A new technique for finite element limit-analysis of Hill materials, with an application to the assessment of criteria for anisotropic plastic porous solids

Abstract

The present work is devoted to the numerical limit-analysis of Hill materials with particular emphasis on anisotropically plastic porous solids. Its aim is to provide an efficient method of limit-analysis based on the standard finite element method including elasticity, and present a few applications.We first present the numerical implementation of Hill’s criterion. We then describe the procedure used for the numerical limit-analysis, which basically consists of using a single large load step ensuring that the limit-load is reached, without updating the geometry. Also, the convergence of the elasto–plastic iterations is accelerated by suitably adjusting the elastic properties of the material.The method is applied to assess Gurson-like criteria for orthotropically plastic materials containing spheroidal voids. This is done by performing numerical limit-analyses of elementary cells made of a Hill material and containing confocal spheroidal voids, subjected to classical conditions of homogeneous boundary strain rate. The numerical results are compared to the model predictions for both the yield surface and the flow rule, and this permits to discuss the accuracy of the theoretical models considered.