Shakedown Analysis of Porous Mohr–Coulomb Materials: A Computational Homogenization Approach

Abstract

This paper presents a computational approach to define the effective fatigue criterion of porous Mohr–Coulomb materials under cyclic loads. The homogenization theory for periodic microstructures is combined with kinematic shakedown theorem, resulting in an auxiliary fatigue analysis in the form of an optimization problem at the microscale. The overall strength and fatigue criterion of porous materials are then obtained by solving several optimization problems under plane strain conditions. The effects of the porosity and shape of voids in regular and random cases on the overall behavior are studied. The obtained macroscopic strength and fatigue domains are compared with other numerical solutions in the literature.