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.
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