Stochastic Properties of Static Friction

Abstract

The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the applied force at this particular instant when the frictional interface loses stability. However, experimental studies are known to present important scatter in the measurement of static friction; the origin of which remains unexplained.Here, we study the nucleation of local slip at interfaces with slip-weakening friction of random strength and analyze the resulting variability in the measured global strength. Using numerical simulations that solve the elastodynamic equations, we observe that multiple slip patches nucleate simultaneously, many of which are stable and grow only slowly, but one reaches a critical length and starts propagating dynamically. We show that a theoretical criterion based on a static equilibrium solution predicts quantitatively well the onset of frictional sliding. We develop a Monte-Carlo model by adapting the theoretical criterion and pre-computing modal convolution terms, which enables us to run efficiently a large number of samples and to study variability in global strength distribution caused by the stochastic properties of local frictional strength. The results demonstrate that an increasing spatial correlation length on the interface, representing geometric imperfections and roughness, causes lower global static friction. Conversely, smaller correlation length increases the macroscopic strength while its variability decreases. We further show that randomness in local friction properties is insufficient for the existence of systematic precursory slip events. Random or systematic non-uniformity in the driving force, such as potential energy or stress drop, is required for arrested slip fronts. Our model and observations provide a necessary framework for efficient stochastic analysis of macroscopic frictional strength and establish a fundamental basis for probabilistic design criteria for static friction.

Nucleation of frictional sliding by coalescence of microslip

“…∕ℎ n . This is consistent with observations by Albertini et al (2020) on stochastic interfaces. Here, in this deterministic configuration, the theoretical solution presents oscillations (see Fig.…”

“…We aim to generate random frictional interfaces with given spectral density function and probability distribution, and, therefore, adopted the following procedure (Grigoriu, 2013, ch. 5), which was also used by Albertini et al (2020).…”

“…Ampuero et al (2006) extended this approach from a system with a locally peaked load to a random stress distribution. Recently, Albertini et al (2020) reformulated the problem for an interface with a random strength profile and defined a nucleation stress n ( ), which is given by…”

“…Recently, Albertini et al (2020) demonstrated, using numerical simulations, that the macroscopic strength of a random interface can be quantitatively well predicted with an analytical solution (Uenishi and Rice, 2003;Ampuero et al, 2006), which determines a critical nucleation length and its associated stress level. The simulations confirmed that macroscopic sliding occurs when a slipping region reaches this critical length.…”

“…First, in Sec. 2 we will introduce the physical system used for dynamic simulations, present our approach to generate deterministic frictional interfaces and summarize the method used by Albertini et al (2020) to generate random interfaces with a specific correlation length and probability density. In Sec.…”