Frictional motion is mediated by rapidly propagating ruptures that detach the ensemble of contacts forming the frictional interface between contacting bodies1-7. These ruptures are similar to shear cracks. When this process takes place in natural faults, these rapid ruptures are essentially earthquakes8,9. Although fracture mechanics describe the rapid motion of these singular objects, the nucleation process that creates them is not understood10-19. Here we fully describe the nucleation process by extending fracture mechanics to explicitly incorporate finite interface widths (which are generally ignored20,21). We show, experimentally and theoretically, that slow steady creep ensues at a well-defined stress threshold. Moreover, as slowly creeping patches approach the interface width, a topological transition takes place in which these creeping patches smoothly transition to the rapid fracture that is described by classical fracture mechanics22-26. Apart from its relevance to fracture and material strength, this new picture of rupture nucleation dynamics is directly relevant to earthquake nucleation dynamics; slow, aseismic rupture must always precede rapid seismic rupture (so long as the initial defect in the interface is localized in both spatial dimensions). The theory may provide a new framework for understanding how and when earthquakes nucleate.

Dynamic mode I crack growth in a sheet with an edge pre-crack subject to remote impact tensile loading is investigated experimentally and computationally. Separation is constrained to occur along a weak interface directly ahead of the pre-crack tip. The experiments are carried out on a PDMS sheet composed of two sheets glued together to make the weak surface in front of the pre-crack. The thickness and composition of the glue are varied to provide different cohesive properties. In the calculations, the sheet material is represented by an isotropic hyperelastic constitutive relation and the weak interface is represented by a zero thickness cohesive surface with the cohesive traction related to the displacement jump across the interface. The calculations are in qualitative agreement with the experiments for the propagation speed, the shape of the opening along the interface and general features of the deformation distribution in the material. Both the experiments and the calculations indicate that a characteristic length scale, associated with the cohesive response of the interface plays a key role in affecting the propagation speed and the mode of separation. When the cohesive length scale is sufficiently small, propagation is crack-like and the propagation speed does not exceed the Rayleigh wave speed. An increased value of the cohesive length scale leads to a propagation speed that exceeds the shear wave speed. Transition to a spall-like separation mode occurs when the opening traction on the remaining ligament reaches the cohesive strength of the interface. A cohesive interface with a larger value of the work of separation can have a faster separation speed than one having the same cohesive strength but a smaller value of the work of separation. For calculations with loading imposed on the faces of the pre-crack, so that propagation occurs into unstressed material, the propagation speed does not exceed the Rayleigh wave speed even for a very weak interface.

How do earthquakes begin and what information about this process is contained in a far field seismogram? We present a quantitative analysis of laboratory earthquakes incorporating both laboratory-scale seismic measurements coupled with high-speed imaging of the controlled dynamic ruptures that generated them. We generated variations in the rupture properties by imposing sequences of controlled artificial barriers along the laboratory fault. We first demonstrate that direct measurements of imaged slip events correspond to established seismic analysis of acoustic signals; the seismograms correctly record the rupture moments and maximum moment rates. We then investigate the ruptures’ early growth by comparing their measured seismogram velocities to their final size. Due to higher initial elastic energies imposed prior to nucleation, larger events accelerate more rapidly at the rupture onset. We find that the corresponding seismogram velocities are therefore predictive of the final rupture size. This observation holds in the presence of barriers with one notable exception. Rupture events that overtake a previously arrested rupture are less magnitude predictable, likely because of the stress heterogeneity (and resulting stored elastic energy) induced by the earlier event. For all other events, the higher elastic energy at nucleation results in faster and larger ruptures, and hence the initial seismogram velocity and ultimate size correlate well. This degree of magnitude predictability is consistent with some, but not all recent natural observations. For early warning purposes, we suggest that confining the observational database to the conditions most conducive to magnitude predictability may provide stronger correlations.

Material failure is mediated by the propagation of cracks which, in realistic 3D materials, typically involves multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures, such as step defects on tensile fracture surfaces. Steps form once a slowly moving, distorted crack front segments into disconnected overlapping fracture planes separated by a stabilizing distance hmax. Our experiments on numerous brittle hydrogels reveal that hmax varies linearly with both a nonlinear elastic length and a dissipation length. Here, is the measured crack velocity dependent fracture energy, and is the shear modulus.

Frictional slip between bodies having different elastic or geometrical properties (bimaterial interfaces) creates a unique type of rupture, bimaterial "slip pulses." These slip pulses propagate along the interfaces separating elastically different contacting bodies. They exhibit highly localized slip with accompanying local normal stress reduction. These pulses do not result from properties of "friction laws" but, instead, are formed via the elastic mismatch of the contacting bodies. Here, we experimentally study slip pulse dynamics, evolution, and structure in seven different bimaterial interfaces. We find that slip pulses are a major vehicle for frictional motion in bimaterial interfaces, they exist in well-defined velocity windows and undergo unstable growth consistent with theoretical predictions coined the "Adams instability." When scaled properly, slip pulses exhibit both universal spatial structure and growth dynamics. While slip pulse amplitudes vary considerably within different interfaces, this variation is, surprisingly, not highly dependent on the contrast of the elastic properties of the contacting materials. Instead, slip pulse amplitudes are closely related to the interfaces' aging properties and, hence, to material plasticity at the interface. As bimaterial interfaces are generic, these results are fundamentally important to both frictional dynamics and the dynamics of earthquakes within a wide class of natural faults.

Slow cracks may be simple, with no internal structure. The leading edge of a simple crack, the crack front, forms a single fracture plane in its wake. Slow cracks may also develop segmented crack fronts, each segment propagating along a separate fracture plane. These planes merge at locations that form steps along fracture surfaces. Steps are not stationary, but instead propagate within a crack front. Real-time measurements of crack front structure and energy flux reveal that step dynamics significantly increase energy dissipation and drastically alter crack dynamics. Simple and stepped cracks are each stable. By extending the use of energy balance to include 3D crack front structure, we find that, while energy balance is obeyed, it is insufficient to select the energetically favorable crack growth mode. Transitions from stepped cracks to simple cracks occur only when their in-plane front lengths become equal and a perturbation momentarily changes step topology. Such 3D crack dynamics challenge our traditional understanding of fracture.

A large earthquake unlocks a fault-zone via dynamic rupture while releasing part of the elastic energy stored during the interseismic stage. As earthquakes occur at depth, the analyses of earthquake physics rely primarily on experimental observations and conceptual models. A common view is that the earthquake instability is necessarily related to the frictional weakening that is commonly observed in shear experiments under seismic slip velocities. However, recent experiments with frictional interfaces in brittle acrylics (e.g., Svetlizky & Fineberg, 2014, https://doi.org/10.1038/nature13202) and rocks (e.g., Passelegue et al., 2020, https://doi.org/10.1038/s41467-020-18937-0) have explicitly demonstrated that no characteristic frictional strength exists. Namely, prior to nucleation, frictional interfaces can sustain a wide range of applied stresses (“overstresses”) that exceed the residual stresses, which are the stresses along the interface that remain after the sliding. Moreover, the experimentally observed singular stress-fields and rupture dynamics are precisely those predicted by fracture mechanics (Freund, 1998). We therefore argue here that earthquake dynamics are best understood in terms of dynamic fracture mechanics and not governed by the frictional properties of faults. In this view, rupture dynamics are driven by the release of the elastic energy due to overstresses, whereas the values of the residual stresses and the energy dissipation are determined by fault frictional properties.

Earthquake-like ruptures break the contacts that form the frictional interface separating contacting bodies and mediate the onset of frictional motion (stick-slip). The slip (motion) of the interface immediately resulting from the rupture that initiates each stick-slip event is generally much smaller than the total slip logged over the duration of the event. Slip after the onset of friction is generally attributed to continuous motion globally attributed to ‘dynamic friction’. Here we show, by means of direct measurements of real contact area and slip at the frictional interface, that sequences of myriad hitherto invisible, secondary ruptures are triggered immediately in the wake of each initial rupture. Each secondary rupture generates incremental slip that, when not resolved, may appear as steady sliding of the interface. Each slip increment is linked, via fracture mechanics, to corresponding variations of contact area and local strain. Only by accounting for the contributions of these secondary ruptures can the accumulated interface slip be described. These results have important ramifications both to our fundamental understanding of frictional motion as well as to the essential role of aftershocks within natural faults in generating earthquake-mediated slip.

Frictional interfaces lose stability via earthquake-like ruptures, which are close analogues of shear cracks that are well-described by fracture mechanics. Interface ruptures, however, need to be first formed—or nucleated. Rupture nucleation therefore determines the onset of friction, replacing the concept of a characteristic “static friction coefficient”. Utilizing rupture arrest at an imposed barrier, we experimentally determine nucleation locations, times and stresses at the origin of each subsequent rupture event. This enables us study the nucleation process via real-time measurements of real contact area and local strain. Nucleation events initiate as 2D patches that expand at nearly constant velocities, vnuc, that are orders of magnitude lower than the dynamic rupture velocities described by conventional fracture mechanics. We find that: (a) Nucleation has location-dependent stress thresholds, (b) vnuc is roughly proportional to the local stress level, (c) the nucleation process continues until the patch size reaches Ltran ∼ LG, the Griffith length for the onset of dynamic fracture (d) scaling time by τ = Ltran/vnuc, nucleation patches exhibit self-similar dynamics (e) dynamic ruptures' cohesive zones are not fully established until significantly beyond Ltran. Many details of nucleation are governed by the local contact area topography, which is roughly invariant under successive rupture events in mature interfaces. Topography-dependent details of the nucleation process include: precise nucleation site location, patch geometry, critical stress thresholds and the proportionality constant of vnuc with stress. We believe that these results shed considerable light on both how frictional motion is triggered and earthquake initiation.

Brittle materials fail by means of rapid cracks. Classical fracture mechanics describes the motion of tensile cracks that dissipate released elastic energy within a point-like zone at their tips. Within this framework, a "classical"tensile crack cannot exceed the Rayleigh wave speed, cR. Using brittle neohookean materials, we experimentally demonstrate the existence of "supershear"tensile cracks that exceed shear wave speeds, cR. Supershear cracks smoothly accelerate beyond cR, to speeds that could approach dilatation wave speeds. Supershear dynamics are governed by different principles than those guiding "classical"cracks; this fracture mode is excited at critical (material dependent) applied strains. This nonclassical mode of tensile fracture represents a fundamental shift in our understanding of the fracture process.

Griffith's energetic criterion, or ‘energy balance’, has for a century formed the basis for fracture mechanics; the energy flowing into a crack front is precisely balanced by the dissipation (fracture energy) at the front. If the crack front structure is not properly accounted for, energy balance will either appear to fail or lead to unrealistic results. Here, we study the influence of the secondary structure of low-speed crack propagation in hydrogels under tensile loading conditions. We first show that these cracks are bistable; either simple (cracks having no secondary structure) or faceted crack states (formed by steps propagating along crack fronts) can be generated under identical loading conditions. The selection of either crack state is determined by the form of the initial ‘seed’ crack; perfect seed cracks generate simple cracks while a small local mode III component generates crack fronts having multiple steps. Step coarsening eventually leads to single steps that propagate along crack fronts. As they evolve, steps locally change the instantaneous structure and motion of the crack front, breaking transverse translational invariance. In contrast to simple cracks, faceted cracks can, therefore, no longer be considered as existing in a quasi-2D system. For both simple and faceted cracks we simultaneously measure the energy flux and local dissipation along these crack fronts over velocities, v, spanning 0R (cR is the Rayleigh wave speed). We find that, in the presence of secondary structure within the crack front, the implementation of energy balance must be generalized for 3D systems; faceted cracks reveal energy balance, only when we account for the local dynamic dissipation at each point along the crack front.

Rapid rupture fronts—akin to earthquakes—mediate the transition to frictional motion. Once formed, their singular form, dynamics and arrest are well described by fracture mechanics. Ruptures, however, first need to be created within initially rough frictional interfaces. Hence, static friction coefficients are not well defined, with frictional ruptures nucleating over a wide range of applied forces. A critical open question is, therefore, how the nucleation of rupture fronts actually takes place. Here we experimentally show that rupture fronts are preceded by slow nucleation fronts—self-similar entities not described by fracture mechanics. They emerge from initially rough frictional interfaces at a well-defined stress threshold, evolve at the characteristic velocity and timescales governed by stress levels, and propagate within a frictional interface to form the initial rupture from which fracture mechanics take over. These results are of fundamental importance to questions ranging from earthquake nucleation and prediction to processes governing material failure.

The rupture of the interface joining two materials under frictional contact controls their macroscopic sliding. Interface rupture dynamics depend markedly on the mechanical properties of the bulk materials that bound the frictional interface. When the materials are similar, recent experimental and theoretical work has shown that shear cracks described by Linear Elastic Fracture Mechanics (LEFM) quantitatively describe the rupture of frictional interfaces. When the elastic properties of the two materials are dissimilar, many new effects take place that result from bimaterial coupling: the normal stress at the interface is elastodynamically coupled to local slip rates. At low rupture velocities, bimaterial coupling is not very significant and interface rupture is governed by ‘bimaterial cracks’ that are described well by LEFM. As rupture velocities increase, we experimentally and theoretically show how bimaterial cracks become unstable at a subsonic critical rupture velocity, cT. When the rupture direction opposes the direction of applied shear in the softer material, we show that cT is the subsonic limiting velocity. When ruptures propagate in the direction of applied shear in the softer material, we demonstrate that cT provides an explanation for how and when slip pulses (new rupture modes characterized by spatially localized slip) are generated.

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction.

The cohesive zone is the elusive region in which material fracture takes place. Here, the putatively singular stresses at a crack's tip are regularized. We present experiments, performed on PMMA, in which we visualize the cohesive zone of frictional ruptures as they propagate. Identical to shear cracks, these ruptures range from slow velocities to nearly the limiting speeds of cracks. We reveal that the cohesive zone is a dynamic quantity; its spatial form undergoes a sharp transition between distinct phases at a critical velocity. The structure of these phases provides an important window into material properties under the extreme conditions that occur during fracture.

While we fundamentally understand the dynamics of simple cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly perturbed cracks that propagate between 10% and 95% of their limiting velocity within a brittle material. These cracks are deflected by either interaction with sparsely implanted defects or via an intrinsic oscillatory instability in defect-free media. Dense high-speed measurements of the strain fields surrounding the crack tips reveal that crack paths are governed by the direction of maximal strain energy density, even when the near-tip singular fields are highly disrupted. This fundamentally important result may be utilized to either direct or guide running cracks.

Frictional motion between contacting bodies is governed by propagating rupture fronts that are essentially earthquakes. These fronts break the contacts composing the interface separating the bodies to enable their relative motion. The most general type of frictional motion takes place when the two bodies are not identical. Within these so-called bimaterial interfaces, the onset of frictional motion is often mediated by highly localized rupture fronts, called slip pulses. Here, we show how this unique rupture mode develops, evolves, and changes the character of the interface's behavior. Bimaterial slip pulses initiate as "subshear" cracks (slower than shear waves) that transition to developed slip pulses where normal stresses almost vanish at their leading edge. The observed slip pulses propagate solely within a narrow range of "transonic" velocities, bounded between the shear wave velocity of the softer material and a limiting velocity. We derive analytic solutions for both subshear cracks and the leading edge of slip pulses. These solutions both provide an excellent description of our experimental measurements and quantitatively explain slip pulses' limiting velocities. We furthermore find that frictional coupling between local normal stress variations and frictional resistance actually promotes the interface separation that is critical for slip-pulse localization. These results provide a full picture of slippulse formation and structure that is important for our fundamental understanding of both earthquake motion and the most general types of frictional processes.

This paper is a faithful description of the author’s career as a scientist, which often intersected that of Yves Couder. The emphasis of this paper is a true description of how the science that the author has been associated with really came about. Included are brief descriptions of the science associated with the research paths described. It is hoped that this rather accurate account may be amusing for the senior scientists among us and educational (and possibly useful) for younger scientists.

We experimentally and analytically explore supershear ruptures that are excited at the onset of frictional motion within “bimaterial interfaces,” frictional interfaces formed by contacting bodies having different elastic (or geometric) properties. Our experiments on PMMA blocks sliding on polycarbonate show that the structure, transition sequence, and range of existence of such supershear ruptures are highly dependent on their propagation direction relative to the slip direction in the softer of the two materials. These properties are characterized for both the positive (parallel) and negative (antiparallel) propagation directions. An analytic, fracture-mechanics based description of supershear ruptures is derived. The theory quantitatively predicts both supershear structure and the allowed propagation range of supershear ruptures. The latter compares well with both the experimentally observed supershear ruptures in the negative direction as well as localized slip pulses in the positive direction, whose propagation speed lies between the shear velocities of both materials. Supershear ruptures in the positive direction, which are composed of trains of propagating slip pulses, evade this theoretical description.

Contacting bodies subjected to sufficiently large applied shear will undergo frictional sliding. The onset of this motion is mediated by dynamically propagating fronts, akin to earthquakes, that rupture the discrete contacts that form the interface separating the bodies. Macroscopic motion commences only after these ruptures have traversed the entire interface. Comparison of measured rupture dynamics with the detailed predictions of fracture mechanics reveals that the propagation dynamics, dissipative properties, radiation, and arrest of these “laboratory earthquakes” are in excellent quantitative agreement with the predictions of the theory of brittle fracture. Thus, interface fracture replaces the idea of a characteristic static friction coefficient as a description of the onset of friction. This fracture-based description of friction additionally provides a fundamental description of earthquake dynamics and arrest.