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Eran Bouchbinder

Publications and source records attributed to Eran Bouchbinder.

At least 55 records · Page 3Linked to original sources
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↗
arXiv2021

Brittle to ductile transitions in glasses: Roles of soft defects and loading geometry

Understanding the fracture toughness of glasses is of prime importance for science and technology. We study it here using extensive atomistic simulations in which the interaction potential, glass transition cooling rate and loading geometry are systematically varied, mimicking a broad range of experimentally accessible properties. Glasses' nonequilibrium mechanical disorder is quantified through $A_{\rm g}$, the dimensionless prefactor of the universal spectrum of nonphononic excitations, which measures the abundance of soft glassy defects that affect plastic deformability. We show that while a brittle-to-ductile transition might be induced by reducing the cooling rate, leading to a reduction in $A_{\rm g}$, iso-$\!A_{\rm g}$ glasses are either brittle or ductile depending on the degree of Poisson contraction under unconstrained uniaxial tension. Eliminating Poisson contraction using constrained tension reveals that iso-$\!A_{\rm g}$ glasses feature similar toughness, and that varying $A_{\rm g}$ under these conditions results in significant toughness variation. Our results highlight the roles played by both soft defects and loading geometry (which affects the activation of defects) in the toughness of glasses.

cond-mat.soft↗
arXiv2021

Oscillatory and tip-splitting instabilities in 2D dynamic fracture: The roles of intrinsic material length and time scales

Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales -- a nonlinear elastic length scale $\ell$ and a dissipation length scale $ξ$ -- that do not exist in the classical theory of cracks. In particular, it has been shown that at a high propagation velocity $v$, cracks in 2D brittle materials undergo an oscillatory instability whose wavelength varies linearly with $\ell$, and at yet higher propagation velocities and larger loading levels, a tip-splitting instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the oscillatory instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit $\ell\!\to\!0$, with a wavelength determined by the dissipation length scale $ξ$. This result shows that the instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the fracture energy $Γ(v)$ that is controlled by a dissipation time scale. These results substantiate the universal nature of the oscillatory instability of ultra-high speed cracks in 2D. In addition, we provide evidence indicating that the ultra-high velocity tip-splitting instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach.

cond-mat.mtrl-sci↗
arXiv2021

Elastic moduli fluctuations predict wave attenuation rates in glasses

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate $Γ(ω)$ in the low-frequency limit ($ω\!\to\!0$), and on its dependence on glass history and properties. A theoretical framework -- termed Fluctuating Elasticity Theory (FET) -- predicts low-frequency Rayleigh scattering scaling in $d$ spatial dimensions, $Γ(ω)\!\sim\!γ\,ω^{d+1}$, where $γ\!=\!γ(V_{\rm c})$ quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume $V_{\rm c}$ that remains debated. Here, using extensive computer simulations, we show that $Γ(ω)\!\sim\!γ\,ω^3$ is asymptotically satisfied in two dimensions ($d\!=\!2$) once $γ$ is interpreted in terms of ensemble -- rather than spatial -- averages, where $V_{\rm c}$ is replaced by the system size. In so doing, we also establish that the finite-size ensemble-statistics of elastic moduli is anomalous and related to the universal $ω^4$ density of states of soft quasilocalized modes. These results not only strongly support FET, but also constitute a strict benchmark for the statistics produced by coarse-graining approaches to the spatial distribution of elastic moduli.

cond-mat.soft↗
arXiv2020

Low-frequency vibrational spectrum of mean-field disordered systems

We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $\mathcal{D}(ω)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness $κ$ drawn from a distribution $p(κ)$, subjected to a constant field $h$ and interacting bilinearly with a coupling of strength $J$. We investigate the vibrational properties of its ground state at zero temperature. When $p(κ)$ is gapped, the emergent $\mathcal{D}(ω)$ is also gapped, for small $J$. Upon increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase diagram, whereupon replica symmetry is broken. At small $h$, the form of this pseudogap is quadratic, $\mathcal{D}(ω)\simω^2$, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough $h$, a quartic pseudogap $\mathcal{D}(ω)\simω^4$, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition.

cond-mat.dis-nn↗
arXiv2020

Mean-field model of interacting quasilocalized excitations in glasses

Structural glasses feature quasilocalized excitations whose frequencies $ω$ follow a universal density of states ${\cal D}(ω)\!\sim\!ω^4$. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $κ_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${\cal D}(ω)\!=\!A_{\rm g}\,ω^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then -- using scaling theory and numerical simulations -- we provide a complete understanding of the non-universal prefactor $A_{\rm g}(h,J,κ_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{\rm g}(h,J,κ_0)$ is a nonmonotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(κ_0 h^{2/3}\!/J^2)$ in the weak interactions (small $J$) regime -- reminiscent of recent observations in computer glasses -- and predominantly decaying as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.

cond-mat.dis-nn↗
arXiv2020

Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals and boundary effects

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e. feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes experience boundary effects related to the simulation box shape and the widely employed periodic boundary conditions. In particular, image interactions mediated by the box shape and the periodic boundary conditions induce fields' rotation and orientation-dependent suppression of their long-range decay. We then develop a continuum theory that quantitatively predicts these finite-size boundary effects and support it by extensive computer simulations. The theory accounts for the finite-size boundary effects and at the same time allows the extraction of the short-range core properties, such as their typical strain ratios and orientation. The theory is extensively validated in both 2D and 3D. Overall, our results offer a useful tool for extracting the intrinsic core properties of nonphononic modes and plastic rearrangements in computer glasses.

cond-mat.soft↗
arXiv2020

Universality of the nonphononic vibrational spectrum across different classes of computer glasses

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies $ω$ follow a gapless, universal distribution ${\cal D}(ω)\!\sim\!ω^4$. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially-symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear. Here we demonstrate the emergence of the universal $ω^4$ nonphononic spectrum in a broad variety of realistic computer glass models, ranging from tetrahedral network glasses with three-body interactions, through molecular glasses and glassy polymers, to bulk metallic glasses (BMGs). Taken together with previous observations, our results indicate that the low-frequency nonphononic vibrational spectrum of any glassy solid quenched from a melt features the universal $ω^4$ law, independently of the nature of its microscopic interactions.

cond-mat.soft↗
arXiv2020

The fracture of highly deformable soft materials: A tale of two length scales

The fracture of highly deformable soft materials is of great practical importance in a wide range of technological applications, emerging in fields such as soft robotics, stretchable electronics and tissue engineering. From a basic physics perspective, the failure of these materials poses fundamental challenges due to the strongly nonlinear and dissipative deformation involved. In this review, we discuss the physics of cracks in soft materials and highlight two length scales that characterize the strongly nonlinear elastic and dissipation zones near crack tips in such materials. We discuss physical processes, theoretical concepts and mathematical results that elucidate the nature of the two length scales, and show that the two length scales can classify a wide range of materials. The emerging multi-scale physical picture outlines the theoretical ingredients required for the development of predictive theories of the fracture soft materials. We conclude by listing open challenges and future investigation directions.

cond-mat.soft↗
arXiv2020

Pinching a glass reveals key properties of its soft spots

It is now well established that glasses feature quasilocalized nonphononic excitations --- coined "soft spots"---, which follow a universal $ω^4$ density of states in the limit of low frequencies $ω$. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the non-universal prefactor of the universal $ω^4$ law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner. We show that by pinching a glass, i.e. by probing its response to force dipoles, one can disentangle and independently extract these two fundamental pieces of physical information. This analysis reveals that the number of quasilocalized nonphononic excitations follows a Boltzmann-like law in terms of the parent temperature from which the glass is quenched. The latter, sometimes termed the fictive (or effective) temperature, plays important roles in non-equilibrium thermodynamic approaches to the relaxation, flow and deformation of glasses. The analysis also shows that the characteristic stiffness of quasilocalized nonphononic excitations can be related to their characteristic size, a long sought-for length scale. These results show that important physical information, which is relevant for various key questions in glass physics, can be obtained through pinching a glass.

cond-mat.soft↗
arXiv2020

Statistical mechanics of local force dipole responses in computer glasses

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are supposedly involved in a number of glassy anomalies such as the low temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances, however direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g.~phonons). Previous studies to overcome this issue have demonstrated that the response of a glass to local force dipoles serves as a good proxy for its QLMs; we therefore study here the statistical-mechanical properties of the responses to local force dipoles in computer glasses, over a large range of glass stabilities and in various spatial dimensions, with the goal of revealing properties of the yet-inaccessible full distribution of QLMs' frequencies. We find that, as opposed to the spatial-dimension-independent universal distribution of QLMs' frequencies $ω$ (and, consequently, also of their stiffness $κ\!=\!ω^2$), the distribution of stiffnesses associated with responses to local force dipoles features a (weak) dependence on spatial dimension. We rationalize this dependence by introducing a lattice model that incorporates both the real-space profiles of QLMs --- associated with dimension-dependent long-range elastic fields --- and the universal statistical properties of their frequencies. Finally, we discuss possible connections between our findings and basic aspects of the glass transition problem, and to finite-size effects in plastic activity of ultrastable glasses.

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

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate $Γ(k)$ with small wavenumbers $k\!\to\!0$ in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber $k_\dagger$, where phonons are no longer quantized into bands. For $k\!<\!k_\dagger$, finite-size effects dominate $Γ(k)$, which is quantitatively described by a theory of disordered phonon bands. For $k\!>\!k_\dagger$, we find that $Γ(k)$ is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, $Γ(k)$ follows a Rayleigh scattering scaling $\sim\!k^{d+1}$ ($d$ is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form $\sim\!k^{d+1}\log\!{(k_0/k)}$ emerges ($k_0\!>k_\dagger$ is a characteristic wavenumber). Our results suggest that macroscopic glasses --- and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations --- exhibit Rayleigh scaling at the lowest wavenumbers $k$ and a crossover to generalized-Rayleigh scaling at higher $k$. Some supporting experimental evidence from recent literature is presented.

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↗
arXiv2019

Anisotropic Structural Predictor in Glassy Materials

There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial/anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation. Here we derive from first principles the linear response coupling between the local heat capacity of glasses, previously shown to provide a measure of glassy softness, and external deformation in different directions. We first show that this linear response quantity follows an anomalous, fat-tailed distribution related to the universal $ω^4$ density of states of quasilocalized, nonphononic excitations in glasses. We then construct a structural predictor as the product of the local heat capacity and its linear response to external deformation, and show that it offers enhanced predictability of plastic rearrangements under deformation in different directions, compared to the purely scalar predictor.

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↗