Approximate macroscopic yield criteria for Drucker-Prager type solids with spheroidal voids

The present study is devoted to the theoretical determination and a numerical assessment of macroscopic yield criteria for ductile porous materials consisting of a pressure sensitive matrix and spheroidal voids. The plastic matrix obeys a Drucker-Prager type criterion. The theoretical derivation is done by carefully implementing an appropriate kinematical limit analysis with a relaxed plastic admissibility condition in an average sense. The resulting closed form expression of the macroscopic yield criterion explicitly accounts for the void shape effects and for the plastic compressibility of the matrix. A first comparison of the theoretical predictions to available numerical upper and lower bounds in the case of oblate voids. This suggests a need of improvement of the macroscopic criterion which is carried out after carefully examining some particular loading cases. The modified criterion is shown to be in satisfactory agreement with the numerical bounds corresponding to different aspect ratios of oblate voids and different values of the matrix friction angle. For the purpose of a wider assessment, we perform new standard finite element based limit analysis which provides estimates not only for oblate voids but also for prolate voids with different aspect ratios, porosity and of the matrix friction angle. These new data are used for a complete validation of the modified macroscopic criterion.