arXiv subjects

David Richard

Publications and source records attributed to David Richard.

At least 19 recordsLinked to original sources

arXiv2026

Large dilatational hyperelasticity of glasses en route to cavitation failure

Materials deform elasto-plastically and fail under various loading conditions, typically quantified by the stress triaxiality, which is the ratio between the dilatational (hydrostatic) stress and the deviatoric (shear-like) one. We show that the elasto-plastic deformation of glasses approaching failure qualitatively differ for large and small stress triaxiality levels. Specifically, in the former limit, glasses reveal a strong hyperelastic (nonlinear elastic) response with minute plasticity, largely independently of the quenching rate across the glass transition. Yet, glassy disorder gives rise to significant elastic (reversible) nonaffine deformation, accompanied by the formation of micro-cavities. A small fraction of the latter is irreversible, i.e., survives unloading prior to the onset of failure, and may serve as nucleation sites for failure in the form of large-scale cavitation, involving a topological transition accompanied by the formation of an internal free surface, upon which the glass loses a significant fraction of its load-bearing capacity. These results are contrasted with glass behavior in the limit of vanishing stress triaxiality and their universality across different glass formers is demonstrated. Finally, the implications of our findings for understanding glass deformation and failure under realistic stress conditions are discussed.

cond-mat.soft↗

arXiv2025

How rigidity percolation and bending stiffness shape colloidal gel elasticity

Dispersed colloidal particles within a suspension can aggregate and spontaneously self-organize into a robust, percolating structure known as a gel. These network-like structures are prevalent in nature and play a critical role in many industrial processes, including those involving batteries, food products, and pharmaceutical formulations. In this paper, we examine the emergence of elasticity in colloidal gels. We show that gelation is governed by a rigidity percolation transition. We identify a characteristic correlation length that quantifies the extent of elastic and structural inhomogeneities, which diverges at the critical point. Our findings reveal that, regardless of the interaction types, the particle concentration, or the specific route to non-ergodicity i.e. the preparation protocol, the elastic moduli and vibrational properties of gels can be accurately predicted within a unifying framework, in which the bending modes of fractal clusters -- approximately the size of this correlation length -- dominate under small deformations.

cond-mat.soft↗

arXiv2024

Elementary processes in dilatational plasticity of glasses

Materials typically fail under complex stress states, essentially involving dilatational (volumetric) components that eventually lead to material decohesion/separation. It is therefore important to understand dilatational irreversible deformation -- i.e., dilatational plasticity -- en route to failure. In the context of glasses, much focus has been given to shear (volume-preserving) plasticity, both in terms of the stress states considered and the corresponding material response. Here, using a recently-developed methodology and extensive computer simulations, we shed basic light on the elementary processes mediating dilatational plasticity in glasses. We show that plastic instabilities, corresponding to singularities of the glass Hessian, generically feature both dilatational and shear irreversible strain components. The relative magnitude and statistics of the strain components depend both on the symmetry of the driving stress (e.g., shear vs.~hydrostatic tension) and on the cohesive (attractive) part of the interatomic interaction. We further show that the tensorial shear component of the plastic strain is generally non-planar and also extract the characteristic volume of plastic instabilities. Elucidating the fundamental properties of the elementary micro-mechanical building blocks of plasticity in glasses sets the stage for addressing larger-scale, collective phenomena in dilatational plasticity such as topological changes in the form of cavitation and ductile-to-brittle transitions. As a first step in this direction, we show that the elastic moduli markedly soften during dilatational plastic deformation approaching cavitation.

cond-mat.soft↗

arXiv2023

Connecting microscopic and mesoscopic mechanics in model structural glasses

We present a novel formalism to characterize elastic heterogeneities in amorphous solids. In particular, we derive high-order strain-energy expansions for pairwise energies under athermal quasistatic dynamics. We then use the presented formalism to study the statistical properties of pairwise expansion coefficients and their link with the statistics of soft, quasilocalized modes, for a wide range of formation histories in both two- and three-dimensional systems. We further exploit the presented framework to access local yield stress maps by performing a non-linear stress-strain expansion within a cavity embedded in a frozen matrix. We show that our "bond micromechanics" compare well with the original "frozen matrix" method, with the caveat of overestimating large stress activations. We additionally show how local yield rules can be used as input for a scalar elasto-plastic model (EPM) to predict the stress response of materials ranging from ductile to brittle. Finally, we highlight some of the limits of simple mesoscale models in capturing the aging dynamics of post-yielding systems. Intriguingly, we observe subdiffusive and diffusive shearband growths for particle-based simulations and EPMs, respectively.

cond-mat.soft↗

arXiv2023

Detecting low-energy quasilocalized excitations in computer glasses

Soft, quasilocalized excitations (QLEs) are known to generically emerge in a broad class of disordered solids, and to govern many facets of the physics of glasses, from wave attenuation to plastic instabilities. In view of this key role of QLEs, shedding light upon several open questions in glass physics depends on the availability of computational tools that allow to study QLEs' statistical mechanics. The latter is a formidable task since harmonic analyses are typically contaminated by hybridizations of QLEs with phononic excitations at low frequencies, obscuring a clear picture of QLEs' abundance, typical frequencies and other important micromechanical properties. Here we present an efficient algorithm to detect the field of quasilocalized excitations in structural computer glasses. The algorithm introduced takes a computer-glass sample as input, and outputs a library of QLEs embedded in that sample. We demonstrate the power of the new algorithm by reporting the spectrum of glassy excitations in two-dimensional computer glasses featuring a huge range of mechanical stability, which is inaccessible using conventional harmonic analyses due to phonon-hybridizations. Future applications are finally discussed.

cond-mat.soft↗

arXiv2022

Bridging necking and shear-banding mediated tensile failure in glasses

The transition between necking-mediated tensile failure of glasses, at elevated temperatures and/or low strain-rates, and shear-banding-mediated tensile failure, at low temperatures and/or high strain-rates, is investigated using tensile experiments on metallic glasses and atomistic simulations. We experimentally and simulationally show that this transition occurs through a sequence of macroscopic failure patterns, parametrized by the ultimate tensile strength. Quantitatively analyzing the spatiotemporal dynamics preceding failure, using large scale atomistic simulations corroborated by experimental fractography, reveals how the collective evolution and mutual interaction of shear-driven plasticity and dilation-driven void formation (cavitation) control the various macroscopic failure modes. In particular, we find that at global failure, the size of the largest cavity in the loading direction exhibits a nonmonotonic dependence on the temperature at a fixed strain rate, which is rationalized in terms of the interplay between shear- and dilation-driven plasticity. We also find that the size of the largest cavity scales with the cross-sectional area of the undeformed sample. These results shed light on tensile failure of glasses, and highlight the need to develop elasto-plastic constitutive models of glasses incorporating both shear- and dilation-driven irreversible processes.

cond-mat.mtrl-sci↗

arXiv2022

Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids

We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and meso-scale elasto-plastic models (EPM) for amorphous solids sheared in the athermal quasi-static limit. We show that the spatial correlations in plastic activity exhibit a short lengthscale that grows as $t^{3/4}$ in MD and ballistically in EPM, and is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.

cond-mat.soft↗

arXiv2021

Bond-space operator disentangles quasi-localized and phononic modes in structural glasses

The origin of several emergent mechanical and dynamical properties of structural glasses is often attributed to populations of localized structural instabilities, coined quasilocalized modes (QLMs). Under a restricted set of circumstances, glassy QLMs can be revealed by analyzing computer glasses' vibrational spectra in the harmonic approximation. However, this analysis has limitations due to system-size effects and hybridization processes with low energy phononic excitations (plane waves) that are omnipresent in elastic solids. Here we overcome these limitations by exploring the spectrum of a linear operator defined on the space of particle interactions (bonds) in a disordered material. We find that this bond-force-response operator offers a unique interpretation of QLMs in glasses, and cleanly recovers some of their important statistical and structural features. The analysis presented here reveals the dependence of the number density (per frequency) and spatial extent of QLMs on material preparation protocol (annealing). Finally, we discuss future research directions and possible extensions of this work.

cond-mat.dis-nn↗

arXiv2021

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase of the activation barrier $\Delta E(T)$ with decreasing temperature $T$. A class of theoretical frameworks -- known as elastic models -- attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus $G_\infty(T)$. While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids. Here, we propose that viscous slowing down is controlled by a mesoscopic elastic stiffness $\kappa(T)$, defined as the characteristic stiffness of response fields to local dipole forces in the liquid's underlying inherent states. First, we show that $\kappa(T)$ -- which is intimately related to the energy and length scales characterizing quasilocalized, nonphononic excitations in glasses -- increases more strongly with decreasing $T$ than the macroscopic inherent state shear modulus $G(T)$ in several computer liquids. Second, we show that the simple relation $\Delta E(T)\propto\kappa(T)$ holds remarkably well for some computer liquids, implying a direct connection between the liquid's underlying mesoscopic elasticity and enthalpic energy barriers. On the other hand, we show that for other computer liquids, the above relation fails. Finally, we provide strong evidence that what distinguishes computer liquids in which the $\Delta E(T) \propto \kappa(T)$ relation holds, from those in which it does not, is that the latter feature highly granular potential energy landscapes, where many sub-basins separated by low activation barriers exist. [Rest of abstract abridged]

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↗

arXiv2020

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 $\Gamma(\omega)$ in the low-frequency limit ($\omega\!\to\!0$), 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, $\Gamma(\omega)\!\sim\!\gamma\,\omega^{d+1}$, where $\gamma\!=\!\gamma(V_{\rm c})$ 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 $\Gamma(\omega)\!\sim\!\gamma\,\omega^3$ is asymptotically satisfied in two dimensions ($d\!=\!2$) once $\gamma$ 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 $\omega^4$ 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

A simple and broadly-applicable definition of shear transformation zones

Plastic deformation in amorphous solids is known to be carried by stress-induced localized rearrangements of a few tens of particles, accompanied by the conversion of elastic energy to heat. Despite their central role in determining how glasses yield and break, the search for a simple and generally applicable definition of the precursors of those plastic rearrangements -- the so-called shear transformation zones (STZs) -- is still ongoing. Here we present a simple definition of STZs -- based solely on the harmonic approximation of a glass' energy. We explain why and demonstrate directly that our proposed definition of plasticity carriers in amorphous solids is more broadly applicable compared to anharmonic definitions put forward previously. Finally, we offer an open-source library that analyzes low-lying STZs in computer glasses and in laboratory materials such as dense colloidal suspensions for which the harmonic approximation is accessible. Our results constitute a physically motivated methodological advancement towards characterizing mechanical disorder in glasses, and understanding how they yield.

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 $\omega$ follow a gapless, universal distribution ${\cal D}(\omega)\!\sim\!\omega^4$. 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 $\omega^4$ 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 $\omega^4$ law, independently of the nature of its microscopic interactions.

cond-mat.soft↗

arXiv2019

Nonlinear quasilocalized excitations in glasses. I. True representatives of soft spots

Structural glasses formed by quenching a melt possess a population of soft quasilocalized excitations --- often called `soft spots' --- that are believed to play a key role in various thermodynamic, transport and mechanical phenomena. Under a narrow set of circumstances, quasilocalized excitations assume the form of vibrational (normal) modes, that are readily obtained by a harmonic analysis of the multi-dimensional potential energy. In general, however, direct access to the population of quasilocalized modes via harmonic analysis is hindered by hybridizations with other low-energy excitations, e.g.~phonons. In this series of papers we re-introduce and investigate the statistical-mechanical properties of a class of low-energy quasilocalized modes --- coined here \emph{nonlinear quasilocalized excitations} (NQEs) --- that are defined via an anharmonic (nonlinear) analysis of the potential energy landscape of a glass, and do not hybridize with other low-energy excitations. In this first paper, we review the theoretical framework that embeds a micromechanical definition of NQEs. We demonstrate how harmonic quasilocalized modes hybridize with other soft excitations, whereas NQEs properly represent soft spots without hybridization. We show that NQEs' energies converge to the energies of the softest, non-hybridized harmonic quasilocalized modes, cementing their status as true representatives of soft spots in structural glasses. Finally, we perform a statistical analysis of the mechanical properties of NQEs, which results in a prediction for the distribution of potential energy barriers that surround typical inherent states of structural glasses, as well as a prediction for the distribution of local strain thresholds to plastic instability.

cond-mat.soft↗

arXiv2019

Classical Nucleation Theory for the Crystallization Kinetics in Sheared Liquids

While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds particles.

cond-mat.stat-mech↗

arXiv2018

Is directed percolation in colloid-polymer mixtures linked to dynamic arrest?

Using computer simulations, we study the dynamic arrest in a schematic model of colloid-polymer mixtures combining short-ranged attractions with long-ranged repulsions. The arrested gel is a dilute rigid network of colloidal particles bonded due to the strong attractions. Without repulsions, the gel forms at the spinodal through arrested phase separation. In the ergodic suspension at sufficiently high densities, colloidal clusters form temporary networks that percolate space. Recently [Nat. Commun. 7, 11817 (2016)], it has been proposed that the transition of these networks to directed percolation coincides with the onset of the dynamic arrest, thus linking structure to dynamics. Here, we evaluate for various screening lengths the underlying gas-liquid binodal and the percolation transitions. We find that directed percolation shifts the continuous percolation line to larger densities, but even beyond this line the suspension remains ergodic. Only when approaching the spinodal does dynamic arrest occur. Competing repulsions thus do not modify the qualitative scenario for non-equilibrium gelation, although the structure of the emerging percolating network shows some differences.

cond-mat.soft↗

arXiv2018

Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

Combining three numerical methods (forward flux sampling, seeding of droplets, and finite size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining the nucleation work with the pressure difference allows us to calculate the interfacial tension of small droplets. Our results demonstrate that employing bulk quantities yields inaccurate results for the nucleation rate.

cond-mat.soft↗

arXiv2018

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, the second on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow to probe a wide range of supersaturations, and to reconstruct the kinetics and the free energy landscape from the same simulation. Results are consistent with the scaling predicted by classical nucleation theory although a quantitative fit requires a rather large, effective interfacial tension.

cond-mat.soft↗