A Note on Frictional Slip Patterns

Abstract

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].