  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.
