Steady and transient sliding under rate-and-state friction

The physics of dry friction is often modeled by assuming that static and kinetic frictional forces can be represented by a pair of coefficients usually referred to as [mu[subs]] and [mu[subk]] respectively. In this paper we re-examine this discontinuous dichotomy and relate it quantitatively to the more general, and smooth, framework of rate-and-state friction. We consider specific dynamical models for the motion of a rigid block sliding on an inclined surface. Next, we revisit the often-cited experiments of Rabinowicz. In the rate-and-state formalism steady sliding states exist, and analyzing their existence and stability enables us to show that the static friction coefficient [mu[subs]] should be interpreted as the local maximum at very small slip rates of the steady state rate-and-state friction law. We show that a second definition of[mu[subs]] is possible, compatible with the first one, as the weighted average of the rate- and-state friction coefficient over the time the block is in motion.