A micromechanics-based modification of the Gurson criterion by using Eshelby-like velocity fields

In this study, we propose a micromechanics-based modification of the Gurson criterion for porous media subjected to arbitrary loadings. The proposed formulation, derived in the framework of limit analysis, consists in the consideration of Eshelby-like exterior point trial velocity fields for the determination of the macroscopic dissipation. This approach is implemented for perfectly plastic rigid von Mises matrix containing spherical voids. After the minimization procedure required by the use of the Eshelby-like trial velocity fields, we derive a two-field estimate of the macroscopic yield function. It is shown that the obtained closed-form estimate provides a significant modification of the Gurson criterion, particularly in the domain of low stress triaxialities. This estimate is first compared with existing criteria. Moreover, its accuracy is assessed through comparison with results derived from numerical exact two-field criterion and with recently available numerical bounds.