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, <i>P</i>(<i>x</i>), which is the density of microscopic regions that yield if the shear load is increased by some amount <i>x</i>. 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: <i>P</i>(<i>x</i>) then vanishes at small argument as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>P</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo></mml:mrow> <mml:mo>∼</mml:mo> <mml:msup><mml:mi>x</mml:mi> <mml:mi>θ</mml:mi></mml:msup> </mml:mrow> </mml:math> (de Geus et al., Proc Natl Acad Sci USA 116(48):23977-23983, 2019. 10.1073/pnas.1906551116). The exponent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>θ</mml:mi></mml:math> is non-zero only in the presence of inertia (otherwise <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>θ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:mrow> </mml:math> ). 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>θ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn></mml:mrow> </mml:math> , which we can analytically relate to the statistics of the disorder.