Rheology and structure of granular materials near the jamming transition

The shear stress of non-cohesive granular material in the vicinity of the jamming transition is supposed to be connected to the formation of transient rigid clusters of particles. The characteristics of these transient clusters are investigated as a function of the imposed pressure, the solid volume fraction and the shear rate. This is responsible for an increase of the shear stress for a vanishing shear rate, which leads to an instability close to the jamming transition. We discuss the consequences for stick-slip motion and flows down an inclined plane, in agreement with the observations. Then, the oscillation of the granular material between two jam-flow states generates fast velocity fluctuations which result in a mean frictional force proportional to the mean velocity relative to the jammed state in the flow direction. Accordingly the velocity field in a simple shear flow is governed by a Brinkman equation and any symmetry break favours a strain localization. This analysis might be extended to the case of granular pastes.