Eur. Phys. J. B 4, 233-246 (1998)
https://doi.org/10.1007/s100510050374

Hysteresis and elastic interactions of microasperities in dry friction

¹ Groupe de Physique des Solides, Université Paris 6 et Paris 7 et CNRS, Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France
² Institut Laue-Langevin et Collège de France, BP 156, 38042 Grenoble Cedex 9, France

Corresponding author: ^a nozieres@ill.fr

Received: 3 February 1998
Accepted: 19 March 1998
Published online: 15 July 1998

Abstract

Velocity independent dry friction of a slider upon a base is due to an hysteretic response of relative displacement ρ to a tangential driving force F. We show that the purely elastic model for multistability considered in a previous publication is in no way essential: multistability arises just as well from adhesion. We emphasize the physical consequences of multistability for dynamic/static, a.c./d.c. friction. When the slider is moved from rest by an amount ρ the transition from the zero force static configuration to dynamic behaviour is progressive, spreading on a range equal to the width of the hysteresis cycle. When ρ is small, an elastic restoring force ensues, in agreement with observations. The competition of that elastic pinning with bulk elasticity generates a screening length which we believe is the natural size of Burridge Knopoff blocks. We then study the effect of elastic interactions between asperities: it is weak for dilute asperities, but its long range makes it important. In lowest order the interaction mediated displacement of a given asperity has logarithmically divergent fluctuations: they become comparable to the asperity radius when the slider size reaches another characteristic "Larkin length" , which for dilute micronic asperities is exponentially large. We give arguments suggesting that individually monostable asperities display collective multistability on scales larger than . For individually multistable sites we show that elastic interactions give rise to cascade processes in which the spinodal jump of a given asperity triggers the jump of others. We estimate the size of these cascades that should show up in the noise spectrum.