Dynamic hysteresis of a confined lubricant under shear

A nonlinear model inspired by the tribological problem of a thin solid lubricant layer between two sliding periodic surfaces is used to analyze the novel phenomenon of hysteresis at pinning or 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 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 accessed by varying mechanical parameters other than F_{ext} . The hysteretic phenomena are confined to the underdamped dynamics, and the overdamped dynamics of the same model is generally not hysteretic, much like in static friction.