Dynamical friction modeling

A five-dimensional dynamical model of friction is proposed based on a macroscopic description of the interactions between nominally flat surfaces. In particular, dynamical contacts between surface inhomogeneities result in coupling between the tangential motion and the separation of the surfaces and corresponding variations in interfacial forces. The model is shown to exhibit qualitative agreement with experimentally observed properties of dynamical friction. For example, an apparent dependence of the friction force on tangential velocity is deduced albeit not a priori assumed. Moreover, hysteretic behavior in the quasi-static case due to micro-slip, as well as in the fully dynamical case, is observed. Finally, the appearance of stick-slip oscillations is found to be associated with a Hopf bifurcation from the steady-state equilibrium. The dependence of the Hopf instability on physical parameters also appears consistent with experimental results. The low-dimensionality of the present model and its derivation from physical and geometric consideration suggests its suitability both in understanding dynamical frictional behavior as well as control thereof in physical systems.