A macroscopic description of the quasi-static behavior of granular materials based on the theory of porous media

Granular materials fall into the class of porous media. But in contrast to materials like foams and sponges their structure is discontinous on a microscopic level. For this reason the particles may undergo independent displacements and rotations. This is the classical kinematics which may be captured by a micropolar or Cosserat theory on the macroscopic level. The goal of this paper is to combine the theory of porous media as a macroscopic theory dealing with multiphase systems and the micropolar theory describing extended kinematics and taking care of the discountinous structure of granular media on the micro scale. The resulting micropolar theory of porous media may be used to describe the quasistatic behavior of granular materials. In the present contribution thermodynamically consistent constitutive relations for the elastic response of a dense granular matrix material saturated by a viscous pore fluid are given and applied to some boundary value problems which demonstrate the physical relevance of the proposed model.