On distribution softening in the yielding of porous materials

Abstract

The effect of void distribution on yielding is investigated using periodic single-void tetragonal unit cells subjected to symmetric and asymmetric loading conditions. The behavior is compared to that of reference, cubic lattice and random dispersions across porosity levels spanning two orders of magnitude. Small-strain FFT-based simulations are performed using three-dimensional periodic cells with equiaxed voids embedded in an elastic–perfectly plastic matrix. Emphasis is placed on a regime termed unhomogeneous yielding, where deformation localizes into “layered” bands or columnar regions the orientation of which depends on void distribution as well as on the loading. A key feature is the percolation of nondeforming regions within the cell. It is found that elongated tetragonal distributions consistently exhibit a softer response compared to both cubic and random distributions. On the other hand, flat cells are found to alter the mode of percolation. The extent of the apparent first-order effect of void distribution on yielding is analyzed in terms of the concept of band porosity.