TOWARD FINITE-THEORIES OF LIQUID-SATURATED ELASTOPLASTIC POROUS-MEDIA

The present article concerns a general approach to porous media elasto-plasticity by use of the theory of mixtures extended by the volume fraction concept. The investigations are based on a macroscopic binary model of incompressible constituents, solid skeleton and liquid, where, in the constitutive range, use is made of the second-grade character of general heterogeneous media. Thus, finite elasto-plasticity results in a multiplicative decomposition of both the first and the second solid deformation gradients. Apart from the general set of thermodynamical restrictions, the inclusion of the plastic deformation gradients among the list of constitutive variables reveals a restriction for a finite representation for the back-stress tensor of kinematically hardening second-grade solid materials. A simplified constitutive model is included and, in addition, finite constitutive equations are given suitable to describe the elastic as well as the plastic response of the medium under discussion. The constitutive model applies to ductile as well as to brittle and granular liquid-saturated or empty solid materials.