Interfacial localisation in a granular medium modelled as a Cosserat continuum

When the interface between a rigid and rough structure and a granular soil is loaded tangentially, one can observe the formation of a thin zone, called interface layer, where shear deformations concentrate. The thickness of this layer is typically a few grain diameter thick and varies depending on the roughness of the structural member. Modelling of such phenomena within the framework of a classical continuum is not possible. Limitations of a classical continuum can be overcome within the framework of a Cosserat continuum, which can adequately modelled granular media. When compared to a classical continuum, a Cosserat continuum owns two features of interest for modelling interfacial localisation. First, the constitutive equations introduce an internal length which can be related to the grain size based on micro-mechanical considerations. Secondly, corresponding to the extra-degrees of freedom, additional boundary conditions stem naturally out of the principle of virtual work. To show the importance of those points, two extreme cases of constitutive equations: anisotropic linear elastic and isotropic rigid plastic, are considered to analyse respectively the plane simple shear and the ring simple shear.