The macroscopic behavior of power-law and ideally plastic materials with elliptical distribution of porosity

New theoretical predictions are given for the mechanical behavior of two-dimensional porous media comprised of a power-law or ideally plastic matrix containing an ‘elliptical’ distribution of porosity. The predictions follow from the homogenization estimates recently proposed by Idiart [Idiart, M.I., 2008. Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates. J. Mech. Phys. Solids 56, 2599–2617] for two-phase nonlinear composites. In view of the preliminary results given in this work, it is conjectured that the new estimates provide more reliable predictions for viscoplastic porous media than standard Gurson-type models.