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A two-dimensional Frenkel-Kontorova model is set up. Its application to the tribology is considered. The materials and the commensurability between two layers strongly affect the static friction force. It is found that the static friction force is larger between two layer of same materials than that for different materials. For two-dimensional case the averaged static friction force is larger for the uncommensurate case than that for the commensurate case, which is completely different from one-dimensional case. The directions of the propagation of the center of mass and the external driving force are usually different except at some special symmetric directions. The possibility to obtain superlubricity is suggested.
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 stra
A 1D model of interacting particles moving over a periodic substrate and in a position dependent temperature profile is considered. When the substrate and the temperature profile are spatially asymmetric a center-of-mass velocity develops, correspond
We solved the Frenkel-Kontorova model with the potential $V(u)= -frac{1}{2} |lambda|(u-{rm Int}[u]-frac{1}{2})^2$ exactly. For given $|lambda|$, there exists a positive integer $q_c$ such that for almost all values of the tensile force $sigma$, the w
The Frenkel Kontorova (FK) model is known to exhibit the so called Aubrys transition which is a jamming or frictional transition at zero temperature. Recently we found similar transition at zero and finite temperatures in a super-conducting Josephson
By means of atomistic simulations, we demonstrate that a dislocation core exhibits intermittent quasistatic restructuring during incremental shear within the same Peierls valley. This can be regarded as a stick-slip transition, which is also reproduc