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Soft Matter and Biological Physics

Eur. Phys. J. E 2, 181-189

Dilatancy and friction in sheared granular media

F. Lacombe - S. Zapperi - H.J. Herrmann

PMMH-ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France

Received 16 November 1999

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 $\dot{x}$ 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 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.

81.40.Pq Friction, lubrication, and wear - 83.20.Bg Macroscopic (phenomenological) theories - 83.70.Fn Granular solids

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