Dynamics of dry friction: A numerical investigation

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, 10 359 ~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. @S1063-651X~98!01311-7#