Emergent friction in two-dimensional Frenkel-Kontorova models

TL;DR

This study extends the Frenkel-Kontorova model to two dimensions to analyze static and dynamic friction, revealing that while static friction remains consistent, dynamic friction is significantly affected by the second dimension and anisotropic effects.

Contribution

The paper introduces a physically realistic two-dimensional extension of the FK model and explores how the second dimension influences static and dynamic friction behaviors.

Findings

Static friction behavior is robust in two dimensions.

Dynamic friction is strongly influenced by the second dimension.

Friction anisotropy can cause direction-dependent motion.

Abstract

Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature-dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.