A homogenization based yield criterion for a porous Tresca material with ellipsoidal voids

This paper presents a rate-independent analytical model for porous Tresca (J₃-dependent) materials containing general ellipsoidal voids. The model is based on the nonlinear variational homogenization method which uses a linear comparison material to estimate the response of the nonlinear porous solid and is denoted as “MVAR”. Specifically, the model is derived by an original approach starting from a novel porous single crystal model (Mbiakop et al. in Int J Solids Struct 64–65:100–119, 2015b, J Mech Phys Solids 84:436–467, 2015c) by considering the limiting case of infinite slip systems which leads readily to the corresponding Tresca criterion. The MVAR yield surface is then validated using FEM on different unit-cells and various parameters including several porosity levels, several stress triaxiality ratios, different Lode angle and general void shapes and orientations. The MVAR model is found to be in good agreement with the finite element results for all cases considered in this study. Both the MVAR and the FEM computations reveal a strong sensitivity upon the microstructure anisotropy (void shape and orientation), and a dependence of the effective behavior on the third invariant of the applied stress. To the best knowledge of the authors, this is the first model in the literature that is able to deal with porous Tresca material and general void shapes and orientations. Moreover, the MVAR is used in a predictive manner to investigate the complex response of porous Tresca cases with strong coupling between the J₃-dependent matrix behavior and the (morphological) anisotropy induced by the shape and orientation of the voids. The simplicity of the present analytical study opens the possibility to adapt the present model to experimental results for various materials.