Hysteresis from dynamically pinned sliding states

TL;DR

This paper reveals a hysteretic behavior in a one-dimensional nonlinear model of sliding surfaces with a lubricant layer, showing a critical force threshold for changing the quantized sliding state, with implications for tribology.

Contribution

It demonstrates hysteresis in the dynamics of a nonlinear sliding model, highlighting a force-induced transition between quantized and intermediate sliding states, which was not previously observed.

Findings

Hysteresis occurs under external force in the sliding dynamics.

A critical force threshold F_c is needed to alter the quantized state.

No hysteresis observed as a function of external velocity.

Abstract

We report a surprising hysteretic behavior in the dynamics of a simple one-dimensional nonlinear model inspired by the tribological problem of two sliding surfaces with a thin solid lubricant layer in between. In particular, we consider the frictional dynamics of a harmonic chain confined between two rigid incommensurate substrates which slide with a fixed relative velocity. This system was previously found, by explicit solution of the equations of motion, to possess plateaus in parameter space exhibiting a remarkable quantization of the chain center-of-mass velocity (dynamic pinning) solely determined by the interface incommensurability. Starting now from this quantized sliding state, in the underdamped regime of motion and in analogy to what ordinarily happens for static friction, the dynamics exhibits a large hysteresis under the action of an additional external driving force F_ext. A critical threshold value F_c of the adiabatically applied force F_ext is required in order to alter the robust dynamics of the plateau attractor. When the applied force is decreased and removed, the system can jump to intermediate sliding regimes (a sort of ``dynamic'' stick-slip motion) and eventually returns to the quantized sliding state at a much lower value of F_ext. On the contrary no hysteretic behavior is observed as a function of the external driving velocity.