Micro and macro aspects of the elastoplastic behaviour of sand piles

We use a discrete element method to simulate the dynamics of granulates made up from arbitrarily shaped particles. Static and dynamic friction are accounted for in our force laws, which enables us to simulate the relaxation of (two-dimensional) sand piles to their final static state. Depending on the growth history, a dip in the pressure under a heap may or may not appear. Properties of the relaxed state are measured and averaged numerically to obtain the values of field quantitities pertinent for a continuum description. In particular, we show that it is possible to obtain not only stresses but also displacements in the heap, by judicious use of an adiabatic relaxation experiment, in which gravity is slowly changed. Hence the full set of variables of the theory of elastiticity is available, allowing comparison with elastoplastic models for granular aggregates. A surprising finding is the behaviour of the material density in a heap with dip, which increases where the pressure is minimum.