Coarse graining for granular materials: micro-polar balances

Abstract

In this work, we extend a previously discussed averaging method for granular materials (Artoni and Richard in Phys Rev E 91:032202, 2015), by considering average balance equations related to particle rotations (the micro-inertia, the angular momentum and the rotational energy balances). The method is based on a fluctuation decomposition taking into account velocity gradients and on a local homogeneity assumption. After having developed the coarse-grained balances, we study the simplifications related to some classes of simple flows and particularly assess the relation between the micro-inertia balance and the average orientation of particles in a simple shear flow.