration algorithms, with applications to the numerical simulation of porous metals

In this paper, we develop numerical algorithms for the integration of the c ontinuum plastic damage models formulated in the general framework identifi ed in Part I of this work. More specifically, we focus our attention on a p articular plastic damage model of porous metals, involving a classical von Mises yield criterion coupled with a pressure dependent damage surface to m odel the nucleation and growth of voids in the metallic matrix. Unilateral damage leading to a sudden change of stiffness in the material's response d ue to the closing/opening of these voids is also incorporated through the i mposition of the unilateral constraint of a positive void fraction, thus, i llustrating the clear physical significance added by this framework in the resulting constitutive models. The proposed integration algorithms fully us e the modularity of the identified framework, leading in this way to indepe ndent integration algorithms for the elastoplastic part and each damage mec hanism. Remarkably, all these individual integration schemes share the same formal structure as the classical return mapping algorithms employed in th e numerical integration of elastoplastic models, namely an operator split s tructure consisting of a trial state and the return map imposing the plasti c and damage consistency, respectively. A Newton iterative scheme imposes t he equilibrium (equal stresses) among the different mechanisms of the respo nse of the material. This modular structure allows to obtain the closed-for m consistent linearization, involving in a simple form the algorithmic cons istent tangents corresponding to each independent mechanism, thus resulting in a very modular and efficient computational implementation. The performa nce of the proposed algorithms is illustrated in several representative num erical simulations. (C) 2000 Elsevier Science Ltd. All rights reserved.