Dry friction in the Frenkel-Kontorova-Tomlinson model: Static properties

We investigate wearless friction in a simple mechanical model called the Frenkel-Kontorova-Tomlinson model. It combines the Frenkel-Kontorova model (i.e., a harmonic chain in a spatially periodic potential) with the Tomlinson model (i.e., independent oscillators connected to a sliding surface in a fixed potential describing the other surface). We investigate static properties like the ground state, the metastable states, and static friction, as well as the kinetic friction in the limit of quasistatic sliding. As in the Frenkel-Kontorova model the behavior strongly depends on whether the ratio of lattice constants is commensurate or incommensurate. In the incommensurate case, Aubry's transition by breaking of analyticity also appears in the Frenkel-Kontorova-Tomlinson model. The behavior depends strongly on the strength of the interaction between the sliding surfaces. For increasing interaction, we find three thresholds which denote the appearance of static friction, of kinetic friction in the quasistatic limit, and of metastable states in that order. These are identical only in the incommensurate case. In the commensurate case, static friction can be nonzero even though the kinetic friction vanishes for sliding velocity going to zero.