Transition from static to dynamic macroscopic friction in the framework of the Frenkel-Kontorova model

TL;DR

This paper demonstrates that the Frenkel-Kontorova model effectively describes the complex, non-uniform transition from static to dynamic friction, predicting detachment front types and their velocities, aligning well with experimental observations.

Contribution

It introduces a novel application of the Frenkel-Kontorova model to describe the spatial-temporal dynamics of frictional transitions, including detachment front types and velocity relations.

Findings

Two types of detachment fronts are predicted, explaining experimental variability.

The velocity of detachment fronts relates to shear and normal stress ratios.

Slip velocity is shown to be independent of normal stress.

Abstract

A new generation of experiments on dry macroscopic friction has revealed that the transition from static to dynamic friction is essentially a spatially and temporally non-uniform process, initiated by a rupture-like detachment front. We show the suitability of the Frenkel-Kontorova model for describing this transition. The model predicts the existence of two types of detachment fronts, explaining both the variability and abrupt change of velocity observed in experiments. The quantitative relation obtained between the velocity of the detachment front and the ratio of shear to normal stress is consistent with experiments. The model provides a functional dependence between slip velocity and shear stress, and predicts that slip velocity is independent of normal stress. Paradoxically, the transition from static to dynamic friction does not depend explicitly on ether the static or the dynamic friction coefficient, although the beginning and end of transition process are controlled by these coefficients.