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...

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Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2015-05, Vol.78, p.70-93
Main Authors: Putelat, Thibaut, Dawes, Jonathan H.P.
Format: Article
Language:English
Subjects:
Blocking
Dichotomies
Formalism
Friction
Mathematical models
Sliding
Static friction
Steady state
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Summary: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.
ISSN:0022-5096
DOI:10.1016/j.jmps.2015.01.016