How collective asperity detachments nucleate slip at frictional interfaces

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 ) ∼ x θ (de Geus et al., Proc Natl Acad Sci USA 116(48):23977-23983, 2019. 10.1073/pnas.1906551116). The exponent θ is non-zero only in the presence of inertia (otherwise θ = 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 θ > 0 , which we can analytically relate to the statistics of the disorder.

Experimental evidence of seismic ruptures initiated by aseismic slip

Seismic faults release the stress accumulated during tectonic movement through rapid ruptures or slow-slip events. The role of slow-slip events is crucial as they impact earthquakes occurrence. However, the mechanisms by which slow-slip affects the failure of frictionally locked regions remain elusive. Here, building on laboratory experiments, we establish that a slow-slip region acts as a nucleation center for seismic rupture, enhancing earthquakes' frequency. We emulate slow-slip regions by introducing a granular material along part of a laboratory fault. Measuring the fault's response to shear reveals that the heterogeneity serves as an initial rupture, reducing the fault shear resistance. Additionally, the slow-slip region extends beyond the heterogeneity with increasing normal load, demonstrating that fault composition is not the only requirement for slow-slip. Our results show that slow-slip modifies rupture nucleation dynamics, highlighting the importance of accounting for the evolution of the slow-slip region under varying conditions for seismic hazard mitigation.

Model of Friction with Plastic Contact Nudging: Amontons-Coulomb Laws, Aging of Static Friction, and Nonmonotonic Stribeck Curves with Finite Quasistatic Limit

We introduce a model of friction between two contacting (stationary or cosliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact with each other only pairwise elastic repulsion and dissipative drag. These minimal ingredients are sufficient to capture a static state of jammed, interlocking contacting bumps, below a critical frictional force that is proportional to the normal load and independent of the apparent contact area, consistent with the Amontons-Coulomb laws of friction. However, they fail to capture two widespread observations: (i) that the dynamic friction coefficient (ratio of frictional to normal force in steady sliding) is a roughly constant or slightly weakening function of the sliding velocity U, at low U, with a nonzero quasistatic limit as U→0 and (ii) that the static friction coefficient (ratio of frictional to normal force needed to initiate sliding) increases ("ages") as a function of the time that surfaces are pressed together in stationary contact, before sliding commences. To remedy these shortcomings, we incorporate a single additional model ingredient: that contacting bumps plastically nudge one another slightly sideways, above a critical contact-contact load. With this additional insight, the model also captures observations (i) and (ii).

Temperature dependent model for the quasi-static stick-slip process on a soft substrate

The classical Prandtl-Tomlinson model is the most famous and efficient method to describe the stick-slip phenomenon and the resulting friction between a slider and a corrugated substrate. It is widely used in all studies of frictional physics and notably in nanotribology. However, it considers a rigid or undeformable substrate and therefore is hardly applicable for investigating the physics of soft matter and in particular biophysics. For this reason, we introduce here a modified model that is capable of taking into consideration a soft or deformable substrate. It is realized by a sequence of elastically bound quadratic energy wells, which represent the corrugated substrate. We study the quasi-static behavior of the system through the equilibrium statistical mechanics. We thus determine the static friction and the deformation of the substrate as a function of temperature and substrate stiffness. The results are of interest for the study of cell motion in biophysics and for haptic and tactile systems in microtechnology.

Static friction coefficient depends on the external pressure and block shape due to precursor slip

Amontons' law states that the maximum static friction force on a solid object is proportional to the loading force and is independent of the apparent contact area. This law indicates that the static friction coefficient does not depend on the external pressure or object shape. Here, we numerically investigate the sliding motion of a 3D viscoelastic block on a rigid substrate using the finite element method (FEM). The macroscopic static friction coefficient decreases with an increase in the external pressure, length, or width of the object, which contradicts Amontons' law. Precursor slip occurs in the 2D interface between the block and substrate before bulk sliding. The decrease in the macroscopic static friction coefficient is scaled by the critical area of the precursor slip. A theoretical analysis of the simplified models reveals that bulk sliding results from the instability of the quasi-static precursor slip caused by velocity-weakening local friction. We also show that the critical slip area determines the macroscopic static friction coefficient, which explains the results of the FEM simulation.

Scaling theory for the statistics of slip at frictional interfaces

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress σ^{*}, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a power law corresponding to "avalanches" and a "narrow" distribution of system-spanning "fracture" events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.

The nanocaterpillar's random walk: diffusion with ligand-receptor contacts

Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) and present guidelines to control the mode of motion for materials design.

Earthquake Nucleation Along Faults With Heterogeneous Weakening Rate

The transition from quasistatic slip growth to dynamic rupture propagation constitutes one possible scenario to describe earthquake nucleation. If this transition is rather well understood for homogeneous faults, how the friction properties of multiscale asperities may influence the overall stability of seismogenic faults remains largely unclear. Combining classical nucleation theory and concepts borrowed from condensed matter physics, we propose a comprehensive analytical framework that predicts the influence of heterogeneities of weakening rate on the nucleation lengthL c for linearly slip-dependent friction laws. Model predictions are compared to nucleation lengths measured from 2D dynamic simulations of earthquake nucleation along heterogeneous faults. Our results show that the interplay between frictional properties and the asperity size gives birth to three instability regimes (local, extremal, and homogenized), each related to different nucleation scenarios, and that the influence of heterogeneities at a scale far lower than the nucleation length can be averaged.

Different Fault Response to Stress during the Seismic Cycle

Seismic prediction was considered impossible, however, there are no reasons in theoretical physics that explicitly prevent this possibility. Therefore, it is quite likely that prediction is made stubbornly complicated by practical difficulties such as the quality of catalogs and data analysis. Earthquakes are sometimes forewarned by precursors, and other times they come unexpectedly; moreover, since no unique mechanism for nucleation was proven to exist, it is unlikely that single classical precursors (e.g., increasing seismicity, geochemical anomalies, geoelectric potentials) may ever be effective in predicting impending earthquakes. For this reason, understanding the physics driving the evolution of fault systems is a crucial task to fine-tune seismic prediction methods and for the mitigation of seismic risk. In this work, an innovative idea is inspected to establish the proximity to the critical breaking point. It is based on the mechanical response of faults to tidal perturbations, which is observed to change during the “seismic cycle”. This technique allows to identify different seismic patterns marking the fingerprints of progressive crustal weakening. Destabilization seems to arise from two different possible mechanisms compatible with the so called preslip patch, cascade models and with seismic quiescence. The first is featured by a decreasing susceptibility to stress perturbation, anomalous geodetic deformation, and seismic activity, while on the other hand, the second shows seismic quiescence and increasing responsiveness. The novelty of this article consists in highlighting not only the variations in responsiveness of faults to stress while reaching the critical point, but also how seismic occurrence changes over time as a function of instability. Temporal swings of correlation between tides and nucleated seismic energy reveal a complex mechanism for modulation of energy dissipation driven by stress variations, above all in the upper brittle crust. Some case studies taken from recent Greek seismicity are investigated.

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius [Formula: see text] governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding [Formula: see text] presents a pseudogap [Formula: see text], where θ is a nonuniversal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudogap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite-size effect, while the slip nucleation radius [Formula: see text] diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally.