1. Introduction

The finite element method is nowadays widely applied to crashworthiness or sheet metal forming. In order to accurately predict the damage and failure evolution occurring in such simulations, a realistic material description is required. For this purpose, this paper presents a damage model for elasto-viscoplastic materials, taking into account both the material and the damage anisotropy. On the microscale, the material is composed of a pore-free matrix, inclusions and second phase particles and microvoids randomly distributed. During the straining process, the volume of microvoids growths under hydrostatic stress and the number of microvoids increases by nucleation due to the fracture of inclusions and to the decohesion of second phase-matrix interfaces. The evolution of the geometrical form and the volume of the microvoids may lead to the coalescence of some cavities. Therefore, ductile rupture may occur when the stress-carrying capacity has vanished.

To describe the previous damage process, a coupling mechanical-damage model is used. The description of the porous material is based on the introduction of an internal variable representing the microvoid volume fraction and defined as the ratio of the microvoid volume and the material volume. The microvoid growth, nucleation and coalescence are described. The growth of existing microvoids is determined from the plastic incompressibility relation. The microvoid nucleation is related to the plastic strain and depends on the distribution of the inclusions and second phase particles. An additional term is used to ensure some...