Velocity weakening in a dynamical model of friction

Abstract

We introduce a discrete model for friction between rough elastic surfaces which is based on the microscopic description of contacts between asperities. Rough surfaces are modeled as spring-mass arrays with superposed asperities. The linear elastodynamics of the underlying surfaces is treated in the model separately from the nonlinear contact behavior of asperities. Unlike usual spring-block models, noa priori friction law is imposed in the model, which allows the frictional behavior corresponding to a chosen microscopic physics of contacts and topography of the rough surfaces to be simulated. We use the model to study the elastodynamical mechanism of friction related to the inertial response of the elastic medium to suddenly imposed tractions, and perturbations of contact properties due to the elastic waves propagating along the interface. The contribution of this mechanism to friction becomes important at high slip rates (above 1% of the wave speed in our simulations), where it results in the velocity weakening behavior. The mechanism of velocity weakening is first studied analytically on an isolated model element. The predicted behavior is then reproduced in numerical simulations with large surfaces. Simulations with stepping of the driving velocity demonstrate a difference between the frictional force measured directly on contacts, and at the loading point. The latter corresponds to laboratory measurements and includes the inertial response of both the loading mechanism and the elastic body to the variations of driving velocity. We speculate that a similar inertial response is present in certain experimental data.