A Gurson-type layer model for ductile porous solids containing arbitrary ellipsoidal voids with isotropic and kinematic hardening

Extensions of Gurson’s model for porous ductile materials have been done by Madou and Leblond (2012) for general ellipsoidal cavities made of rigid-plastic materials, and Morin et al. (2017), for spherical voids with rigid-hardenable matrices. The aim of this work is to provide a homogenized criterion for porous ductile materials incorporating both void shape effects and isotropic and kinematic hardening. A sequential limit-analysis is performed on an ellipsoidal representative volume made of some rigid-hardenable material, containing a confocal ellipsoidal cavity. The overall plastic dissipation is obtained by using the velocity field proposed by Leblond and Gologanu (2008) and that satisfies conditions of homogeneous strain rate on an arbitrary family of confocal ellipsoids. The heterogeneity of hardening is accounted for by discretizing the cell into a finite number of ellipsoids between each of which the quantities characterizing hardening are considered as homogeneous. The model is finally assessed through comparison of its predictions with the results of micromechanical finite element simulations. The numerical and theoretical overall yield loci are compared for various distributions of isotropic and kinematic pre-hardening with a very good agreement.