Construction of an averaged stress tensor for a granular medium

The aim of this paper is to construct an averaged stress tensor for a granular media, valid in static and in dynamics, which takes into account the contact reactions and the body forces acting at the grain level. The construction, based on a simple formula of linear algebra, is inspired from the Cauchy processes. General balance principles ensure the fundamental properties of the averaged stress tensor so defined: it is automatically symmetric and invariant by translation (independent from the origin chosen). In the second part, a simple analytical example shows that taking account of the inertia forces is essential to insure the symmetry of the averaged stress tensor in dynamics. Finally, numerical simulations illustrating this definition of the averaged stress tensor are presented for granular media containing a large number of grains.