Static equations of the Cosserat continuum derived from intra-granular stresses

Abstract

I present a derivation of the static equations of a granular mechanical interpretation of Cosserat continuum based on a continuum formulated in the intra-granular fields. I assume granular materials with three-dimensional, non-spherical, and deformable grains, and interactions given by traction acting on finite contact areas. Surface traction is decomposed into a mean and a fluctuating part. These account for forces and contact moments. This decomposition leads to a split of the Cauchy stress tensor into two tensors, one of them corresponding to the stress tensor of the Cosserat continuum. Macroscopic variables are obtained by averaging over representative volume. The macroscopic Cauchy stress tensor is shown to be symmetric even in non-equilibrium. The stress tensor of the Cosserat continuum becomes asymmetric when the sum of the contact moments acting on the boundary of the representative volume is different from zero.