Dynamics of Dry Friction: A Numerical Investigation

TL;DR

This paper presents a numerical study of dry friction dynamics, revealing phase diagrams and bifurcation behaviors consistent with experimental observations, and linking phenomenological models to established friction laws.

Contribution

It introduces a numerical simulation approach that connects phenomenological dry friction models with state- and rate-dependent laws, explaining bifurcation transitions.

Findings

Phase diagram matches experimental results

Bifurcation type changes with velocity

Steady and stick-slip motions are characterized

Abstract

We perform extended numerical simulation of the dynamics of dry friction, based on a model derived from the phenomenological description proposed by T. Baumberger et al.. In the case of small deviation from the steady sliding motion, the model is shown to be equivalent to the state- and rate-dependent friction law which was first introduced by Rice and Ruina on the basis of experiments on rocks. We obtain the dynamical phase diagram that agrees well with the experimental results on the paper-on-paper systems. In particular, the bifurcation between stick-slip and steady sliding are shown to change from a direct (supercritical) Hopf type to an inverted (subcritical) one as the driving velocity increases, in agreement with the experiments.