Microstructures and Granular Media

A general model of solids with vectorial microstructures is introduced. The field equationsare the obtained as Euler-Lagrange equations of a suitable energetic functional. The Cosserat model is encompassed in this model and it can be used to study the behaviour of granular media. A first approach to this problem deals with a two dimensional model, since in such a case the field equations have a simpler form, the rotation of the single grain depends on one parameter only, the angle of rotation, but the model is still physically meaningful. In order to obtain constitutive equations rigorously deduced from the principles of Continuum Mechanics, we must take in account both the interaction matrix-grains and grain-grain. As a first step, we deal with linear dissipation, as already done in general for vector microstructures, such that we can also study some simpler problems of wave propagation.