Deriving the slip front propagation velocity with the slip- and slip-velocity-dependent friction laws via the use of the linear marginal stability hypothesis

Abstract

We analytically and numerically investigate the determining factors of the slip front propagation (SFP) velocity. The slip front has two forms characterized by intruding or extruding front. We assume a 1D viscoelastic medium on a rigid and fixed substrate, and we employ the friction law depending on the slip and slip velocity. Despite this dependency potentially being nonlinear, we use the linear marginal stability hypothesis, which linearizes the governing equation for the slip, to investigate the intruding and extruding front velocities. The analytically obtained velocities are found to be consistent with the numerical computation where we assume the friction law nonlinearly depends on both the slip and slip velocity. This implies that the linearized friction law is sufficient to capture the dominant features of SFP behavior.