Steady and transient sliding under rate-and-state friction

Putelat, Thibaut; Dawes, Jonathan

doi:10.1016/j.jmps.2015.01.016

Cited by 36 publications

(27 citation statements)

References 58 publications

(136 reference statements)

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“…The PLC effect is commonly explained through the use of continuum constitutive models that incorporate phenomenological strain-rate softening at low rates followed by hardening at high rates. Quite similarly, bifurcated stick-slip motions in fault gouges have been described through socalled 'rate and state friction' phenomenological models [15][16][17][18][19], and oscillatory, transient, and chaotic bifurcated motions associated with fractures in polymeric and amorphous brittle materials have been explained using a velocity-stress relationship (at the fracture tip) that also obeys a velocity-softening law [20].…”

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confidence: 99%

Evidence That Strain-Rate Softening Is Not Necessary for Material Instability Patterns

2017

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confidence: 99%

Evidence That Strain-Rate Softening Is Not Necessary for Material Instability Patterns

2017

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“…Varying the shear stressτ between the local extrema of a spinodal friction model [13], we find the occurrence of travelling self-healing 'slip pulses', reminiscent of the pulses described by Heaton [8], arising from a homoclinic bifurcation of travelling periodic slip patterns born in a Hopf bifurcation promoted by velocity-weakening friction, see Fig. 1(B,C).…”

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confidence: 71%

“…The phenomenological rate-and-state framework of friction [16,1,13] is a physically motivated smooth regularisation of Coulomb friction where three crucial experimental observations are incorporated, namely: the time dependence of static friction in quasi-stationary contact and the velocity dependence of dynamic friction, together with sliding memory effects via an interfacial state variable φ(t) quantifying the interface resistance to slip whose characteristic relaxation timescale is denoted t * . Accordingly classical rate-and-state models are usually defined by the pair of empirical equations…”

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A Note on Frictional Slip Patterns

Putelat

2017

Trends in Mathematics

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A possible origin of the frictional travelling waves usually occuring between sliding interfaces is discussed: various solutions, including propagating wavetrains, pulses and fronts, can appear under rate-and-state friction from homoclinic or heteroclinic bifurcations.Introduction. The understanding of the spatio-temporal dynamics of frictional slip along extended solid interfaces is of great importance, both theoretically and in practice, across many industrial or natural contexts such as brake squeal or earthquake mechanics. Various regimes of stick-slip travelling waves are often observed numerically as for instance in the recent simulations of a brake pad [2], or experimentally as in the careful monitoring of friction rupture fronts controlling the onset of frictional slip [6]. The intricate nature and diversity of earthquakes recorded over the past decade ranging from aseismic events, episodic tremors, slow and fast earthquakes is also most startling, e.g. see [11,9]. The emergence of such a variety of inhomogeneous frictional sliding modes, either in engineering or geophysical contexts, is a difficult problem due to its multiple scales nature caused by the complexity of the friction phenomenon, its modelling and its coupling with the elastic wave radiation. Even in the case of the idealised situation of a long thin elastic plate, a plethora of solution types, including propagating wavetrains, pulses and fronts, can appear under non-monotonic rate-and-state friction from homoclinic or heteroclinic bifurcations [14]. Here we briefly sketch the analysis for visco-elastic rate-and-state friction models motivated by the experimental results reported in [7].

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“…Chart (q = 1,¯ = 1,w = 1) 122 . In this chart, we obtain the following equations:ẏ = ρ 2 2 2 ρ 2 2 + y x 22 ξ , (6.9)…”

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confidence: 99%

“…The more recently developed spinodal rate-and-state friction law, see [22] and references therein, has been developed to capture the missing near-vertical and increasing pieces of the -profile, producing a potentially widely applicable, yet complicated, friction law. In [23], travelling wave solutions of a simple model for a thin sliding slab with this friction law were analyzed numerically.…”

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confidence: 99%

A new type of relaxation oscillation in a model with rate-and-state friction

Kristiansen

2020

Nonlinearity

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In this paper we prove the existence of a new type of relaxation oscillation occurring in a one-block Burridge-Knopoff model with Ruina rateand-state friction law. In the relevant parameter regime, the system is slowfast with two slow variables and one fast. The oscillation is special for several reasons: Firstly, its singular limit is unbounded, the amplitude of the cycle growing like log −1 as → 0. As a consequence of this estimate, the unboundedness of the cycle cannot be captured by a simple -dependent scaling of the variables, see e.g. [12]. We therefore obtain its limit on the Poincaré sphere. Here we find that the singular limit consists of a slow part on an attracting critical manifold, and a fast part on the equator (i.e. at ∞) of the Poincaré sphere, which includes motion along a center manifold. The reduced flow on this center manifold runs out along the manifold's boundary, in a special way, leading to a complex return to the slow manifold. We prove the existence of the limit cycle by showing that a return map is a contraction. The main technical difficulty in this part is due to the fact that the critical manifold loses hyperbolicity at an exponential rate at infinity. We therefore use the method in [16], applying the standard blowup technique in an extended phase space. In this way we identify a singular cycle, consisting of 12 pieces, all with desirable hyperbolicity properties, that enables the perturbation into an actual limit cycle for 0 < 1. The result proves a conjecture in [1]. The reference [1] also includes a priliminary analysis based on the approach in [16] but several details were missing. We provide all the details in the present manuscript and lay out the geometry of the problem, detailing all of the many blowup steps.

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Steady and transient sliding under rate-and-state friction

Cited by 36 publications

References 58 publications

Evidence That Strain-Rate Softening Is Not Necessary for Material Instability Patterns

Evidence That Strain-Rate Softening Is Not Necessary for Material Instability Patterns

A Note on Frictional Slip Patterns

A new type of relaxation oscillation in a model with rate-and-state friction

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