arXiv subjects

Efim A. Brener

Publications and source records attributed to Efim A. Brener.

At least 19 recordsLinked to original sources

arXiv2024

A steady-state frictional crack in a strip

The analogy between frictional cracks, propagating along interfaces in frictional contact, and ordinary cracks in bulk materials is important in various fields. We consider a stress-controlled frictional crack propagating at a velocity $c_{\rm r}$ along an interface separating two strips, each of height $H$, the frictional counterpart of the classical problem of a displacement-controlled crack in a strip, which played central roles in understanding material failure. We show that steady-state frictional cracks in a strip geometry require a nonmonotonic dependence of the frictional strength on the slip velocity and, in sharp contrast to their classical counterparts, feature a vanishing stress drop. Here, rupture is driven by energy flowing to its edge from behind, generated by an excess power of the external stress, and to be accompanied by an increase in the stored elastic energy, in qualitative contrast to the classical counterpart that is driven by the release of elastic energy stored ahead of the propagating edge. Finally, we derive a complete set of mesoscopic and macroscopic scaling relations for frictional cracks in a strip geometry and demonstrate that the stress singularity near their edges is proportional to $(Δ{v}/c_{\rm r})\sqrt{H}$, where $Δ{v}$ is the slip velocity rise accompanying their propagation.

cond-mat.mtrl-sci↗

arXiv2024

A finite geometry, inertia assisted coarsening-to-complexity transition in homogeneous frictional systems

The emergence of statistical complexity in frictional systems, manifested in broad distributions of various observables, is not yet understood. We study this problem in velocity-driven, homogeneous (no quenched disorder) unstable frictional systems of height $H$. The latter are described at the continuum scale within a realistic rate-and-state friction interfacial constitutive framework, where elasto-frictional instabilities emerge from rate-weakening friction. For large $H$, such frictional systems were recently shown to undergo continuous coarsening until settling into a spatially periodic traveling solution. We show that when the system's height-to-length ratio becomes small, coarsening is less effective and the periodic solution is dynamically avoided. Instead, and consistently with previous reports, the system settles into a stochastic, statistically stationary state. The latter features slip bursts, classified into predominantly non-propagating small bursts and propagating large bursts, which are non-trivially distributed. The statistical distributions emerge from dynamically self-generated heterogeneity, where both the non-equilibrium history of the interface and wave reflections from finite boundaries, mediated by material inertia, play central roles. Specifically, the dynamics and statistics of large bursts reveal a timescale $\sim\!H/c_{\rm s}$, where $c_{\rm s}$ is the shear wave-speed. We discuss the robustness of our findings against variations of the frictional parameters, most notably affecting the magnitude of frictional rate-weakening, as well as against different interfacial state evolution laws. Finally, we demonstrate a reverse transition in which statistical complexity disappears in favor of the spatially periodic traveling solution. Overall, our results elucidate how relatively simple physical ingredients can give rise to the emergence of slip complexity.

cond-mat.mtrl-sci↗

arXiv2023

The dynamics of unsteady frictional slip pulses

Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size $L(t)$ and a propagation velocity $c_{\rm p}(t)$ ($t$ is time). Here, we develop a theory of slip pulses in realistic rate-and-state dependent frictional systems. We show that slip pulses are intrinsically unsteady objects -- in agreement with previous findings -- yet their dynamical evolution is closely related to their unstable steady-state counterparts. In particular, we show that each point along the time-independent $L^{\mbox{(0)}}(τ_{\rm d})\!-\!c^{\mbox{(0)}}_{\rm p}(τ_{\rm d})$ line, obtained from a family of steady-state pulse solutions parameterized by the driving shear stress $τ_{\rm d}$, is unstable. Nevertheless, and remarkably, the $c^{\mbox{(0)}}_{\rm p}[L^{\mbox{(0)}}]$ line is a dynamic attractor such that the unsteady dynamics of slip pulses (when they exist) -- whether growing ($\dot{L}(t)\!>\!0$) or decaying ($\dot{L}(t)\!<\!0$) -- reside on the steady-state line. The unsteady dynamics along the line are controlled by a single slow unstable mode. The slow dynamics of growing pulses, manifested by $\dot{L}(t)/c_{\rm p}(t)\!\ll\!1$, explain the existence of sustained pulses, i.e.~pulses that propagate many times their characteristic size without appreciably changing their properties. Our theoretical picture of unsteady frictional slip pulses is quantitatively supported by large-scale, dynamic boundary-integral method simulations.

cond-mat.mtrl-sci↗

arXiv2022

Self-healing (solitonic) slip pulses in frictional systems

A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse solutions along generic and realistic rate-and-state dependent frictional interfaces, separating large deformable bodies in contact. Such nonlinear interfaces feature a non-monotonic frictional strength as a function of the slip velocity, with a local minimum. The solutions exhibit a diverging length and strongly inertial propagation velocities, when the driving stress approaches the frictional strength characterizing the local minimum from above, and change their character when it is away from it. An approximate scaling theory quantitatively explains these observations. The derived pulse solutions also exhibit significant spatially-extended dissipation in excess of the edge-localized dissipation (the effective fracture energy) and an unconventional edge singularity. The relevance of our findings for available observations is discussed.

cond-mat.mtrl-sci↗

arXiv2021

Velocity-driven frictional sliding: Coarsening and steady-state pulse trains

Frictional sliding is an intrinsically complex phenomenon, emerging from the interplay between driving forces, elasto-frictional instabilities, interfacial nonlinearity and dissipation, material inertia and bulk geometry. We show that homogeneous rate-and-state dependent frictional systems, driven at a prescribed boundary velocity -- as opposed to a prescribed stress -- in a range where the frictional interface is rate-weakening, generically host self-healing slip pulses, a sliding mode not yet fully understood. Such velocity-driven frictional systems are then shown to exhibit coarsening dynamics saturated at the system length in the sliding direction, independently of the system's height, leading to steadily propagating pulse trains. The latter may be viewed as a propagating phase-separated state, where slip and stick characterize the two phases. While pulse trains' periodicity is coarsening-limited by the system's length, the single pulse width, characteristic slip velocity and propagation speed exhibit rich properties, which are comprehensively understood using theory and extensive numerics. Finally, we show that for sufficiently small system heights, pulse trains are accompanied by periodic elasto-frictional instabilities.

cond-mat.soft↗

arXiv2021

Theory of unconventional singularities of frictional shear cracks

Crack-like objects that propagate along frictional interfaces, i.e.~frictional shear cracks, play a major role in a broad range of frictional phenomena. Such frictional cracks are commonly assumed to feature the universal square root near-edge singularity of ideal shear cracks, as predicted by Linear Elastic Fracture Mechanics. Here we show that this is not the generic case due to the intrinsic dependence of the frictional strength on the slip rate, even if the bodies forming the frictional interface are identical and predominantly linear elastic. Instead, frictional shear cracks feature unconventional singularities characterized by a singularity order $ξ$ that differs from the conventional $-\tfrac{1}{2}$ one. It is shown that $ξ$ depends on the friction law, on the propagation speed and on the symmetry mode of loading. We discuss the general structure of a theory of unconventional singularities, along with their implications for the energy balance and dynamics of frictional cracks. Finally, we present explicit calculations of $ξ$ and the associated near-edge fields for linear viscous-friction -- which may emerge as a perturbative approximation of nonlinear friction laws or on its own -- for both in-plane (mode-II) and anti-plane (mode-III) shear loadings.

cond-mat.soft↗

arXiv2021

Unconventional singularities, scale separation and energy balance in frictional rupture

A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conventional square root singularity remains approximately valid. Here we develop a macroscopic theory that shows that the generic rate-dependent nature of friction leads to deviations from the conventional singularity, and that even if this deviation is small, significant non-edge-localized rupture-related dissipation emerges. The physical origin of the latter, which is predicted to vanish identically in the crack analogy, is the breakdown of scale separation that leads an accumulated spatially-extended dissipation, involving macroscopic scales. The non-edge-localized rupture-related dissipation is also predicted to be position dependent. The theoretical predictions are quantitatively supported by available numerical results, and their possible implications for earthquake physics are discussed.

cond-mat.soft↗

arXiv2019

The emergence of crack-like behavior of frictional rupture: Edge singularity and energy balance

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. An important 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.

cond-mat.soft↗

arXiv2019

The emergence of crack-like behavior of frictional rupture: The origin of stress drops

The process of frictional rupture, i.e. the failure of frictional systems, abounds in the technological and natural world around us, ranging from squealing car brake pads to earthquakes along geological faults. A general framework for understanding and interpreting frictional rupture commonly involves an analogy to ordinary crack propagation, with far-reaching implications for various disciplines, from engineering tribology to geophysics. An important feature of the analogy to cracks is the existence of a reduction in the stress-bearing capacity of the ruptured interface, i.e. of a drop from the applied stress, realized far ahead of a propagating rupture, to the residual stress left behind it. Yet, how and under what conditions such finite and well-defined stress drops emerge from basic physics are not well understood. Here we show that for rapid rupture a stress drop is directly related to wave radiation from the frictional interface to the bodies surrounding it and to long-range bulk elastodynamics, and not exclusively to the physics of the contact interface. Furthermore, we show that the emergence of a stress drop is a transient effect, affected by the wave travel time in finite systems and by the decay of long-range elastic interactions. Finally, we supplement our results for rapid rupture with predictions for slow rupture. All of the theoretical predictions are supported by available experimental data and by extensive computations. Our findings elucidate the origin of stress drops in frictional rupture, i.e. they offer a comprehensive and fundamental understanding of why, how and to what extent frictional rupture might be viewed as an ordinary fracture process.

cond-mat.soft↗

arXiv2019

Spatiotemporal dynamics of frictional systems: The interplay of interfacial friction and bulk elasticity

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.

cond-mat.soft↗

arXiv2018

Unstable slip pulses and earthquake nucleation as a non-equilibrium first-order phase transition

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 $L_G\!<\!L^*$ gives rise to a richer phase-diagram that features also sustained slip pulses.

physics.geo-ph↗

arXiv2017

Critical nucleation length for accelerating frictional slip

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 $L_c$. The critical nucleation length $L_c$ 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 $L_c$ that features the same scaling structure, but with substantially different numerical pre-factors, resulting in a significantly larger $L_c$ 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 $L_c$ 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.

cond-mat.mtrl-sci↗

arXiv2017

Non-monotonicity of the frictional bimaterial effect

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 non-monotonic 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 non-monotonic function of the bimaterial contrast, and provide analytic insight into the origin of this non-monotonicity. 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 non-monotonic 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 non-monotonicity persists in non-steady, transient frictional dynamics.

cond-mat.mtrl-sci↗

arXiv2016

Frictional sliding without geometrical reflection symmetry

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.

cond-mat.mtrl-sci↗

arXiv2015

Dynamic instabilities of frictional sliding at a bimaterial interface

We study the 2D linear stability analysis of a deformable solid of a finite height $H$, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e.~an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number $k$ limit and demonstrate that homogeneous sliding in this case is universally unstable, independently of the details of the friction law. This universal instability is mediated by propagating waveguide-like modes, whose fastest growing mode is characterized by a wave-number satisfying $k H\!\sim\!{\cal O}(1)$ and by a growth rate that scales with $H^{-1}$. We then consider the limit $k H\!\to\!\infty$ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability.

cond-mat.mtrl-sci↗

arXiv2014

Elimination of surface diffusion in the non-diagonal phase field model

We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of the artificial surface diffusion effect. The model is non-diagonal since it incorporates the kinetic cross coupling between the non-conserved and the conserved fields that was recently introduced [{Phys. Rev. E {\bf 86}, 060601(R), (2012)}]. We test numerically this model for the two-dimensional relaxation of a weakly perturbed interface toward its flat equilibrium.

cond-mat.mtrl-sci↗

arXiv2014

Velocity-strengthening friction significantly affects interfacial dynamics, strength and dissipation

Frictional interfaces are abundant in natural and manmade systems and their dynamics still pose challenges of fundamental and technological importance. A recent extensive compilation of multiple-source experimental data has revealed that velocity-strengthening friction, where the steady-state frictional resistance increases with sliding velocity over some range, is a generic feature of such interfaces. Moreover, velocity-strengthening friction has very recently been linked to slow laboratory earthquakes and stick-slip motion. Here we elucidate the importance of velocity-strengthening friction by theoretically studying three variants of a realistic rate-and-state friction model. All variants feature identical logarithmic velocity-weakening friction at small sliding velocities, but differ in their higher velocity behaviors. By quantifying energy partition (e.g. radiation and dissipation), the selection of interfacial rupture fronts and rupture arrest, we show that the presence or absence of velocity-strengthening friction can significantly affect the global interfacial resistance and the total energy released during frictional instabilities ("event magnitude"). Furthermore, we show that different forms of velocity-strengthening friction (e.g. logarithmic vs. linear) may result in events of similar magnitude, yet with dramatically different dissipation and radiation rates. This happens because the events are mediated by interfacial rupture fronts with vastly different propagation velocities, where stronger velocity-strengthening friction promotes slower rupture. These theoretical results may have significant implications on our understanding of frictional dynamics.

cond-mat.mtrl-sci↗

arXiv2014

On the velocity-strengthening behavior of dry friction

The onset of frictional instabilities, e.g. earthquakes nucleation, is intimately related to velocity-weakening friction, in which the frictional resistance of interfaces decreases with increasing slip velocity. While this frictional response has been studied extensively, less attention has been given to steady-state velocity-strengthening friction, in spite of its potential importance for various aspects of frictional phenomena such as the propagation speed of interfacial rupture fronts and the amount of stored energy released by them. In this note we suggest that a crossover from steady-state velocity-weakening friction at small slip velocities to steady-state velocity-strengthening friction at higher velocities might be a generic feature of dry friction. We further argue that while thermally activated rheology naturally gives rise to logarithmic steady-state velocity-strengthening friction, a crossover to stronger-than-logarithmic strengthening might take place at higher slip velocities, possibly accompanied by a change in the dominant dissipation mechanism. We sketch a few physical mechanisms that may account for the crossover to stronger-than-logarithmic steady-state velocity-strengthening and compile a rather extensive set of experimental data available in the literature, lending support to these ideas.

physics.geo-ph↗