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 term of the horizontal velocity v and the vertical position z of the slider, interpreting z as a constitutive variable characterizing the contact. Dilatancy is shown to play an essential role in the dynamic, 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.