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The rupture of dry frictional interfaces occurs through the propagation of fronts breaking the contacts at the interface. Recent experiments have shown that the velocities of these rupture fronts range from quasi-static velocities proportional to the external loading rate to velocities larger than the shear wave speed. The way system parameters influence front speed is still poorly understood. Here we study steady-state rupture propagation in a one-dimensional (1D) spring-block model of an extended frictional interface, for various friction laws. With the classical Amontons--Coulomb friction law, we derive a closed-form expression for the steady-state rupture velocity as a function of the interfacial shear stress just prior to rupture. We then consider an additional shear stiffness of the interface and show that the softer the interface, the slower the rupture fronts. We provide an approximate closed form expression for this effect. We finally show that adding a bulk viscosity on the relative motion of blocks accelerates steady-state rupture fronts and we give an approximate expression for this effect. We demonstrate that the 1D results are qualitatively valid in 2D. Our results provide insights into the qualitative role of various key parameters of a frictional interface on its rupture dynamics. They will be useful to better understand the many systems in which spring-block models have proved adequate, from friction to granular matter and earthquake dynamics., Comment: 16 pages, 10 figures, 1 table

Cooperative binding affects many processes in biology, but it is commonly addressed only in equilibrium. In this work we explore dynamical cooperativity in driven systems, where the cooperation occurs because some of the bonds change the dynamical response of the system to a regime where the other bonds become active. To investigate such cooperativity we study the frictional binding between two flow driven surfaces that interact through a large population of activated bonds. In particular, we study systems where each bond can have two different modes: one mode corresponds to a fast forming yet weak bond, and the other is a strong yet slow forming bond. We find considerable cooperativity between both types of bonds. Under some conditions the system behaves as if there were only one binding mode, corresponding to a strong and fast forming bond. Our results may have important implications on the friction and adhesion between sliding surfaces containing complementary binding motifs, such as in the case of cells binding to the vessel walls under strong flowing conditions., Comment: 5 pages, 4 figures main text; 1 page 1, figure supplemental material; computer code

The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasi-static fronts with speeds proportional to external loading rates, via fronts much slower than the Rayleigh wave speed, and fronts that propagate near the Rayleigh wave speed, to fronts that travel faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic 2D spring--block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that a proportionality between material slip speed and rupture front speed, previously reported for slow fronts, actually holds across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even in homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Lastly, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically-based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed., Comment: 29 pages, 21 figures

To study the microscopic origins of friction, we build a framework to describe the collective behaviour of a large number of individual micro-junctions forming a macroscopic frictional interface. Each micro-junction can switch in time between two states: A pinned state characterized by a displacement-dependent force, and a slipping state characterized by a time-dependent force. Instead of tracking each micro-junction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. We show how this framework represents an overarching structure for important models existing in the friction literature. We then use it to study systematically the effect of the time-scale that controls the duration of the slipping state. We first find the steady-state friction force as a function of the sliding velocity. As the framework allows for a whole family of micro-junction behaviour laws, we show how these laws can be chosen to obtain monotonic (strengthening or weakening) or non-monotonic velocity dependence at the macroscale. By then considering transient situations, we predict that the macroscopic static friction coefficient is strongly influenced by the way the interface was prepared, in particular by the slip dynamics of the previous sliding event. We also show that slow slip spontaneously occurs in the framework for a wide range of behaviour laws., Comment: 20 pages, 10 figures

The failure of the population of micro-junctions forming the frictional interface between two solids is central to fields ranging from biomechanics to seismology. This failure is mediated by the propagation along the interface of various types of rupture fronts, covering a wide range of velocities. Among them are so-called slow fronts, which are recently discovered fronts much slower than the materials' sound speeds. Despite intense modelling activity, the mechanisms underlying slow fronts remain elusive. Here, we introduce a multi-scale model capable of reproducing both the transition from fast to slow fronts in a single rupture event and the short-time slip dynamics observed in recent experiments. We identify slow slip immediately following the arrest of a fast front as a phenomenon sufficient for the front to propagate further at a much slower pace. Whether slow fronts are actually observed is controlled both by the interfacial stresses and by the width of the local distribution of forces among micro-junctions. Our results show that slow fronts are qualitatively different from faster fronts. Since the transition from fast to slow fronts is potentially as generic as slow slip, we anticipate that it might occur in the wide range of systems in which slow slip has been reported, including seismic faults., Comment: 35 pages, 5 primary figures, 6 supporting figures. Post-print version with improvements from review process included

We study the dynamic behaviour of 1D spring-block models of friction when the external loading is applied from a side, and not on all blocks like in the classical Burridge-Knopoff-like models. Such a change in the loading yields specific difficulties, both from numerical and physical viewpoints. To address some of these difficulties and clarify the precise role of a series of model parameters, we start with the minimalistic model by Maegawa et al. (Tribol. Lett. 38, 313, 2010) which was proposed to reproduce their experiments about precursors to frictional sliding in the stick-slip regime. By successively adding (i) an internal viscosity, (ii) an interfacial stiffness and (iii) an initial tangential force distribution at the interface, we manage to (i) avoid the model's unphysical stress fluctuations, (ii) avoid its unphysical dependence on the spatial resolution and (iii) improve its agreement with the experimental results, respectively. Based on the behaviour of this improved 1D model, we develop an analytical prediction for the length of precursors as a function of the applied tangential load. We also discuss the relationship between the microscopic and macroscopic friction coefficients in the model., Comment: 13 pages, 14 figures, accepted in Tribology Letters

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic slider/rigid substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory micro-slip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress build-up due to both elastic loading and micro-slip-related relaxations depend only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a non-trivial scaling parameter., Comment: 5 pages, 4 figures, accepted for publication in Physical Review Letters