Nonlinear hysteretic behavior of a confined sliding layer

A nonlinear model representing the tribological problem of a thin solid lubricant layer between two sliding periodic surfaces is used to analyze the phenomenon of hysteresis at pinning/depinning around a moving state rather than around a statically pinned state. The cycling of an external driving force F(ext) is used as a simple means to destroy and then to recover the dynamically pinned state previously discovered for the lubricant center-of-mass velocity. Depinning to a quasi-freely sliding state occurs either directly, with a single jump, or through a sequence of discontinuous transitions. The intermediate sliding steps are reminiscent of phase-locked states and stick-slip motion in static friction, and can be interpreted in terms of the appearance of traveling density defects in an otherwise regular arrangement of kinks. Repinning occurs more smoothly, through the successive disappearance of different traveling defects. The resulting bistability and multistability regions may also be explored by varying mechanical parameters other than F(ext), e.g. the sliding velocity or the corrugation amplitude of the sliders.