How does dissipation affect the transition from static to dynamic macroscopic friction?

TL;DR

This paper extends a friction model to include dissipation effects, revealing that rupture velocity during static-to-dynamic transition depends solely on stress ratio, not friction, and covers a wide velocity range including seismic events.

Contribution

The study introduces a dissipation-inclusive modification to the Frenkel-Kontorova-based friction model, elucidating the independence of rupture velocity from friction and its dependence on stress ratio.

Findings

Rupture velocity is independent of friction.

Rupture velocity depends only on shear to normal stress ratio.

Model applies to seismic events from earthquakes to slow slip.

Abstract

Description of the transitional process from a static to a dynamic frictional regime is a fundamental problem of modern physics. Previously we developed a model based on the well-known Frenkel-Kontorova model to describe dry macroscopic friction. Here this model has been modified to include the effect of dissipation in derived relations between the kinematic and dynamic parameters of a transition process. The main (somewhat counterintuitive) result is a demonstration that the rupture (i.e. detachment front) velocity of the slip pulse which arises during the transition does not depend on friction. The only parameter (besides the elastic and plastic properties of the medium) controlling the rupture velocity is the shear to normal stress ratio. In contrast to the rupture velocity, the slip velocity does depend on friction. The model we have developed describes these processes over a wide range of rupture and slip velocities (up to 7 orders of magnitude) allowing, in particular, the consideration of seismic events ranging from regular earthquakes, with rupture velocities on the order of a few km/s, to slow slip events, with rupture velocities of a few km/day.