Dynamics of dry friction: A numerical investigation

Abstract

We perform extended numerical simulation of the dynamics of dry friction, based on a model derived from the phenomenological description proposed by Baumberger et al. [Nature (London) 367, 544 (1994)] and Heslot et al. [Phys. Rev. E 49, 4973 (1994)]. Under a quasistationary approximation, the model is related to the Dieterich-Ruina aging (or slowness) law, which was introduced by Dieterich [Pure Appl. Geophys. 116, 790 (1978); J. Geophys. Res. 84, 2161 (1979); in Mechanical Behavior of Crustal Rocks, edited by N. L. Carter et al. Geophysics Monograph No. 24 (AGU, Washington, DC, 1981), p. 103] and Ruina [J. Geophys. Res. 88, 10359 (1983)] on the basis of experiments on rocks. We obtain a dynamical phase diagram that agrees well with the experimental results on the paper-on-paper systems. In particular, the bifurcation between the stickslip motion and steady sliding is shown to change from a direct (supercritical) Hopf type to an inverted (subcritical) one as the driving velocity increases, in agreement with the experiments.