An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields

New expressions of the macroscopic criteria of perfectly plastic rigid matrix containing prolate and oblate cavities are presented. The proposed approach, derived in the framework of limit analysis, consists in the consideration of Eshelby-like trial velocity fields for the determination of the macroscopic dissipation. It is shown that the obtained results significantly improve existing criteria for ductile porous media. Moreover, for low stress triaxialities, these new results also agree perfectly with the (nonlinear) Hashin–Shtrikhman bound established by Ponte-Castañeda and Suquet