On the overall yielding of an isotropic porous material with a matrix obeying a non-quadratic criterion

Gurson’s approach for investigating the overall response of a rigid-plastic porous representative volume element (RVE) leads to explicit upper-bound estimates only in few particular cases, e.g., when the matrix of the RVE obeys a quadratic criterion (von Mises or Hill’48). The formal difficulties that prevent the application of Gurson’s methodology to a wider range of materials, of current technological interest, can be circumvented by a numerical approach. We show illustrations for an idealized RVE in the form of a hollow sphere with von Mises and Hershey-Hosford matrix, respectively. In both cases the overall yield surface is revealed to have a complex geometry, the most notable features being the variation of the overall measure of equivalent stress along the pressure axis and a significant asymmetry of its level sets in the range of high triaxialities.