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...

The incomplete understanding of glacier dynamics is a major source of uncertainty in assessments of sea-level rise from land-based ice. Through increased ice discharge into the oceans, accelerating glacier flow has the potential to considerably enhance expected sea-level change, well ahead of scenarios considered by the IPCC. Central in our incomplete understanding is the motion at the glacier bed, responsible for flow transients and instabilities involving switches from slow to fast flow. We introduce a rate-and-state framework for the transient evolution of basal shear stress, which we incorporate in glacier simulations. We demonstrate that a velocity-strengthening-weakening transition combined with a characteristic length scale for the opening of subglacial cavities is sufficient to reproduce several previously unexplained features of glacier surges. The rate-and-state framework opens for new ways to analyze, understand and predict transient glacier dynamics as well as to assess the stability of glaciers and ice caps.

To study how macroscopic friction phenomena originate from microscopic junction laws, we introduce a general statistical framework describing the collective behavior 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. This framework allows for a whole family of micro-junction behavior laws, and we show how it represents an overarching structure for many existing models found in the friction literature. We then use this framework to pinpoint the effects of the time-scale that controls the duration of the slipping state. First, we show that the model reproduces a series of friction phenomena already observed experimentally. The macroscopic steady-state friction force is velocity-dependent, either monotonic (strengthening or weakening) or non-monotonic (weakening-strengthening), depending on the microscopic behavior of individual junctions. In addition, slow slip, which has been reported in a wide variety of systems, spontaneously occurs in the model if the friction contribution from junctions in the slipping state is time-weakening. Next, we show that the model predicts a non-trivial history-dependence of the macroscopic static friction force. In particular, the static friction coefficient at the onset of sliding is shown to increase with increasing deceleration during the final phases of the preceding sliding event. We suggest that this form of history-dependence of static friction should be investigated in experiments, and we provide the acceleration range in which this effect is expected to be experimentally observable.