Stability of Steady Frictional Slipping

Rice, James R.; Ruina, Andy

doi:10.1115/1.3167042

Cited by 991 publications

(828 citation statements)

References 16 publications

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“…Like for the anti-plane case, large |k| values (short wavelengths) have Re(p) ¡ 0 and hence stability, because a ¿ 0. To ÿnd the critical wavenumber at which stability is lost, we observe, like in Rice and Ruina (1983), that roots cannot cross from Re(p) ¡ 0 to Re(p) ¿ 0 at any |k| ¿ 0 by passing through p = 0. Thus we identify k cr by seeking conditions for there to be roots in the form p = i|k|c, where c is real; k cr will be the largest |k| at which such roots occur.…”

Section: Response To In-plane Perturbationsmentioning

confidence: 99%

“…1, which has been drawn for the case of in-plane perturbations considered in Sections 3.3, 3.4, 4 and 5). This problem of linear perturbation was partially addressed by Rice and Ruina (1983). The sliding occurs on the plane y = 0 and we write the displacement ÿeld as u z (x; y; t) = 1 2 V 0 t sign(y) +û z (x; y; t); whereû z is the perturbed part and satisÿes c 2 s ∇ 2û z = 9 2û z =9t 2 .…”

Section: Response To Anti-plane Perturbationsmentioning

confidence: 99%

“…As shown for anti-plane elastodynamics with rate and state friction by Rice and Ruina (1983), the loss of stability on velocity-weakening surfaces, as one considers the response to perturbations of progressively longer wavelengths, occurs as a Hopf bifurcation. At that bifurcation wavelength, the responses to perturbations propagate at a speed c along the interface.…”

Section: Introductionmentioning

confidence: 99%

“…Dependence on those contact properties is represented as a dependence on a state variable, or variables Rice, 1983;Rice and Ruina, 1983;Tullis and Weeks, 1986;Heslot et al, 1994;Marone, 1998). A formulation of friction due to Oden and Martins (1985) can likewise be considered as a special limit of rate and state friction, provided that the small normal motion between sliding surfaces, included in that formulation, is simply considered as a state variable rather than also as a source of alteration of normal stress.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Rice

Lapusta

Ranjith

2001

Journal of the Mechanics and Physics of Solids

571

622

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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 e ect (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 su ciently low slip rate. We discuss the physical basis of rate and state laws, including the likely basis for the direct e ect 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 su ciently 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. ?

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Section: Response To In-plane Perturbationsmentioning

confidence: 99%

Section: Response To Anti-plane Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Rice

Lapusta

Ranjith

2001

Journal of the Mechanics and Physics of Solids

571

622

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“…It was also used in the numerical have been proposed for rock friction. One of the most complete and complex of these models is the statevariable friction law developed by Dieterich [1979a] and consequently refined by Ruina [1983], Rice and Ruina [1983], and Rice and Gu [1983].…”

Section: Introductionmentioning

confidence: 99%

On the importance of normal vibrations in modeling of stick slip in rock sliding

Tworzydlo¹,

Hamzeh²

1997

J. Geophys. Res.

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Abstract. In this paper, numerical studies of friction-induced dynamic instabilities,in particular, stick-slip sliding of rocks, are presented. Of special interest is the importance of normal compliance of the interface and associated normal vibrations in the occurrence of dynamic instabilities. To clearly illustrate this importance, the interface is represented by the Oden-Martins constitutive model which does not exhibit explicit velocity or slip dependence of friction. This friction model is utilized in the context of a rather simple rigid body model to perform numerical studies representative of granite blocks in relative sliding at very slow overall velocities. The model represents a common experimental setting that has been used to study stick slip of sliding rock blocks. To capture the stick-slip phenomenon the detailed dynamic response of this system is modeled numerically. These studies indicate the importance of the normal compliance of the interface on the stability of sliding. In particular, dynamic coupling of the degrees of freedom contributes to dynamic instability of the system and can cause stick-slip motion. Both stable and unstable sliding are predicted and examined.

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Dynamics of three-block assemblies with unilateral deformable contacts. Part 1: contact modelling

Andreaus

Casini

1999

Earthquake Engng. Struct. Dyn.

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Stability of Steady Frictional Slipping

Abstract: The shear resistance of slipping surfaces at fixed normal stress is given by r =

Cited by 991 publications

References 16 publications

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

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

On the importance of normal vibrations in modeling of stick slip in rock sliding

Dynamics of three-block assemblies with unilateral deformable contacts. Part 1: contact modelling

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