arXiv subjects

Eran Bouchbinder

Publications and source records attributed to Eran Bouchbinder.

At least 73 records · Page 4Linked to original sources

arXiv2018

A characteristic energy scale in glasses

Glasses feature a broad distribution of relaxation times and activation energies without an obvious characteristic scale. At the same time, macroscopic quantities such as Newtonian viscosity and nonlinear plastic deformation, are interpreted in terms of a characteristic energy scale, e.g. an effective temperature-dependent activation energy in Arrhenius relations. Nevertheless, despite its fundamental importance, such a characteristic energy scale has not been robustly identified. Inspired by the accumulated evidence regarding the crucial role played by soft quasilocalized excitations in glassy dynamics, we propose that the bulk average of the glass response to a localized force dipole defines such a characteristic energy scale. We show that this characteristic glassy energy scale features remarkable properties: $(i)$ It increases dramatically with decreasing temperature of equilibrium supercooled states, significantly surpassing the corresponding increase in the shear modulus, dismissing the common view that structural variations in supercooled liquids upon vitrification are minute $(ii)$ Its variation with annealing and system size is very similar in magnitude and form to that of the energy of the softest non-phononic vibrational mode, thus establishing a very unusual relation between a rare glassy fluctuation and a bulk average $(iii)$ It exhibits striking dependence on spatial dimensionality and system size, due to the long-ranged fields associated with quasilocalization, which are speculated to be related to peculiarities of the glass transition in two dimensions. In addition, we identify a truly-static growing lengthscale associated with the characteristic glassy energy scale, and discuss possible connections between the increase of this energy scale and the slowing down of dynamics near the glass transition temperature. Open questions and future directions are discussed.

cond-mat.soft↗

arXiv2018

Universal disorder-induced broadening of phonon bands: from disordered lattices to glasses

The translational symmetry of solids gives rise to the existence of low-frequency phonons. In ordered systems, some phonons characterized by different wavevectors are degenerate, i.e. they share the same frequency $ω$; in finite-size systems, phonons form a discrete set of bands with $n_q(ω)$-fold degeneracy. Here we focus on understanding how this degeneracy is lifted in the presence of disorder, and its physical implications. Using standard degenerate perturbation theory and simple statistical considerations, we predict the dependence of the disorder-induced frequency width of phonon bands to be $Δω\!\sim\!σ\,ω\sqrt{n_q}/\sqrt{N}$, where $σ$ is the strength of disorder and $N$ is the total number of particles. This theoretical prediction is supported by extensive numerical calculations for disordered lattices characterized by topological, mass, stiffness and positional disorder, and for computer glasses, where disorder is self-generated, thus establishing its universal nature. The predicted scaling leads to the identification of a crossover frequency $ω_\dagger\!\sim\!L^{-2/(d+2)}$ in systems of linear size $L$ in $d\!>\!2$ dimensions, where the disorder-induced width of phonon bands becomes comparable to the frequency gap between neighboring bands. Consequently, phonons continuously cover the frequency range $ω\!>\!ω_\dagger$, where the notion of discrete phonon bands becomes ill-defined. Two basic applications of the theory are presented; first, we show that the phonon scattering lifetime is proportional to $(Δω)^{-1}$ for $ω\!<\!ω_\dagger$. Second, the theory is applied to the basic physics of glasses, allowing to determine the range of frequencies in which the recently established universal density of states of non-phononic excitations can be directly probed for different system sizes.

cond-mat.stat-mech↗

arXiv2018

Universal non-phononic density of states in 2D, 3D and 4D glasses

It is now well established that structural glasses possess disorder- and frustration-induced soft quasilocalized excitations, which play key roles in various glassy phenomena. Recent work has established that in model glass-formers in three dimensions, these non-phononic soft excitations may assume the form of quasilocalized, harmonic vibrational modes whose frequency follows a universal density of states $D(ω)\!\sim\!ω^4$, independently of microscopic details, and for a broad range of glass preparation protocols. Here we further establish the universality of the non-phononic density of vibrational modes by direct measurements in model structural glasses in two dimensions and four dimensions. We also investigate their degree of localization, which is generally weaker in lower spatial dimensions, giving rise to a pronounced system-size dependence of the non-phononic density of states in two dimensions, but not in higher dimensions. Finally, we identify a fundamental glassy frequency scale $ω_c$ above which the universal $ω^4$ law breaks down.

cond-mat.soft↗

arXiv2018

Universality and stability phase-diagram of two-dimensional brittle fracture

The two-dimensional oscillatory crack instability, experimentally observed in a class of brittle materials under strongly dynamic conditions, has been recently reproduced by a nonlinear phase-field fracture theory. Here we highlight the universal character of this instability by showing that it is present in materials exhibiting widely different near crack tip elastic nonlinearity, and by demonstrating that the oscillations wavelength follows a universal master curve in terms of dissipation-related and nonlinear elastic intrinsic length scales. Moreover, we show that upon increasing the driving force for fracture, a high-velocity tip-splitting instability emerges, as experimentally demonstrated. The analysis culminates in a comprehensive stability phase-diagram of two-dimensional brittle fracture, whose salient properties and topology are independent of the form of near tip nonlinearity.

cond-mat.soft↗

arXiv2018

Necking instabilities in elasto-viscoplastic materials

Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline, polycrystalline and other materials --- feature a predominantly elastic response at small stresses, plasticity onset at a rather well-defined yield stress and rate-dependence. Necking instabilities involve a unique coupling between the system's geometry and its constitutive behavior. We consider generic elasto-viscoplastic constitutive relations involving an internal-state field, which represents the structural evolution of the material during plastic deformation, and study necking in the long-wavelength approximation (sometimes termed the lubrication or slender-bar approximation). We derive a general expression for the largest time-dependent eigenvalue in an approximate WKB-like linear stability analysis, highlighting various basic physical effects involved in necking. This expression is then used to propose criteria for the onset of necking and more importantly for the emergence of strong localization. Applications to strain-softening amorphous plasticity, in the framework of the Shear-Transformation-Zone model, and to strain-hardening crystalline/polycrystalline plasticity, in the framework of the Kocks-Mecking model, are presented. These quantitative analyses of widely different material models support the theoretical predictions, most notably for the strong localization during necking.

cond-mat.mtrl-sci↗

arXiv2018

Frustration-induced internal stresses are responsible for quasilocalized modes in structural glasses

It has been recently shown [E. Lerner, G. Düring, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)] that the non-phononic vibrational modes of structural glasses at low-frequencies $ω$ are quasi-localized and follow a universal density of states $D(ω)\!\sim\!ω^4$. Here we show that the gapless nature of the observed density of states depends on the existence of internal stresses which generically emerge in glasses due to frustration, thus elucidating a basic element underlying this universal behavior. Similarly to jammed particulate packings, low-frequency modes in structural glasses emerge from a balance between a local elasticity term and an internal stress term in the dynamical matrix, where the difference between them is orders of magnitude smaller than their typical magnitude. By artificially reducing the magnitude of internal stresses in a computer glass former in three dimensions, we show that a gap is formed in the density of states below which no vibrational modes exist, thus demonstrating the crucial importance of internal stresses. Finally, we show that while better annealing the glass upon cooling from the liquid state significantly reduces its internal stresses, the self-organizational processes during cooling render the gapless $D(ω)\!\sim\!ω^4$ density of state unaffected.

cond-mat.soft↗

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

Effect of instantaneous and continuous quenches on the density of vibrational modes in model glasses

Computational studies of supercooled liquids often focus on various analyses of their "underlying inherent states" --- the glassy configurations at zero temperature obtained by an infinitely-fast (instantaneous) quench from equilibrium supercooled states. Similar protocols are also regularly employed in investigations of the unjamming transition at which the rigidity of decompressed soft-sphere packings is lost. Here we investigate the statistics and localization properties of low-frequency vibrational modes of glassy configurations obtained by such instantaneous quenches. We show that the density of vibrational modes grows as $ω^β$ with $β$ depending on the parent temperature $T_{0}$ from which the glassy configurations were instantaneously quenched. For quenches from high temperature liquid states we find $β\!\approx\!3$, whereas $β$ appears to approach the previously-observed value $β\!=\!4$ as $T_0$ approaches the glass transition temperature. We discuss the consistency of our findings with the theoretical framework of the Soft Potential Model, and contrast them with similar measurements performed on configurations obtained by continuous quenches at finite cooling rates. Our results suggest that any physical quench at rates sufficiently slower than the inverse vibrational timescale --- including all physically-realistic quenching rates of molecular or atomistic glasses --- would result in a glass whose density of vibrational modes is universally characterized by $β\!=\!4$.

cond-mat.soft↗

arXiv2017

Statistics and properties of low-frequency vibrational modes in structural glasses

Low-frequency vibrational modes play a central role in determining various basic properties of glasses, yet their statistical and mechanical properties are not fully understood. Using extensive numerical simulations of several model glasses in three dimensions, we show that in systems of linear size $L$ sufficiently smaller than a crossover size $L_{D}$, the low-frequency tail of the density of states follows $D(ω)\!\sim\!ω^4$ up to the vicinity of the lowest Goldstone mode frequency. We find that the sample-to-sample statistics of the minimal vibrational frequency in systems of size $L\!<\!L_D$ is Weibullian, with scaling exponents in excellent agreement with the $ω^4$ law. We further show that the lowest frequency modes are spatially quasi-localized, and that their localization and associated quartic anharmonicity are largely frequency-independent. The effect of preparation protocols on the low-frequency modes is elucidated and a number of glassy lengthscales are briefly discussed.

cond-mat.soft↗

arXiv2017

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change due to thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses --- an intrinsic signature of glassy frustration ---, anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal $ω^4$ density of states of quasi-localized low-frequency vibrational modes. When the spatial thermal energy field --- a `softness field' --- is considered, this power-law tail manifests itself by highly localized spots which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal-modes-based approach. These results offer a general, system/model-independent, physical-observable-based approach to identify structural properties of quiescent glasses and to relate them to glassy dynamics.

cond-mat.soft↗

arXiv2017

Instability in dynamic fracture and the failure of the classical theory of cracks

Cracks, the major vehicle for material failure, tend to accelerate to high velocities in brittle materials. In three-dimensions, cracks generically undergo a micro-branching instability at about 40% of their sonic limiting velocity. Recent experiments showed that in sufficiently thin systems cracks unprecedentedly accelerate to nearly their limiting velocity without micro-branching, until they undergo an oscillatory instability. Despite their fundamental importance and apparent similarities to other instabilities in condensed-matter physics and materials science, these dynamic fracture instabilities remain poorly understood. They are not described by the classical theory of cracks, which assumes that linear elasticity is valid inside a stressed material and uses an extraneous local symmetry criterion to predict crack paths. Here we develop a model of two-dimensional dynamic brittle fracture capable of predicting arbitrary paths of ultra-high-speed cracks in the presence of elastic nonlinearity without extraneous criteria. We show, by extensive computations, that cracks undergo a dynamic oscillatory instability controlled by small-scale elastic nonlinearity near the crack tip. This instability occurs above a ultra-high critical velocity and features an intrinsic wavelength that increases proportionally to the ratio of the fracture energy to an elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics. Those results pave the way for resolving other long-standing puzzles in the failure of materials.

cond-mat.soft↗

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

Gaussian fluctuations of spatially inhomogeneous polymers

Inhomogeneous polymers play an important role in various cellular processes, both in nature and in biotechnological applications. At finite temperatures, inhomogeneous polymers exhibit non-trivial thermal fluctuations. In a broader context, these are relatively simple examples for fluctuations in spatially inhomogeneous systems, which are less understood compared to their homogeneous counterparts. We develop a statistical theory of torsional, extensional and bending Gaussian fluctuations of inhomogeneous polymers, where the inhomogeneity is an inclusion of variable size and mechanical properties, using both continuum and discrete approaches. First, we analytically calculate the complete eigenvalue and eigenmode spectrum of the inhomogeneous polymer within a continuum field theory. In particular, we show that the wavenumber inside and outside of the inclusion is nearly linear in the eigenvalue index, with a nontrivial coefficient. Second, we solve the corresponding discrete problem, and highlight fundamental differences between the continuum and discrete spectra. In particular, we demonstrate that above a certain wavenumber the discrete spectrum changes qualitatively and discrete evanescent eigenmodes, that do not have continuum counterparts, emerge. The statistical thermodynamic implications of these differences are then explored by calculating fluctuation-induced forces associated with free-energy variations with either the inclusion properties (e.g.~inhomogeneity formed by adsorbing molecules) or with an external geometric constraint. The former, which is the fluctuation-induced contribution to the adsorbing molecules binding force, is shown to be affected by short wavelengths and thus cannot be calculated using the continuum approach. The latter, on the other hand, is shown to be dominated by long wavelength shape fluctuations and hence is properly described by the continuum theory.

cond-mat.stat-mech↗

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↗

arXiv2016

Notch fracture toughness of glasses: Rate, age and geometry dependence

Understanding the fracture toughness (resistance) of glasses is a fundamental problem of prime theoretical and practical importance. Here we theoretically study its dependence on the loading rate, the age (history) of the glass and the notch radius $ρ$. Reduced-dimensionality analysis suggests that the notch fracture toughness results from a competition between the initial, age- and history-dependent, plastic relaxation timescale $τ^{pl}_0$ and an effective loading timescale $τ^{ext}(\dot{K}_I,ρ)$, where $\dot{K}_I$ is the tensile stress-intensity-factor rate. The toughness is predicted to scale with $\sqrtρ$ independently of $ξ\!\equiv\!τ^{ext}\!/τ^{pl}_0$ for $ξ\!\ll\! 1$, to scale as $T\sqrtρ\,\log(ξ)$ for $ξ\!\gg\!1$ (related to thermal activation, where $T$ is the temperature) and to feature a non-monotonic behavior in the crossover region $ξ\!\sim\!{\cal O}(1)$ (related to plastic yielding dynamics). These predictions are verified using novel 2D computations, providing a unified picture of the notch fracture toughness of glasses. The theory highlights the importance of timescales competition and far from steady-state elasto-viscoplastic dynamics for understanding the toughness, and shows that the latter varies quite significantly with the glass age (history) and applied loading rate. Experimental support for bulk metallic glasses is presented.

cond-mat.mtrl-sci↗

arXiv2015

An Eulerian projection method for quasi-static elastoplasticity

A well-established numerical approach to solve the Navier--Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. We highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.

cond-mat.mtrl-sci↗

arXiv2015

Recent developments in dynamic fracture: Some perspectives

We briefly review a number of important recent experimental and theoretical developments in the field of dynamic fracture. Topics include experimental validation of the equations of motion for straight tensile cracks (in both infinite media and strip geometries), validation of a new theoretical description of the near-tip fields of dynamic cracks incorporating weak elastic nonlinearities, a new understanding of dynamic instabilities of tensile cracks in both 2D and 3D, crack front dynamics, and the relation between frictional motion and dynamic shear cracks. Related future research directions are briefly discussed.

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↗