Propagation velocity of slip front and emergence of macroscopic static friction in the system with vanishing local static friction

Abstract

We investigate the propagation of the slip front in the elastic body on the rigid substrate. We first obtain the slip profile and the slip front velocity of the steady state by employing the local friction law with the quadratic form of the slip velocity and with vanishing static friction stress. The macroscopic static friction stress emerges spontaneously, which is expressed in terms of the parameter emerging in the friction law. For the model with viscosity, the macroscopic static friction stress again emerges spontaneously. The analytical treatment gives estimations for two slip front propagation velocities. They corresponds to two different boundary conditions, and one of them describes the framework employed here. Linear Marginal Stability Hypothesis based on the linearized equation of motion shows that two slip front propagation velocities exist in this system, both of which coincide with the analytical solutions noted above. These imply that the linearized friction law dominantly governs the slip front propagation behavior. Seismological implications are also given based on the analytical and numerical results.