A closed-form yield criterion for porous materials with Mises–Schleicher–Burzyński matrix containing cylindrical voids

Abstract

This work develops a closed-form yield criterion applicable to porous materials with pressure-dependent matrix presenting tension–compression asymmetry (Mises–Schleicher–Burzynski material) containing parallel cylindrical voids. To develop the strength criterion, the stress-based variational homogenization approach due to Cheng et al. (Int J Plast 55:133–151, 2014) is extended to the case of a hollow cylinder under generalized plane strain conditions subjected to axisymmetric loading. Adopting a strictly statically admissible trial stress field, the homogenization procedure results in an approximate yield locus depending on the current material porosity, tension–compression material asymmetry, the mean lateral stress, and an equivalent shear stress. The analytical criterion provides exact solutions for purely hydrostatic loading. Theoretical results are compared with finite element (FE) simulations considering cylindrical unit-cells with distinct porosity levels, different values of the tension–compression asymmetry, and a wide range of stress triaxialities. Based on comparisons, the theoretical results are found to be in good agreement with FE simulations for most of the loading conditions and material features considered in this study. More accurate theoretical predictions are provided when higher material porosities and/or lower tension–compression asymmetries are considered. Overall, the main outcome of this work is a closed-form yield function proving fairly accurate predictions to engineering applications, in which pressure-dependent and tension–compression asymmetric porous materials with cylindrical voids are dealt with. This can be the case of honeycomb structures or additively manufactured materials, in which metal matrix composites are employed.