Micromechanical modelling of granular materials and FEM simulations

We present a micro-mechanical continuum model used for the description of dilatant granular materials with incompressible rotating grains for which the kinetic energy, in addition to the usual translational one, consists of other two terms owing to microstructural motions: in particular, it includes the dilatational expansions and contractions of the granules relative to one another, as well as the rotation movements of each grain compared to the others. Next, we propose a linear theory in which the representations of constitutive functionals are linear with respect to both the volume fraction and the micro-rotation gradients, and to the dissipative variables. At the end we test the linear model on a two-dimensional domain, in which the arising system of partial differential equations is solved using the finite element method; thus we obtain a numerical solution in the case of a simplified granular micromechanics. The obtained computations of the early granular dynamics are consistent with theoretical insights as deduced from the proposed model. Viscous and rotational contributions to the granular dynamics have been identified and compared each others.