On the microphysical foundations of rate-and-state friction

Thibaut Putelat, Jonathan H P Dawes, John R Willis

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Abstract

The rate-and-state formulation of friction is well established as a phenomenological yet quantitative description of friction dynamics, in particular the onset of stick-slip instabilities arising from an oscillatory bifurcation. We first discuss the physical origins of two theories for the derivation of friction coefficients used in rate-and-state models, both derived from thermally activated rate processes. Secondly, we propose a general expression for the state evolution law in the form of a first order kinetics which describes the relaxation to a velocity dependent equilibrium interfacial state {symbol}ss (v) over a velocity dependent dynamic rejuvenation time-scale t{symbol} (v). We show that the unknown relation {symbol}ss (v), defined as the ratio of t{symbol} to a constant interfacial stationary healing time-scale t* *, can be estimated directly from the experimental measurements of the steady-state friction coefficient and the critical stiffness for the onset of stick-slip behaviour of a spring-block system. Using a specific experimental dataset, we finally illustrate that this method provides the experimental measurements of the apparent memory length La (v) = v t* * {symbol}ss (v) and the constant characteristic relaxation time t* * from which a constant intrinsic memory length L = V* t* * can be defined once a slip rate of reference V* is chosen. As a result the complete state evolution law can be experimentally characterised.
Original languageEnglish
Pages (from-to)1062-1075
Number of pages14
JournalJournal of the Mechanics and Physics of Solids
Volume59
Issue number5
DOIs
Publication statusPublished - May 2011

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friction
Friction
Stick-slip
slip
coefficient of friction
Data storage equipment
Relaxation time
healing
Stiffness
stiffness
derivation
relaxation time
Kinetics
formulations
kinetics

Cite this

On the microphysical foundations of rate-and-state friction. / Putelat, Thibaut; Dawes, Jonathan H P; Willis, John R.

In: Journal of the Mechanics and Physics of Solids, Vol. 59, No. 5, 05.2011, p. 1062-1075.

Research output: Contribution to journalArticle

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