Crack in the frictional interface as a solitary wave

Abstract : We introduce and investigate a multiscale model for the propagation of rupture fronts in friction. Taking advantage of the correlation length for the motion of individual contacts in elastic theory, we introduce collective contacts which can be characterized by a master equation approach. The problem of the dynamics of a chain of those effective contacts under stress is studied. We show that it can be reduced to an analog of the Frenkel-Kontorova model. In some limits this allows us to derive analytical solutions for kinks describing the rupture fronts. Numerical simulations are used to study more complex cases.