  We study the effect of viscoelastic dynamics on the frictional properties of
a (mean field) spring-block system pulled on a rough surface by an external
drive. When the drive moves at constant velocity V, two dynamical regimes are
observed: at fast driving, above a critical threshold Vc, the system slides at
the drive velocity and displays a friction force with velocity weakening. Below
Vc the steady sliding becomes unstable and a stick-slip regime sets in. In the
slide-hold-slide driving protocol, a peak of the friction force appears after
the hold time and its amplitude increases with the hold duration. These
observations are consistent with the frictional force encoded
phenomenologically in the rate-and-state equations. Our model gives a
microscopical basis for such macroscopic description.
