arXiv subjects

Eran Bouchbinder

Publications and source records attributed to Eran Bouchbinder.

At least 91 records · Page 5Linked to original sources

arXiv2015

On the spatial distribution of thermal energy in equilibrium

The equipartition theorem states that in equilibrium thermal energy is equally distributed among uncoupled degrees of freedom which appear quadratically in the system's Hamiltonian. However, for spatially coupled degrees of freedom --- such as interacting particles --- one may speculate that the spatial distribution of thermal energy may differ from the value predicted by equipartition, possibly quite substantially in strongly inhomogeneous/disordered systems. Here we show that for systems undergoing simple Gaussian fluctuations around an equilibrium state, the spatial distribution is universally bounded from above by $\frac{1}{2}k_BT$. We further show that in one-dimensional systems with short-range interactions, the thermal energy is equally partitioned even for coupled degrees of freedom in the thermodynamic limit and that in higher dimensions non-trivial spatial distributions emerge. Some implications are discussed.

cond-mat.stat-mech↗

arXiv2015

Failing softly: A fracture theory of highly-deformable materials

Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation during failure, are not yet fully understood. Here we propose a theoretical framework for the dynamic fracture of highly-deformable materials, in which the effects of a dynamic crack are treated with respect to the nonlinearly deformed (pre-stressed/strained), non-cracked, state of the material. Within this framework, we derive analytic and semi-analytic solutions for the near-tip deformation fields and energy release rates of dynamic cracks propagating in incompressible neo-Hookean solids under biaxial and uniaxial loading. We show that moderately large pre-stressing has a marked effect on the stress fields surrounding a crack's tip. We verify these predictions by performing extensive experiments on the fracture of soft brittle elastomers over a range of loading levels and propagation velocities, showing that the newly developed framework offers significantly better approximations to the measurements than standard approaches at moderately large levels of external loadings and high propagation velocities. This framework should be relevant to the failure analysis of soft and tough, yet brittle, materials.

cond-mat.mtrl-sci↗

arXiv2014

Cell reorientation under cyclic stretching

Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations -- cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell's passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells, measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.

physics.bio-ph↗

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↗

arXiv2014

Variable-amplitude oscillatory shear response of amorphous materials

Variable-amplitude oscillatory shear tests are emerging as powerful tools to investigate and quantify the nonlinear rheology of amorphous solids, complex fluids and biological materials. Quite a few recent experimental and atomistic simulation studies demonstrated that at low shear amplitudes, an amorphous solid settles into an amplitude- and initial conditions-dependent dissipative limit cycle, in which back-and-forth localized particle rearrangements periodically bring the system to the same state. At sufficiently large shear amplitudes, the amorphous system loses memory of the initial conditions, exhibits chaotic particle motions accompanied by diffusive behavior and settles into a stochastic steady-state. The two regimes are separated by a transition amplitude, possibly characterized by some critical-like features. Here we argue that these observations support some of the physical assumptions embodied in the nonequilibrium thermodynamic, internal-variables based, Shear-Transformation-Zone model of amorphous visco-plasticity; most notably that "flow defects" in amorphous solids are characterized by internal states between which they can make transitions, and that structural evolution is driven by dissipation associated with plastic deformation. We present a rather extensive theoretical analysis of the thermodynamic Shear-Transformation-Zone model for a variable-amplitude oscillatory shear protocol, highlighting its success in accounting for various experimental and simulational observations, as well as its limitations. Our results offer a continuum-level theoretical framework for interpreting the variable-amplitude oscillatory shear response of amorphous solids and may promote additional developments.

cond-mat.mtrl-sci↗

arXiv2014

Two-temperature continuum thermomechanics of deforming amorphous solids

There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent, finite-deformation, continuum framework for deforming amorphous solids. The basic premise is that the configurational degrees of freedom of the material --- the part of the internal energy/entropy that corresponds to mechanically stable microscopic configurations --- are characterized by a configurational temperature that might differ from that of the vibrational degrees of freedom, which equilibrate rapidly with an external heat bath. This results in an approximate internal energy decomposition into weakly interacting configurational and vibrational subsystems, which exchange energy following a Fourier-like law, leading to a thermomechanical framework permitting two well-defined temperatures. In this framework, internal variables that carry information about the state of the material equilibrate with the configurational subsystem, are explicitly associated with energy and entropy of their own, and couple to a viscoplastic flow rule. The coefficients that determine the rate of flow of entropy and heat between different internal systems are proposed to explicitly depend on the rate of irreversible deformation. As an application of this framework, we discuss two constitutive models for the response of glassy materials, a simple phenomenological model and a model related to the concept of Shear-Transformation-Zones as the basis for internal variables. The models account for several salient features of glassy deformation phenomenology. Directions for future investigation are briefly discussed.

cond-mat.mtrl-sci↗

arXiv2013

Instabilities at Frictional Interfaces: Creep Patches, Nucleation and Rupture Fronts

The strength and stability of frictional interfaces, ranging from tribological systems to earthquake faults, are intimately related to the underlying spatially-extended dynamics. Here we provide a comprehensive theoretical account, both analytic and numeric, of spatiotemporal interfacial dynamics in a realistic rate-and-state friction model, featuring both velocity-weakening and strengthening behaviors. Slowly extending, loading-rate dependent, creep patches undergo a linear instability at a critical nucleation size, which is nearly independent of interfacial history, initial stress conditions and velocity-strengthening friction. Nonlinear propagating rupture fronts -- the outcome of instability -- depend sensitively on the stress state and velocity-strengthening friction. Rupture fronts span a wide range of propagation velocities and are related to steady state fronts solutions.

cond-mat.mtrl-sci↗

arXiv2013

Slow rupture of frictional interfaces

The failure of frictional interfaces and the spatiotemporal structures that accompany it are central to a wide range of geophysical, physical and engineering systems. Recent geophysical and laboratory observations indicated that interfacial failure can be mediated by slow slip rupture phenomena which are distinct from ordinary, earthquake-like, fast rupture. These discoveries have influenced the way we think about frictional motion, yet the nature and properties of slow rupture are not completely understood. We show that slow rupture is an intrinsic and robust property of simple non-monotonic rate-and-state friction laws. It is associated with a new velocity scale $c_{min}$, determined by the friction law, below which steady state rupture cannot propagate. We further show that rupture can occur in a continuum of states, spanning a wide range of velocities from $c_{min}$ to elastic wave-speeds, and predict different properties for slow rupture and ordinary fast rupture. Our results are qualitatively consistent with recent high-resolution laboratory experiments and may provide a theoretical framework for understanding slow rupture phenomena along frictional interfaces.

cond-mat.mtrl-sci↗

arXiv2013

Nonequilibrium thermodynamics and glassy rheology

Mechanically driven glassy systems and complex fluids exhibit a wealth of rheological behaviors that call for theoretical understanding and predictive modeling. A distinct feature of these nonequilibrium systems is their dynamically evolving state of structural disorder, which determines their rheological responses. Here we highlight a recently developed nonequilibrium thermodynamic framework in which the structural state is characterized by an evolving effective disorder temperature that may differ from the ordinary thermal temperature. The specific properties of each physical system of interest are described by a small set of coarse-grained internal state variables and their associated energies and entropies. The dynamics of the internal variables, together with the flow of energy and entropy between the different parts of the driven system, determine continuum-level rheological constitutive laws. We conclude with brief descriptions of several successful applications of this framework.

cond-mat.soft↗

arXiv2013

The Dynamics of Rapid Fracture: Instabilities, Nonlinearities and Length Scales

The failure of materials and interfaces is mediated by cracks, nearly singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation -- the dynamic process of fracture -- couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme conditions within the nearly singular region where material failure occurs. Here, we first briefly review the classic approach to dynamic fracture, "Linear Elastic Fracture Mechanics" (LEFM), and discuss its successes and limitations. We show how, on the one hand, recent experiments performed on straight cracks propagating in soft brittle materials have quantitatively confirmed the predictions of this theory to an unprecedented degree. On the other hand, these experiments show how LEFM breaks down as the singular region at the tip of a crack is approached. This breakdown naturally leads to a new theoretical framework coined "Weakly Nonlinear Fracture Mechanics", where weak elastic nonlinearities are incorporated. The stronger singularity predicted by this theory gives rise to a new and intrinsic length scale, $\ell_{nl}$. These predictions are verified in detail through direct measurements. We then theoretically and experimentally review how the emergence of $\ell_{nl}$ is linked to a new equation for crack motion, which predicts the existence of a high-speed oscillatory crack instability whose wave-length is determined by $\ell_{nl}$. We conclude by delineating outstanding challenges in the field.

cond-mat.mtrl-sci↗

arXiv2013

The cooling rate dependence of the shear modulus of amorphous solids

Rapidly cooling a liquid may result in a glass transition, creating an amorphous solid whose shear and bulk moduli are finite. Even when done with constant density, these resulting moduli depend strongly on the rate of cooling. Understanding this phenomenon calls for analyzing separately the "Born term" that exists also in perfectly ordered materials and the contributions of the "excess modes" that result from glassy disorder. We show that the Born term is very insensitive to the cooling rate, and all the variation in the shear modulus is due to the excess modes. We argue that this approach provides a quantitative understanding of the cooling rate dependence of a basic linear response coefficient, i.e. the shear modulus.

cond-mat.mtrl-sci↗

arXiv2012

Dynamic stability of crack fronts: Out-of-plane corrugations

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.

cond-mat.mtrl-sci↗

arXiv2012

Fracture Toughness of Metallic Glasses: Ductile-to-Brittle Transition?

Quantitative understanding of the fracture toughness of metallic glasses, including the associated ductile-to-brittle transitions, is not yet available. Here we use a simple model of plastic deformation in glasses, coupled to an advanced Eulerian level set formulation for solving complex free boundary problems, to calculate the fracture toughness of metallic glasses as a function of the degree of structural relaxation corresponding to different annealing times near the glass temperature. Our main result indicates the existence of an elasto-plastic crack tip instability for sufficiently relaxed glasses, resulting in a marked drop in the toughness, which we interpret as a ductile-to-brittle transition similar to experimental observations.

cond-mat.mtrl-sci↗

arXiv2012

A simple nonlinear equation for structural relaxation in glasses

A wide range of glassy and disordered materials exhibit complex, non-exponential, structural relaxation (aging). We propose a simple nonlinear rate equation dδ/dt = a [1-exp (bδ)], where 'δ' is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where 'a' and 'b' are both temperature-, and more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single non-equilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a super-molecular scale.

cond-mat.dis-nn↗

arXiv2011

A nonlinear symmetry breaking effect in shear cracks

Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including possibly opening displacements, in agreement with Stephenson's prediction. We quantify this nonlinear symmetry breaking effect, under two-dimensional deformation conditions, by an explicit inequality in terms of the first and second order elastic constants in the quasi-static regime and semi-analytic calculations in the fully dynamic regime. Our general results are applied to various materials. Finally, we discuss available works in the literature and note the potential relevance of elastic nonlinearities for frictional cracks.

cond-mat.mtrl-sci↗

arXiv2011

An intrinsic nonlinear scale governs oscillations in rapid fracture

When branching is suppressed, rapid cracks undergo a dynamic instability from a straight to an oscillatory path at a critical velocity $v_c$. In a systematic experimental study using a wide range of different brittle materials, we first show how the opening profiles of straight cracks scale with the size $\ell_{nl}$ of the nonlinear zone surrounding a crack's tip. We then show, for all materials tested, that $v_c$ is both a fixed fraction of the shear speed and, moreover, that the instability wavelength is proportional to $\ell_{nl}$. These findings directly verify recent theoretical predictions and suggest that the nonlinear zone is not passive, but rather is closely linked to rapid crack instabilities.

cond-mat.mtrl-sci↗

arXiv2011

Viscoelastic Fracture of Biological Composites

Soft constituent materials endow biological composites, such as bone, dentin and nacre, with viscoelastic properties that may play an important role in their remarkable fracture resistance. In this paper we calculate the scaling properties of the quasi-static energy release rate and the viscoelastic contribution to the fracture energy of various biological composites, using both perturbative and non-perturbative approaches. We consider coarse-grained descriptions of three types of anisotropic structures: (i) Liquid-crystal-like composites (ii) Stratified composites (iii) Staggered composites, for different crack orientations. In addition, we briefly discuss the implications of anisotropy for fracture criteria. Our analysis highlights the dominant lengthscales and scaling properties of viscoelastic fracture of biological composites. It may be useful for evaluating crack velocity toughening effects and structure-dissipation relations in these materials.

cond-mat.mtrl-sci↗