Simulations of the Velocity Dependence of the Friction Force

Abstract

The motion of an elastic body over a rough surface is simulated in one dimension using Newtonian dynamics. We drive the body by prescribing a constant velocity. We extract the friction force from the work done by the applied force in order to maintain the motion of the body. A positive amount of work is needed because energy is converted into the internal elastic degrees of freedom of the body. The velocity dependence of the friction force is studied as function of the roughness of the surface and the elastic properties of the mobile body. We pay special attention to the low velocity limit. It is shown that the friction force goes to a finite value as the velocity goes to zero when the substrate is sufficiently rough to induce elastic instabilities. For smooth substrates, where elasitc instabilities are absent, the friction force goes to zero when the velocity goes to zero.