Nonlinear dynamics of frictional slip localization

Abstract eng:
An explanation is proposed of the origins of travelling waves of stick and slip that have been observed between frictional sliding surfaces. Such waves, at very different lengthscales, are thought to underlie both earthquakes’ source and the performance of mechanical brakes and dampers. An idealised situation is studied of a long thin elastic plate, subject to uniform shear stress and frictional interaction with a rigid flat surface. Seeking deformation that is uniform in the transverse direction, a nonlinear wave equation is constructed under a long-wave assumption. Appearing from global homoclinic or heteroclinic bifurcations and under non-monotonic rate-and-state friction, a rich variety of solution types is discovered at intermediate shear stress between pure uniform stick and uniform slip, including: periodic stick-slip wave-trains, isolated pulses of stick or slip and detachment or attachment fronts. Careful consideration of the choice of the friction model and interfacial state kinetics is necessary to capture the full richness of wave types.

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