Nonlinear hysteretic behavior of a confined sliding layer

Abstract

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 Fext 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. De-pinning 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 travelling density defects in an otherwise regular arrangement of kinks. Re-pinning occurs more smoothly, through the successive disappearance of different travelling defects. The resulting bistability and multistability regions may also be explored by varying mechanical parameters other than Fext, e.g. the sliding velocity or the corrugation amplitude of the sliders.

Tribology of the lubricant quantized sliding state

“…The occurrence of this surprising and robust regime of motion, giving rise to perfectly flat plateaus in the ratio of the timeaveraged lubricant center-of-mass (CM) velocity to the externally imposed relative speed, was ascribed to the intrinsic topological nature of this quantized dynamics. The phenomenon, investigated in detail in a rather idealized 1D geometry, [9][10][11][12][13][14] was explained by the corrugation of a sliding confining wall rigidly dragging the topological solitons (kinks or antikinks) that the embedded lubricant structure forms with the other substrate. Evidence of the existence of this peculiar regime of motion was then confirmed shortly after for a substantially less idealized 2D model of boundary lubrication, where atoms were allowed to move perpendicularly to the sliding direction and interacted via LJ potentials 15 .…”

Analytic understanding and control of dynamical friction

“…The reader must be warned that the strict applicability of LRT is limited to smooth-sliding regimes where the system remains clear of highly nonlinear effects such as stick-slip dynamics or wear, which can and do occur in the physics of friction. 8,9,[22][23][24][25] In the present weak-perturbation approach however, the Prandtl-Tomlinson smooth-sliding condition 36 is always automatically satisfied. For smooth sliding therefore, one can take advantage of the analytical predictive power of the LRT decomposition, as we shall illustrate in the following sections.…”

Influence of substrate potential shape on the dynamics of a sliding lubricant chain

“…For example, in the Θ = 0.8 simulations producing the secondary plateau characterized by V CM /V ext ≃ 0.802, individual particles do carry out regular periodic trajectories, like in the standard quantized state. These secondary plateaus, observed also for the purely sinusoidal corrugation [21,38], are likely to be due to resonances very much akin to Shapiro steps [15,[39][40][41], excited by the simultaneous action of the periodically oscillating force produced by the sliding substrate and the forward-dragging force produced by the dissipative term in Eq. (1).…”