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.Frictional interfaces are important in many areas of science and technology, including seismology [2], biology [3, 4] and nanomechanics [5]. Whereas a satisfactory picture of the steady sliding regime of such interfaces has been developed during the last twenty years [6][7][8], the dynamics of the transition from static to kinetic friction remains elusive. During the last decade, a renewed interest has grown in such transitions, due to experimental studies that directly measured the local dynamics of frictional interfaces [9][10][11][12][13]. They have shown that macroscopic sliding occurs only after shear crack-like micro-slip fronts have spanned the entire contact interface.Experimentally, micro-slip front nucleation, propagation and arrest was shown to be controlled by the instantaneous stress field at the interface. Fronts nucleate preferentially at the trailing edge of the contact area [9,11,[14][15][16][17], an effect explained either by the enhanced shear stress near the loading point in side-driven systems [11,14,16,18] or by a friction-induced pressure asymmetry in top-driven systems [9,19]. Fronts can arise well below the macroscopic static friction threshold and arrest before the whole contact area has ruptured [14][15][16]. The length and number of these precursors depends on the precise way in which shear [14] and normal [16] forces are applied. Moreover, precursors are associated with significant changes in the spatial distribution of the real contact area [14], a quantity related to the local interfacial pressure. Finally, the propagation speed of micro-slip fronts, which covers a wide range [9][10][11]20], correlates with the local shear to normal stress ratio at nucleation [17].Theoretically, some aspects of these observations have been studied using one-dimensional (1D) models. The conditions leading to a large range of front velocities were addressed using a 1D spring-block model with a timedependent friction law [18]. The role of an asymmetric normal loading on the length of precursors was considered using a 1D spring-block model with Amontons-Coulomb (A-C) friction and different normal forces ascribed...

In this article, 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 an (i) internal viscosity, (ii) interfacial stiffness and (iii) 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.

The failure of the population of microjunctions 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 the so-called slow fronts, which are recently discovered fronts much slower than the materials' sound speeds. Despite intense modeling activity, the mechanisms underlying slow fronts remain elusive. Here, we introduce a multiscale 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 microjunctions. Our results show that slow fronts are qualitatively different from faster fronts. Because 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.friction | multiscale modeling | onset of sliding | stick-slip T he rupture of frictional interfaces is a central mechanism in many processes, including snow slab avalanches, human object grasping, and earthquake dynamics (1). Rupture occurs through the propagation of a crack-like microslip front-the rupture frontacross the interface. This front represents the moving boundary between a stick region and a slipping region that coexist within the interface plane. In so-called partial-slip situations, fronts propagate quasistatically at a pace controlled by the external loading, as studied in mechanical engineering for decades (2, 3). Recently, fast cameras enabled the observation of much faster fronts, which are classified into three types: supershear fronts faster than the material's shear wave speed c s , sub-Rayleigh fronts propagating at velocities close to c s , and slow fronts much slower than c s (4-8). Whereas the first two types have been predicted theoretically, the physical mechanisms underlying slow fronts are still debated.A better understanding of slow fronts appears as a significant step toward an improved assessment of how frictional motion begins. It is also expected to shed light on the important topic of slow earthquakes, which have been increasingly reported in the last decade (1). In this context, an intense theoretical and numerical activity arose to investigate the origins and properties of rupture fronts. Two different approaches have been explored.On the one hand, 2D or 3D elastodynamic models have been used to relate the macroscopic loading conditions to the stress field along the contact interface (9-13). These local stresses were indeed shown experimentally to play a role in the selectio...