VELOCITY WEAKENING IN A DYNAMICAL MODEL OF FRICTION

We introduce a discrete model for friction between rough elastic surfa ces which is based on the microscopic description of contacts between asperities. Rough surfaces are modeled as spring-mass arrays with supe rposed asperities. The linear elastodynamics of the underlying surface s is treated in the model separately from the nonlinear contact behavi or of asperities. Unlike usual spring-block models, no a priori fricti on law is imposed in the model, which allows the frictional behavior c orresponding to a chosen microscopic physics of contacts and topograph y of the rough surfaces to be simulated. We use the model to study the elastodynamical mechanism of friction related to the inertial respons e of the elastic medium to suddenly imposed tractions, and perturbatio ns of contact properties due to the elastic waves propagating along th e interface. The contribution of this mechanism to friction becomes im portant at high slip rates (above 1% of the wave speed in our simulati ons), where it results in the velocity weakening behavior. The mechani sm 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 driv ing velocity demonstrate a difference between the frictional force mea sured directly on contacts, and at the loading point. The latter corre sponds to laboratory measurements and includes the inertial response o f both the loading mechanism and the elastic body to the variations of driving velocity. We speculate that a similar inertial response is pr esent in certain experimental data.