Abstract

We present a brief introduction of the coarse graining technique, which we shall use to construct a continuous matter field for discrete particulate systems. In particular, we address the problem of the micro to macro transition in the theoretical framework of granular hydrodynamics. The equations for momentum conservation, elastic stress tensor, and elastic energy are obtained introducing a harmonic interaction between the particles. These equations are compared with previous work, where the microscopic discrete nature of granular matter has not been considered. The microscopic description of a granular system leads to a matrix for the definition of the elastic moduli, which depends on position and coarse graining resolution. This provides some insight into the mathematical description of the origin of force chains in granular packings.