A finite elastoplastic flow theory for porous media

Abstract

Abstract A yield criterion and basic flow equations are developed for finite elastoplastic deformation of porous materials. The yield criterion is derived using a specific micromechanical model of moninteracting spherical pores, with the matrix material being of the von Mises types. The criterion satisfies the convexity requirement of plasticity theory and accounts for the effect of hydrostatic stress. The theoretical prediction of yield stress is in good agreement with published experimental data. The field equations for finite elastoplastic derfomation of the porous media are obtained by generalizing those for plastically incompressible materials. The equations are derived in the form of a combined initial- and boundary-value problem whose spatial domain is the current configuration of the deformed body. They are distinguished by their quasi-linear nature. The theoretical model has two important features: 1. 1. It shows an exclusive dependence of the yield surface of the porous medium on the properties of the constituent matrix material. 2. 2. It shows that there is a porosity effect that itself leads to material instability.