  Frictional interfaces are abundant in natural and manmade systems and their
dynamics still pose challenges of fundamental and technological importance. A
recent extensive compilation of multiple-source experimental data has revealed
that velocity-strengthening friction, where the steady-state frictional
resistance increases with sliding velocity over some range, is a generic
feature of such interfaces. Moreover, velocity-strengthening friction has very
recently been linked to slow laboratory earthquakes and stick-slip motion. Here
we elucidate the importance of velocity-strengthening friction by theoretically
studying three variants of a realistic rate-and-state friction model. All
variants feature identical logarithmic velocity-weakening friction at small
sliding velocities, but differ in their higher velocity behaviors. By
quantifying energy partition (e.g. radiation and dissipation), the selection of
interfacial rupture fronts and rupture arrest, we show that the presence or
absence of velocity-strengthening friction can significantly affect the global
interfacial resistance and the total energy released during frictional
instabilities ("event magnitude"). Furthermore, we show that different forms of
velocity-strengthening friction (e.g. logarithmic vs. linear) may result in
events of similar magnitude, yet with dramatically different dissipation and
radiation rates. This happens because the events are mediated by interfacial
rupture fronts with vastly different propagation velocities, where stronger
velocity-strengthening friction promotes slower rupture. These theoretical
results may have significant implications on our understanding of frictional
dynamics.
