1. Introduction

A key process in powder forming is cold compaction. It consists in the vertical compaction of a fine powder material through the movement of a set of punches at room temperature. The process transforms the loose powder into a compacted sample with a volume reduction (and therefore a density increase) of about 2 2.5 times. The design of these processes includes the definition of the initial dimensions of the sample and the movements of the punches that lead to compacted samples with uniform density distributions. In this context, efficient and reliable numerical simulations can play an important role as a complement to experimental tests.

Two ingredients are crucial for the numerical simulation of powder compaction processes: the constitutive model and the kinematics formulation of the problem. Several constitutive models have been proposed, including microscopic models, flow formulations and solid mechanics models; see [OLI 96] and [LEW 98] for a general overview and additional references. One of the most common approaches is the use of elastoplastic models based on porous or frictional materials. Here, an elliptic yield function expressed in terms of the relative density and the Kirchhoff stresses is used [OLI 96]. The plastic model is originally formulated within the framework of isotropic finite strain multiplicative hyperelastoplasticity [SIM 92], with some simplifications derived from the assumption of small elastic strains [OLI 96]. In this work,...