Anisotropic behaviour of porous, ductile media

An orthotropic constitutive model for porous, ductile media is developed, w hich is centred on the micromechanical analysis of a cylindrical representa tive volume element (RVE) with elliptic cross-section containing a coaxial and confocal elliptic-cylindrical cavity. The constitutive model is obtaine d in the case of a rigid ideally plastic behaviour of the matrix material, whose yield condition obeys J(2) flow theory of plasticity with an associat ed flow rule. The following condition is assumed throughout: the longitudin al axis of the hollow cylindrical RVE is a principal direction of the macro scopic strain rate and stress tensors. Cases for which the principal direct ions of the macroscopic strain rate tensor in the RVE cross-section plane a re aligned or rotated with respect to the ellipse axes are both considered. The constitutive behaviour is characterized by the homogenized yield domai n in the macroscopic stress tensor space, by associated flow rules for the plastic components of the macroscopic strain rate tensor and by the evoluti on laws for the internal state variables. These are the void volume fractio n, already appearing in Gurson's model, the aspect ratio of the cavity and its orientation in the RVE cross-section plane, assuming that during the de formation process, the void retains an elliptic shape. The theoretical resu lts are compared with finite element computations of the RVE strength at pl astic collapse to assess the capability of the model to describe the actual micromechanical response to the applied boundary conditions. (C) 2001 Else vier Science Ltd. All rights reserved.