1D Model of Precursors to Frictional Stick-Slip Motion Allowing for Robust Comparison with Experiments

Abstract

In this article, 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 an (i) internal viscosity, (ii) interfacial stiffness and (iii) 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.

The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

“…Generally, each slip event propagates further than the previous rupture, until they reach the leading edge, which is considered to be global sliding. Numerical simulations using mass-spring models (1D (Maegawa et al, 2010;Amundsen et al, 2012) and 2D (Trømborg et al, 2011)) reproduced qualitatively this behavior and show the http://dx.doi.org/10.1016/j.mechmat.2014.03.009 0167-6636/Ó 2014 Elsevier Ltd. All rights reserved.…”

“…Ruptures at bimaterial interfaces are known for their richness of complex mechanics (Coker et al, 2003;Lykotrafitis and Rosakis, 2006) and to date no experiments of similar material interfaces have been conducted to compare with the bimaterial system of Rubinstein et al (2007). In all numerical studies of the transition from sticking to sliding, this bi-material effect has been approximated by a deformable-rigid interface (Maegawa et al, 2010;Amundsen et al, 2012;Trømborg et al, 2011;Kammer et al, 2012;Bar-Sinai et al, 2013;Otsuki and Matsukawa, 2013).…”

Probing the micromechanics of a multi-contact interface at the onset of frictional sliding

“…In the past ten years, several experimental groups developed new optical methods to obtain spatially resolved mechanical measurements [4,5,6,7,8], which triggered intense subsequent theoretical and numerical investigations [9,10,11,12,13,14,15]. Fineberg and collaborators studied the onset of sliding of a multi-contact interface, in a planeplane contact configuration, submitted to an adiabatic tangential loading [6,7].…”

Critical Length Limiting Superlow Friction

“…While we have not yet studied our model in either 2D or 3D systems, previous investigations of edge-driven extended elastic sliders [23][24][25] demonstrated that 1D consideration provides a good description of friction in 3D system. Thus, we expect that qualitative conclusions of this work will hold also for 3D systems, in particular for graphene layers deposited on substrates [26] and clusters studied in the context of nanomanipulation [27].…”