TY - JOUR

T1 - On the microphysical foundations of rate-and-state friction

AU - Putelat, Thibaut

AU - Dawes, Jonathan H P

AU - Willis, John R

PY - 2011/5

Y1 - 2011/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79953652499&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.jmps.2011.02.002

U2 - 10.1016/j.jmps.2011.02.002

DO - 10.1016/j.jmps.2011.02.002

M3 - Article

SN - 0022-5096

VL - 59

SP - 1062

EP - 1075

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

IS - 5

ER -