arXiv subjects

Anaël Lemaître

Publications and source records attributed to Anaël Lemaître.

At least 19 recordsLinked to original sources

arXiv2026

The vibrational spectrum of vitreous silica: rigorous decomposition via recursive orthogonal splitting analysis

Our understanding of vibrations in solids currently rests on concepts and techniques designed for crystals and explicitly relying on periodicity, hence inapplicable to amorphous materials. As a consequence, no established framework enables a systematic decomposition of the vibrational spectrum of amorphous solids into contributions associated with well-defined types of atomic motions. This methodological gap obscures the interpretation of various experimental probes of linear response, based on the measurements of acoustic, thermal, or optical properties. Here, we construct such a framework-Recursive Orthogonal Splitting Analysis (ROSA)-which decomposes the vibrational space by recursive applications of the projection formalism. Each step of the procedure exploits a dominant stiffness contrast to split a vibrational displacement subspace into two weakly coupled orthogonal complements. We illustrate ROSA by applying it to the archetypal covalent glass-vitreous silica. Successively separating bond-stretching, symmetric and antisymmetric oxygen motions, isotropic and deviatoric tetrahedral strains, and distinct classes of tetrahedral bending, reveals a hierarchical structure of the space of vibrational degrees of freedom, involving six mutually orthogonal subspaces. These subspaces selectively capture all salient spectral features, including the two-humped structure in the low-frequency range, the peak near 800 cm -1 , and the high-frequency doublet. In the low-frequency range, rigid-unit tetrahedral rotations do not constitute independent degrees of freedom but are kinematically enslaved to bending coordinates by no-stretch constraints. Because ROSA relies solely on the existence of contrasted stiffness scales associated with the point symmetry of local structural units, and on their separation by enforcing geometric constraints via the projection formalism, it is directly applicable to a broad class of covalent network glasses.

cond-mat.dis-nn↗

arXiv2023

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

cond-mat.soft↗

arXiv2022

Plastic ridge formation in a compressed thin amorphous film

We demonstrate that surface morphogenesis in compressed thin films may result from spatially correlated plastic activity. A soft glassy film strongly adhering to a smooth and rigid substrate and subjected to uniaxial compression, indeed, does not undergo any global elastic pattern-forming instability, but responds plastically via localized burst events that self-organize, leading to the emergence of a series of parallel ridges transverse to the compression axis. This phenomenon has been completely overlooked, but results from common features of the plastic response of glasses, hence should be highly generic for compressed glassy thin films.

cond-mat.soft↗

arXiv2022

A Systematic Error in the Internal Friction Measurement of Coatings for Gravitational Waves Detectors

Low internal friction coatings are key components of advanced technologies such as optical atomic clocks and high-finesse optical cavity and often lie at the forefront of the most advanced experiments in Physics. Notably, increasing the sensitivity of gravitational-wave detectors depends in a very large part on developing new coatings, which entails developing more suitable methods and models to investigate their loss angle. In fact, the most sensitive region of the detection band in such detectors is limited by the coating thermal noise, which is related to the loss angle of the coating. Until now, models which describe only ideal physical properties have been adopted, wondering about the use of one or more loss angles to describe the mechanical properties of coatings. Here we show the presence of a systematic error ascribed to inhomogeneity of the sample at its edges in measuring the coating loss angle. We present a model for disk-shaped resonators, largely used in loss angle measurements, and we compare the theory with measurements showing how this systematic error impacts on the accuracy with which the loss model parameters are known.

astro-ph.IM↗

arXiv2022

Effects of mixing and annealing on the optical and mechanical properties of TiO$_{2}$:Ta$_{2}$O$_{5}$ amorphous coatings

Amorphous mixed titania-tantala coatings are key components of Bragg reflectors in the gravitational wave detectors (GWDs). Attaining the lowest possible values of optical absorption and mechanical losses in the coatings is of paramount importance for GWDs, and this requires a complex optimization of the coating deposition and post-deposition annealing. We present here a systematic investigation of the optical properties and internal friction of amorphous mixed titania-tantala coatings grown by ion beam sputtering. We consider coatings with six different cation mixing ratios and we study them both in the as-deposited and annealed state. By exploiting spectroscopic ellipsometry data and modelling, along with ancillary techniques, we retrieved the dielectric function of the coatings in a wide spectral range. When varying the mixing ratio and performing the annealing we find monotonic trends for most of the aforementioned properties. Remakably, the post-annealing Urbach energy displays a definite minimum for a mixing ratio around 20%, very close to the composition of the coatings showing the lowest optical absorption for GWDs applications. We suggest that the observed minimum in the Urbach energy depends not only on the mixing ratio, but also on the annealing parameters. On the other hand, the minimum coating loss angle was found to be weakly dependent on the considered measurement frequency and to lie within a rather broad range of Ti content, suggesting that the search for an absolute minimum following post-deposition annealing should be rather sought in the study of the best annealing parameters for each specific cation ratio considered. This work constitutes a reference for the optical properties of the amorphous mixed titania-tantala coatings, and highlights the relevance of the Urbach energy in the optimization process of materials for high-performing Bragg reflectors.

physics.app-ph↗

arXiv2021

Yield stress aging in attractive colloidal suspensions

We investigate the origin of yield stress aging in semi-dense, saline, and turbid suspensions in which structural evolution is rapidly arrested by the formation of thermally irreversible roll-resisting interparticle contacts. By performing optical tweezer (OT) three-point bending tests on particle rods, we show that these contacts yield by overcoming a rolling threshold, the critical bending moment of which grows logarithmically with time. We demonstrate that this time-dependent contact-scale rolling threshold controls the suspension yield stress and its aging kinetics. We identify a simple constitutive relation between the contact-scale flexural rigidity and rolling threshold, which transfers to macroscopic scales. This leads us to establishing a constitutive relation between macroscopic shear modulus and yield stress that is generic for an array of colloidal systems.

cond-mat.soft↗

arXiv2021

Anomalous Elasticity and Screening in Amorphous Solids

Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media, plastic responses abound immediately, at any value of the strain. Such plastic responses are quasi-localized in nature, with the ``cheapest" one being a quadrupolar source. The existence of such plastic responses results in {\em screened elasticity} in which strains and stresses can either quantitatively or qualitatively differ from the un-screened theory, depending on the specific screening mechanism. Here we offer a theory of such screening effects by plastic quadrupoles, dipoles and monopoles, explain their natural appearance, and point out the analogy to electrostatic screening by electric charges and dipoles. For low density of quadrupoles the effect is to normalize the elastic moduli without a qualitative change compared to pure elasticity theory; for higher density of quadrupoles the screening effects result in qualitative changes. Predictions for the spatial dependence of displacement fields caused by local sources of strains are provided and compared to numerical simulations. We find that anomalous elasticity is richer than electrostatics in having a screening mode that does not appear in the electrostatic analog

cond-mat.dis-nn↗

arXiv2020

Frictional Granular Matter: Protocol Dependence of Mechanical Properties

Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here we show, based on experiments and numerical simulations, that this is generically not the case since stress auto-correlation functions decay more slowly than the elastic Green's function. It was shown theoretically that standard elastic decay demands pressure and torque density fluctuations to be normal, with possibly one of them being hyperuniform. Generic compressed frictional assemblies exhibit however abnormal pressure fluctuations, failing to conform with the central limit theorem. The physics of this failure is linked to correlations built in the material during compression from a dilute configuration prior to jamming. By changing the protocol of compression one can observe different pressure fluctuations and stress auto-correlations decay at large scales.

cond-mat.soft↗

arXiv2020

Origin of the Bauschinger Effect in Amorphous Solids

We study the structural origin of the Bauschinger effect by accessing numerically the local plastic thresholds in the steady state flow of a two-dimensional model glass under athermal quasistatic deformation. More specifically, we compute the local residual strength, $Δτ^{c}$, for arbitrary loading orientations and find that plastic deformation generically induces material polarization, i.e., a forward-backward asymmetry in the $Δτ^{c}$ distribution. In steady plastic flow, local packings are on average closer to forward (rather than backward) instabilities, due to the stress-induced bias of barriers. However, presumably due to mechanical noise, a significant fraction of zones lie close to reverse (backward) yielding, as the distribution of $Δτ^{c}$ for reverse shearing extends quasilinearly down to zero local residual strength. By constructing an elementary model of the early plastic response, we then show that unloading causes reverse plasticity of a growing amplitude, i.e., reverse softening, while it shifts away forward-yielding barriers. This result in an inversion of polarization in the low-$Δτ^{c}$ region and, consequently, in the Bauschinger effect. This scenario is quite generic, which explains the pervasiveness of the effect.

cond-mat.mtrl-sci↗

arXiv2020

Rejuvenation and Shear-Banding in model amorphous solids

We measure the local yield stress, at the scale of small atomic regions, in a deeply quenched two-dimensional glass model undergoing shear banding in response to athermal quasistatic (AQS) deformation. We find that the occurrence of essentially a single plastic event suffices to bring the local yield stress distribution to a well-defined value for all strain orientations, thus essentially erasing the memory of the initial structure. It follows that in a well-relaxed sample, plastic events cause the abrupt (nucleation-like) emergence of a local softness contrast and thus precipitate the formation of a band, which, in its early stages, is measurably softer than the steady-state flow. Moreover, this postevent yield stress ensemble presents a mean value comparable to that of the inherent states of a supercooled liquid around the mode-coupling temperature $T_{\rm MCT}$. This, we argue, explains that the transition between brittle and ductile yielding in amorphous materials occurs around a comparable parent temperature. Our data also permit to capture quantitatively the contributions of pressure and density changes and demonstrate unambiguously that they are negligible compared with the changes of softness caused by structural rejuvenation.

cond-mat.mtrl-sci↗

arXiv2018

Stress correlations in glasses

We rigorously establish that, in disordered three-dimensional (3D) isotropic solids, the stress autocorrelation function presents anisotropic terms that decay as $1/r^3$ at long-range, with $r$ the distance, as soon as either pressure or shear stress fluctuations are normal. By normal, we mean that the fluctuations of stress, as averaged over spherical domains, decay as the inverse domain volume. Since this property is required for macroscopic stress to be self-averaging, it is expected to hold generically in all glasses and we thus conclude that the presence of $1/r^3$ stress correlation tails is the rule in these systems. Our proof follows from the observation that, in an infinite medium, when both material isotropy and mechanical balance hold, (i) the stress autocorrelation matrix is completely fixed by just two radial functions: the pressure autocorrelation and the trace of the autocorrelation of stress deviators; furthermore, these two functions (ii) fix the decay of the fluctuations of sphere-averaged pressure and deviatoric stresses for windows of increasing volume. Our conclusion is reached because, due to the precise analytic relation (i) fixed by isotropy and mechanical balance, the constraints arising via (ii) from the normality of stress fluctuations demand the spatially anisotropic stress correlation terms to decay as $1/r^3$ at long-range. For the sake of generality, we also examine situations when stress fluctuations are not normal.

cond-mat.soft↗

arXiv2016

Effects of disorder and chain stiffening on the elasticity of flexible polymer networks

We examine how the distribution of contour lengths and the high-stretch stiffening of individual chain segments affect the macroscopic shear modulus of flexible polymer gels, using a 2D numerical model, in which polymer segments form a triangular network and disorder is introduced by varying their contour lengths. We show that in the relevant parameter range: (i) the non-affine contribution to the shear modulus is negligible, i.e. the Born approximation is satisfactory; (ii) the shear modulus is dominated by the contribution originating from equilibrium chain tensions. Moreover, mechanical equilibration at the nodes induces specific correlations between the end-to-end distances and contour lengths of chain segments, which must be properly accounted for to construct reasonable estimates of chain pressure and shear modulus.

cond-mat.soft↗

arXiv2012

Ultrafast spherulitic crystal growth as a stress-induced phenomenon specific of fragile glass-formers

We propose a model for the abrupt emergence, below temperatures close to the glass transition, of the ultra-fast (GC) steady mode of spherulitic crystal growth in deeply undercooled liquids. We interpret this phenomenon as controlled by the interplay between the generation of stresses by crystallization and their partial release by flow in the surrounding amorphous visco-elastic matrix. Our model is consistent with both the observed ratios ($\sim10^4$) of fast-to-slow velocities and the fact that fast growth emerges close to the glass transition. It leads us to conclude that the existence of a fast growth regime requires both (i) a high fragility of the glassformer; (ii) the fine sub-structure specific of spherulites. It finally predicts that the transition is hysteretic, thus allowing for an independent experimental test.

cond-mat.mtrl-sci↗

arXiv2011

A second-order pressure-accurate finite-difference scheme for the Stokes problem with rigid non-conforming boundaries

We present a finite-difference scheme which solves the Stokes problem in the presence of curvilinear non-conforming interfaces and provides second-order accuracy on physical field (velocity, vorticity) and especially on pressure. The gist of our method is to rely on the Helmholtz decomposition of the Stokes equation: the pressure problem is then written in an integral form devoid of the spurious sources known to be the cause of numerical boundary layer error in most implementations, leading to a discretization which guarantees a strict enforcement of mass conservation. The ghost method is furthermore used to implement the boundary values of pressure and vorticity near curved interfaces.

physics.flu-dyn↗

arXiv2011

Shear thickening and migration in granular suspensions

We study the emergence of shear thickening in dense suspensions of non-Brownian particles. We combine local velocity and concentration measurements using Magnetic Resonance Imaging with macroscopic rheometry experiments. In steady state, we observe that the material is heterogeneous, and we find that that the local rheology presents a continuous transition at low shear rate from a viscous to a shear thickening, Bagnoldian, behavior with shear stresses proportional to the shear rate squared, as predicted by a scaling analysis. We show that the heterogeneity results from an unexpectedly fast migration of grains, which we attribute to the emergence of the Bagnoldian rheology. The migration process is observed to be accompanied by macroscopic transient discontinuous shear thickening, which is consequently not an intrinsic property of granular suspensions.

cond-mat.soft↗

arXiv2011

Robustness of avalanche dynamics in sheared amorphous solids as probed by transverse diffusion

Using numerical simulations, we perform an extensive finite-size analysis of the transverse diffusion coefficient in a sheared 2D amorphous solid, over a broad range of strain rates, at temperatures up to the supercooled liquid regime. We thus obtain direct qualitative evidence for the persistence of correlations between elementary plastic events up to the vicinity of the glass transition temperature $T_g$. A quantitative analysis of the data, combined with a previous study of the $T$- and $\dotγ$-dependence of the macroscopic stress \cite{ChattorajCaroliLemaitre2010}, leads us to conclude that the average avalanche size remains essentially unaffected by temperature up to $T\sim0.75 T_g$.

cond-mat.mtrl-sci↗

arXiv2010

Universal, additive effect of temperature on the rheology of amorphous solids

Extensive measurements of macroscopic stress in a 2D LJ glass, over a broad range of temperatures ($T$) and strain rates ($\dotγ$), demonstrate a very significant decrease of the flowing stress with $T$, even much below the glass transition. A detailed analysis of the interplay between loading, thermal activation, and mechanical noise leads us to propose that over a broad ($\dotγ,T$) region, the effect of temperature amounts to a mere lowering of the strains at which plastic events occur, while the athermal avalanche dynamics remains essentially unperturbed. Temperature is then shown to correct the athermal stress by a (negative) additive contribution which presents a universal form, thus bringing support to and extending an expression proposed by Johnson and Samwer [1]. Our prediction is shown to match strikingly well numerical data up to the vicinity of $T_g$.

cond-mat.mtrl-sci↗

arXiv2009

Rate-Dependent Avalanche Size in Athermally Sheared Amorphous Solids

We perform an extensive numerical study of avalanche behavior in a 2D LJ glass at T=0, sheared at finite strain rates $\dotγ$. From the finite size analysis of stress fluctuations and of transverse diffusion we show that flip-flip correlations remain relevant at all realistic strain rates. We predict that the avalanche size scales as $\dotγ^{-1/d}$, with $d$ the space dimension.

cond-mat.mtrl-sci↗