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Rate and state dependent friction and the stability of sliding between elastically deformable solids

Rice, James R. and Lapusta, Nadia and Ranjith, K. (2001) Rate and state dependent friction and the stability of sliding between elastically deformable solids. Journal of the Mechanics and Physics of Solids, 49 (9). pp. 1865-1898. ISSN 0022-5096. doi:10.1016/S0022-5096(01)00042-4.

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We study the stability of steady sliding between elastically deformable continua using rate and state dependent friction laws. That is done for both elastically identical and elastically dissimilar solids. The focus is on linearized response to perturbations of steady-state sliding, and on studying how the positive direct effect (instantaneous increase or decrease of shear strength in response to a respective instantaneous increase or decrease of slip rate) of those laws allows the existence of a quasi-static range of response to perturbations at sufficiently low slip rate. We discuss the physical basis of rate and state laws, including the likely basis for the direct effect in thermally activated processes allowing creep slippage at asperity contacts, and estimate activation parameters for quartzite and granite. Also, a class of rate and state laws suitable for variable normal stress is presented. As part of the work, we show that compromises from the rate and state framework for describing velocity-weakening friction lead to paradoxical results, like supersonic propagation of slip perturbations, or to ill-posedness, when applied to sliding between elastically deformable solids. The case of sliding between elastically dissimilar solids has the inherently destabilizing feature that spatially inhomogeneous slip leads to an alteration of normal stress, hence of frictional resistance. We show that the rate and state friction laws nevertheless lead to stability of response to sufficiently short wavelength perturbations, at very slow slip rates. Further, for slow sliding between dissimilar solids, we show that there is a critical amplitude of velocity-strengthening above which there is stability to perturbations of all wavelengths.

Item Type:Article
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URLURL TypeDescription
Lapusta, Nadia0000-0001-6558-0323
Additional Information:© 2001 Elsevier Science Ltd. This study was supported by grants from the Office of Naval Research, the US Geological Survey, and the NSF Southern California Earthquake Center. We are grateful to C. Marone, M. Nakatani and H. Perfettini for discussions on friction laws, and to R. Madariaga for discussions on purely velocity-dependent friction models of weakening type and supersonic propagation.
Funding AgencyGrant Number
Office of Naval Research (ONR)UNSPECIFIED
Southern California Earthquake Center (SCEC)UNSPECIFIED
Subject Keywords:Tribology; B. Contact mechanics; B. Friction; B. Geological materials; C. Stability and bifurcation
Issue or Number:9
Record Number:CaltechAUTHORS:20130308-134151285
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Official Citation:James R. Rice, Nadia Lapusta, K. Ranjith, Rate and state dependent friction and the stability of sliding between elastically deformable solids, Journal of the Mechanics and Physics of Solids, Volume 49, Issue 9, September 2001, Pages 1865-1898, ISSN 0022-5096, 10.1016/S0022-5096(01)00042-4.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37420
Deposited By: Tony Diaz
Deposited On:12 Mar 2013 21:23
Last Modified:09 Nov 2021 23:28

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