An efficient and reliable model to simulate microscopic mechanical friction in the Frenkel–Kontorova–Tomlinson model

Abstract

The Frenkel–Kontorova–Tomlinson model is composed of a large number of non-linear, coupled differential equations that reproduce the friction occurring in mechanical systems in which the atomic smooth surfaces of two bodies slide against each other. The problem is very interesting since the possible solutions, which are very sensitive to the parameters of the system, range from simple stable harmonic solutions (in which the spectrum of the movement of individual atoms contains one frequency) to chaotic solutions (where the spectrum contains a series of incommensurable frequencies), passing through intermediate solutions formed by a spectrum of commensurable finite frequencies. The design of the model both for the static and dynamic problem, which follows the network method rules, is explained in detail and the model is run on standard electrical circuit simulation software to provide, in its own graphic ambient, the average total friction force, the Fast Fourier Transforms of atom displacement and the phase diagrams. The influence of the main parameters of the system (interaction force amplitude and stiffness between surface atoms and substrate) on the type of pattern of the solution is studied for a practical range of these parameters.