We first present the numerical implementation of Hill鈥檚 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.