Onset of incommensurate interfacial instability in a minimal model of dry friction

Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):036101. doi: 10.1103/PhysRevE.68.036101. Epub 2003 Sep 3.

Abstract

We present a minimal model of dry friction between two incommensurate interfaces sliding at high relative velocity. Many of the features of the friction force for the full two-dimensional many-body dynamical system-particularly in the sub-critical velocity regime-are captured by our one-dimensional Einstein model, where the motion of a typical interfacial atom is constrained to be vertical to the sliding plane. Beyond the linear response of force versus sliding velocity, the anharmonic Einstein model predicts a doublet resonance peak, whereupon a catastrophe in the model signals the onset of a plastic deformation mechanism for frictional sliding, namely, the instability of the interface. Higher velocities than this critical value require a much more sophisticated description of the production and coalescence of dislocations into a microstructure.