Models of stick slip in granular friction

A stochastic model of granular friction, aimed at the description of an experiment of sheared granular layers, is introduced in analogy with the Einstein theory of Brownian motion. For the present problem, a key role is played by the correlations of the random force, which result from the collective interactions between grains. Moreover, a weakening average force has to be introduced in order to describe the fluctuations of the stick-slip dynamics. Nevertheless, the resulting model keeps very simple and allows to quantitatively reproduce several experimental statistics. Moreover, through such a model, it is possible to relate the irregular frictional dynamics with other examples of crackling noise in nature, notably the Barkhausen noise in the hysteresis of ferromagnets. A rate and state variant of the model, without the ad hoc assumption of the weakening force, displays an even richer phenomenology, at the cost of a larger parameter space.