An Extended Continuum Theory for Granular Media

In a dilatant granular material with rotating grains the kinetic energy in addition to the usual translational one consists of three terms owing to the microstructural motion; in particular, it includes the rotation of granules and the dilatational expansion and contraction of the individual (compressible) grains and of the grains relative to one another. Therefore the balance and constitutive equations of the medium are obtained by considering it as a continuum with a constrained affine microstructure. Moreover, the balance of granular energy is demonstrated to be a direct consequence of the balance of micromomentum, while the dilatational and the rotational microstresses are turned out to be of different physical nature. Finally, a kinetic energy theorem implies that, locally, the power of all inertial forces is the opposite of the time-rate of change of kinetic energy plus the divergence of a flux through the boundary. The peculiar case of a suspension of rotating rigid granules puts in evidence the possibility for granular materials of supporting shear stresses through the generation of microrotational gradients.