Extended granular micromechanics

We analyze an extended mechanical model in the conservative case in order to describe a dilatant granular material with rotating grains for which the kinetic energy, in addition to the usual translational one, consists of three terms owing to microstructural motions: in particular, it includes the rotation of the grains, the dilatational expansion and contraction of the individual granules and of the granules relative to one another. Hence, we model the body as a continuum with a peculiar microstructure; after we follow classical procedures and define a variational principle of local type for a perfect fluid with microstructure, in accordance with the fluid-like behavior of granular materials: the motion equations are in good agreement with those obtained by other authors. At the end the particular case of a suspension of rotating rigid granules puts in evidence the possibility for granular materials to support shear stresses through the generation of micro-rotational gradients.