Armouring of a frictional interface by mechanical noise

A dry frictional interface loaded in shear often displays stick-slip. The amplitude of this cycle depends on the probability that a microscopic event nucleates a rupture and on the rate at which microscopic events are triggered. The latter is determined by the distribution of soft spots, $P(x)$, which is the density of microscopic regions that yield if the shear load is increased by some amount $x$. In minimal models of a frictional interface - that include disorder, inertia and long-range elasticity - we discovered an 'armouring' mechanism by which the interface is greatly stabilised after a large slip event: $P(x)$ then vanishes at small argument as $P(x)\sim x^\theta$ [1]. The exponent $\theta$ is non-zero only in the presence of inertia (otherwise $\theta=0$). It was found to depend on the statistics of the disorder in the model, a phenomenon that was not explained. Here, we show that a single-particle toy model with inertia and disorder captures the existence of a non-trivial exponent $\theta>0$, which we can analytically relate to the statistics of the disorder.