On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials

The consideration of saturated and non-saturated porous solid materials as for instance soil, concrete, sinter materials, polymeric and metallic foams, temperate ice, living tissues, etc. naturally falls into the category of multiphase materials, which can be described by use of a macroscopic continuum mechanical approach within the well-founded framework of the Theory of Porous Media (TPM) . In the present contribution, granular elasto-plastic porous solid skeletons ( frictional materials) are taken into consideration, where, regardless of whether or not the solid is fluid-saturated or empty, localization phenomena can occur as a result of local concentrations of plastic strains. As a consequence of localization phenomena, the numerical solution of the governing equations generally reveals an ill-posed problem. In particular, the shear band width strongly depends on the mesh size of the finite element discretization by the fact that each mesh refinement leads to a decrease of the shear band width until one obtains a singular surface. In the present article, it is shown that the inclusion of fluid-viscosity in the saturated case and the inclusion of micropolar grain rotations both in the saturated and in the non-saturated case leads to a regularization of the shear band problem. On the other hand, the inclusion of micropolar degrees of freedom in the sense of the Cosserat brothers additionally allows for the determination of the local average grain rotations. The numerical examples are solved by use of finite element discretization techniques, where, in particular, the computation of shear band localization phenomena is carried out by the example of the well-known geotechnical slope failure problem and two additional academic problems, which clearly demonstrate the efficiency of the proposed procedure.