Dilatancy and friction in sheared granular media

We introduce a simple model to describe the frictional properties of granular media under shear. We model the friction force in terms of the horizontal velocity x and the vertical position z of the slider, interpreting, z as a constitutive variable characterizing the contact. Dilatancy is shown iu play an essential role in the dynamics, inducing a stick-slip instability at low velocity. We compute the phase diagram, analyze numerically the model for a wide range of parameters and compare our results with experiments on dry and wet; granular media, obtaining a good agreement. In particular, we reproduce the hysteretic velocity dependence of the frictional force.