Limit analysis of unidirectional porous media

Abstract

In this paper, an efficient computational approach, that combines the computational homogenization method with conic programming, is proposed to evaluate the macroscopic fatigue domain of anisotropic heterogeneous materials under variable repeated loads. The computational homogenization method is extended for use in the framework of kinematic shakedown analysis of micro-structures under macro-stress control, allowing the direct evaluation of the macroscopic fatigue domains. The discrete optimization problem is cast as conic programming and solved by using highly efficient solvers, demonstrating that the conic algorithm performs well for kinematic shakedown analysis involving a huge number of incompatible strain rate variables arising at each vertex of the convex load domain. The effects of hole shapes, porosity, plastic behaviors of metal matrices and hole distribution on the overall fatigue domains of micro-structures with regular and random patterns are studied. Numerical investigation shows that the Poisson coefficient does not effect on the macroscopic fatigue criterion in 2D analysis, at least for the problems investigated.