Constitutive behavior of porous ductile materials accounting for micro-inertia and void shape

Abstract

The goal of this paper is to characterize the mechanical behavior of porous materials by taking into account the void shape and micro-inertia effects. A representative volume element (RVE) defined by two confocal prolate spheroids is used to describe the porous material. The matrix behavior is assumed to be rigid and non linear viscous. Based on the work of Molinari and Mercier (2001), the macroscopic stress is decomposed into static and dynamic parts. In the present work the static contribution is described by the Gologanu et al. model (1993). The dynamic stress is obtained by choosing the trial velocity field proposed by Gologanu et al. (1993). With the proposed modeling a link is established between the macroscopic dynamic stress, on the one hand and, on the other hand, the macroscopic strain rate tensor and its time derivative. To validate our model, finite element simulations have been performed. Two shapes of void (spherical and prolate with an aspect ratio of 5) and two volume fraction of voids (0.001 or 0.1) are considered. The influence of micro-inertia on the macroscopic flow stress surface is analyzed and it is shown that the flow surface obtained by the analytical approach is in good agreement with finite element computations.