1D model of precursors to frictional stick-slip motion allowing for robust comparison with experiments

TL;DR

This paper develops an improved 1D spring-block model for frictional precursors, addressing previous limitations, and provides analytical predictions for precursor lengths, enhancing understanding of stick-slip dynamics.

Contribution

The study introduces modifications to a minimalistic 1D model, including viscosity, interfacial stiffness, and initial force distribution, to better match experimental results and predict precursor lengths.

Findings

Improved model avoids unphysical stress fluctuations.

Model's dependence on spatial resolution is eliminated.

Analytical prediction for precursor length is developed.

Abstract

We study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38, 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model.