The failure of frictional interfaces -the process of frictional rupture -is widely assumed to feature crack-like properties, with far-reaching implications for various disciplines, ranging from engineering tribology to earthquake physics. A necessary condition for the emergence of a crack-like behavior is the existence of stress drops in frictional rupture, whose basic physical origin has been recently elucidated. Here we show that for generic and realistic frictional constitutive relations, and once the necessary conditions for the emergence of an effective crack-like behavior are met, frictional rupture dynamics are approximately described by a crack-like, fracture mechanics energy balance equation. This is achieved by independently calculating the intensity of the crack-like singularity along with its associated elastic energy flux into the rupture edge region, and the frictional dissipation in the edge region. We further show that while the fracture mechanics energy balance equation provides an approximate, yet quantitative, description of frictional rupture dynamics, interesting deviations from the ordinary crack-like framework -associated with non-edge-localized dissipation -exist. Together with the recent results about the emergence of stress drops in frictional rupture, this work offers a comprehensive and basic understanding of why, how and to what extent frictional rupture might be viewed as an ordinary fracture process. Various implications are discussed.

The onset of rapid slip along initially quiescent frictional interfaces, the process of "earthquake nucleation", and dissipative spatiotemporal slippage dynamics play important roles in a broad range of physical systems. Here we first show that interfaces described by generic friction laws feature stress-dependent steady-state slip pulse solutions, which are unstable in the quasi-1D approximation of thin elastic bodies. We propose that such unstable slip pulses of linear size L * and characteristic amplitude are "critical nuclei" for rapid slip in a non-equilibrium analogy to equilibrium first-order phase transitions, and quantitatively support this idea by dynamical calculations. We then perform 2D numerical calculations that indicate that the nucleation length L * exists also in 2D, and that the existence of a fracture mechanics Griffith-like length LG < L * gives rise to a richer phase-diagram that features also sustained slip pulses. arXiv:1807.06890v2 [physics.geo-ph]

The failure of frictional interfaces -the process of frictional rupture -is widely assumed to feature crack-like properties, with far-reaching implications for various disciplines, ranging from engineering tribology to earthquake physics. Yet, how the effective crack-like behavior emerges from basic physics and what its range of validity is are not understood. Here we show that for rapid rupture a finite and well-defined stress drop, which is a necessary condition for the existence of a crack-like behavior, is directly related to wave radiation from the frictional interface to the bulks surrounding it (the so-called radiation damping effect) and to long-range bulk elastodynamics, and not exclusively to interfacial physics. Furthermore, we show that the emergence of a stress drop is a finite time effect, mainly limited by the wave travel time in finite systems. The results for rapid rupture are supplemented by predictions for slow rupture. All of the theoretical predictions are supported by available experimental data and by extensive computations. They offer a comprehensive and basic understanding of why, how and to what extent frictional rupture might be viewed as an ordinary fracture process. I. BACKGROUND AND MOTIVATIONRapid slip along interfaces separating bodies in frictional contact is mediated by the spatiotemporal dynamics of frictional rupture [1,2]. Frictional rupture is a fundamental process of prime importance for a broad range of physical systems, e.g. it is responsible for squealing in car brake pads [3], for bowing on a violin string [4], and for earthquakes along geological faults [5][6][7], to name just a few well-known examples. The essence of frictional rupture propagation is that a state of relatively high slip rate (the rate of interfacial shear displacement discontinuity) behind the rupture edge propagates into a low/vanishing slip rate state ahead of it, cf. Fig. 1. As such, frictional rupture appears to be essentially similar to ordinary tensile (opening) cracks, where a finite tensile displacement discontinuity (broken material) state behind the crack edge propagates into a zero tensile displacement discontinuity (intact material) state ahead of it [8].There is, however, an important fundamental difference between frictional rupture and ordinary tensile cracks that manifests itself in the stress states associated with these two processes. A tensile crack is composed of surfaces that cannot support stress, so the stress behind its edge vanishes. Consequently, tensile crack propagation is a process in which far-field driving stresses that characterize the material state far ahead of the crack edge are eliminated altogether behind it. The stress drop that accompanies tensile crack propagation has dramatic implications. Most notably, the loss of stress bearing capac- * eran.bouchbinder@weizmann.ac.il † jean-francois.molinari@epfl.ch ity along the crack surfaces is compensated by large concentration of deformation and stress near the crack edge, oftentimes in a way that mimics a mathematical s...

The spontaneous nucleation of accelerating slip along slowly driven frictional interfaces is central to a broad range of geophysical, physical, and engineering systems, with particularly far‐reaching implications for earthquake physics. A common approach to this problem associates nucleation with an instability of an expanding creep patch upon surpassing a critical length Lc. The critical nucleation length Lc is conventionally obtained from a spring‐block linear stability analysis extended to interfaces separating elastically deformable bodies using model‐dependent fracture mechanics estimates. We propose an alternative approach in which the critical nucleation length is obtained from a related linear stability analysis of homogeneous sliding along interfaces separating elastically deformable bodies. For elastically identical half‐spaces and rate‐and‐state friction, the two approaches are shown to yield Lc that features the same scaling structure, but with substantially different numerical prefactors, resulting in a significantly larger Lc in our approach. The proposed approach is also shown to be naturally applicable to finite‐size systems and bimaterial interfaces, for which various analytic results are derived. To quantitatively test the proposed approach, we performed inertial Finite‐Element‐Method calculations for a finite‐size two‐dimensional elastically deformable body in rate‐and‐state frictional contact with a rigid body under sideway loading. We show that the theoretically predicted Lc and its finite‐size dependence are in reasonably good quantitative agreement with the full numerical solutions, lending support to the proposed approach. These results offer a theoretical framework for predicting rapid slip nucleation along frictional interfaces.

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems. arXiv:1605.05378v2 [cond-mat.mtrl-sci]

Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation -the macroscopic friction law -and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of the macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the system's geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially-extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g. rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially-extended frictional systems. * eran.bouchbinder@weizmann.ac.il arXiv:1908.02820v1 [cond-mat.soft]

Sliding along frictional interfaces separating dissimilar elastic materials is qualitatively different from sliding along interfaces separating identical materials due to the existence of an elastodynamic coupling between interfacial slip and normal stress perturbations in the former case. This bimaterial coupling has important implications for the dynamics of frictional interfaces, including their stability and rupture propagation along them. We show that while this bimaterial coupling is a monotonically increasing function of the bimaterial contrast, when it is coupled to interfacial shear stress perturbations through a friction law, various physical quantities exhibit a nonmonotonic dependence on the bimaterial contrast. In particular, we show that for a regularized Coulomb friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is a nonmonotonic function of the bimaterial contrast and provides analytic insight into the origin of this nonmonotonicity. We further show that for velocity‐strengthening rate‐and‐state friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is also a nonmonotonic function of the bimaterial contrast. Results from simulations of dynamic rupture along a bimaterial interface with slip‐weakening friction provide evidence that the theoretically predicted nonmonotonicity persists in nonsteady, transient frictional dynamics.

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