arXiv subjects

Gal Shmuel

Publications and source records attributed to Gal Shmuel.

17 recordsLinked to original sources

arXiv2026

Nonlocal thermal Willis coupling in laminated conductors

Building on Willis' homogenization framework, recent work has revealed that heterogeneous conductors exhibit macroscopic thermal bianisotropy, in which the macroscopic heat flux and entropy are nonlocally coupled to both temperature and temperature gradient. Existing numerical examples, however, are limited to the subwavelength regime. Here, we provide the first explicit demonstration of this spatial nonlocality by computing the effective kernels of a periodic laminate using three independent homogenization methods. The three approaches yield consistent nonlocal cross-coupling terms, clarifying the roles of spatial asymmetry and averaging choice. We also calculate the corresponding thermal impedance and show that it is direction-dependent, highlighting a physical signature of thermal bianisotropy relevant to thermal metamaterials.

math-ph↗

arXiv2024

Symmetry-driven Phononic Metamaterials

Phonons are quasiparticles associated with mechanical vibrations in materials. They are at the root of the propagation of sound and elastic waves, as well as of thermal phenomena, which are pervasive in our everyday life and in many technologies. The fundamental understanding and control of phonon responses in natural and artificial media are key in the context of communications, isolation, energy harvesting and control, sensing and imaging. It has recently been realized that controlling different symmetry classes at the microscopic and mesoscopic scales in synthetic media offers a powerful tool to precisely tailor phononic responses for advanced acoustic and elastodynamic wave control. In this Review, we survey the recent progress in the design and synthesis of artificial phononic media, namely phononic crystals and metamaterials, guided by symmetry principles. Starting from tailored broken spatial symmetries, we discuss their interplay with time symmetries for non-reciprocal and non-conservative phenomena. We also address broader concepts that combine multiple symmetry classes to induce exotic phononic wave transport. We conclude with an outlook on future research directions based on symmetry engineering for the advanced control of phononic waves.

physics.app-ph↗

arXiv2024

Perspective on Non-Hermitian Elastodynamics

The manipulation of mechanical waves is a long-standing challenge for scientists and engineers, as numerous devices require their control. The current forefront of research in the control of classical waves has emerged from a seemingly unrelated field, namely, non-Hermitian quantum mechanics. By drawing analogies between this theory and those of classical systems, researchers have discovered phenomena that defy conventional intuition and have exploited them to control light, sound, and elastic waves. Here, we provide a brief perspective on recent developments, challenges and intricacies that distinguish non-Hermitian elastodynamics from optics and acoustics. We close this perspective with an outlook on potential directions such as topological phases in non-Hermitian elastodynamics and broken Hermitian symmetry in materials with electromomentum couplings.

physics.class-ph↗

arXiv2023

Discrete One-dimensional Models for the Electromomentum Coupling

Willis dynamic homogenization theory revealed that the effective linear momentum of elastic composites is coupled to their effective strain. % This result, which is partially due to asymmetry at the subwavelength scale, implies that spatially-uniform but time-varying stress can induce temporal variations in the macroscopically observable momentum. Recent generalization of Willis' dynamic homogenization theory to the case of piezoelectric composites further revealed that their effective linear momentum is also coupled to the effective electric field. Here, we introduce the simplest possible model -- a one-dimensional discrete model -- that exhibits this so-called electromomentum coupling in subwavelength composites. We utilize our model to elucidate the physical origins of this phenomenon, illustrate its mechanism, and identify local resonances which lead to elevated Willis- and electromomentum coupling in narrow frequency bands. The results provide intuitive guidelines for the design of this coupling in piezoelectric metamaterials.

cond-mat.mtrl-sci↗

arXiv2022

Oblique scattering from non-Hermitian optical waveguides

A judicious design of gain and loss leads to counterintuitive wave phenomena that are inaccessible by conservative systems. Notably, such designs can give rise to laser-absorber modes and anisotropic transmission resonances. Here, we analyze the emergence of these phenomena in an optical scatterer with sinusoid gain-loss modulation that is subjected to monochromatic oblique waves. We derive an analytical solution to the problem, with which we show how the scatterer parameters, and specifically the modulation phase and incident angle, constitute a real design space to access these phenomena.

physics.optics↗

arXiv2022

Maximizing the electromomentum coupling in piezoelectric laminates

Asymmetric piezoelectric composites exhibit coupling between their macroscopic linear momentum and electric field, a coupling that does not appear at the microscopic scale. This electromomentum coupling constitutes an additional knob to tailor the dynamic response of the medium, analogously to the Willis coupling in elastic composites. Here, we employ topology- and free material optimization approaches to maximize the electromomentum coupling of periodic piezoelectric laminates in the low frequency, long-wavelength limit. We find that the coupling can be enhanced by orders of magnitude, depending on the degrees of freedom in the optimization process. The optimal compositions that we find provide guidelines for the design of metamaterials with maximum electromomentum coupling, paving the way for their integration in wave control applications.

cond-mat.mtrl-sci↗

arXiv2020

Fundamental principles for generalized Willis metamaterials

Metamaterials whose momentum is constitutively coupled with their strain show promise in wave manipulation for engineering purposes and are called Willis materials. They were discovered using an effective medium theory which shows that their response is non-local in space and time. Recently, we generalized this theory to account for piezoelectricity and demonstrated that the effective momentum can depend constitutively on the electric field, thereby enlarging the design space for metamaterials. Here, we develop the mathematical restrictions on the effective properties of such generalized Willis materials, owing to passivity, reciprocity, and causality. Establishing these restrictions is of fundamental significance, as they test the validity of theoretical and experimental results and applicational importance since they provide elementary bounds for the maximal response that potential devices may achieve.

physics.app-ph↗

arXiv2020

Oscillating vector solitary waves in soft laminates

Vector solitary waves are nonlinear waves of coupled polarizations that propagate with constant velocity and shape. In mechanics, they hold the potential to control locomotion, mitigate shocks and transfer information, among other functionalities. Recently, such elastic waves were numerically observed in compressible rubber-like laminates. Here, we conduct numerical experiments to characterize the possible vector solitary waves in these laminates, and expose a new type of waves whose amplitude and velocity oscillate periodically without dispersing in time. This oscillation is a manifestation of a periodic transfer of energy between the two wave polarizations, which we consider as internal mode of the solitary wave. We find that the vector solitary waves propagate faster at higher amplitudes, and determine a lower bound for their velocity. We describe a procedure for identifying which initial strains generate such vector solitary waves. This procedure also enables an additional classification between tensile and compressive solitary waves, according to the way that the axial strain changes as the waves propagate.

cond-mat.soft↗

arXiv2019

Linking scalar elastodynamics and non-Hermitian quantum mechanics

Recent years have seen a fascinating pollination of ideas from quantum theories to elastodynamics---a theory that phenomenologically describes the time-dependent macroscopic response of materials. Here, we open route to transfer additional tools from non-Hermitian quantum mechanics. We begin by identifying the differences and similarities between the one-dimensional elastodynamics equation and the time-independent Schrodinger equation, and finding the condition under which the two are equivalent. Subsequently, we demonstrate the application of the non-Hermitian perturbation theory to determine the response of elastic systems; calculation of leaky modes and energy decay rate in heterogenous solids with open boundaries using a quantum mechanics approach; and construction of degeneracies in the spectrum of these assemblies. The latter result is of technological importance, as it introduces an approach to harness extraordinary wave phenomena associated with non-Hermitian degeneracies for practical devices, by designing them in simple elastic systems. As an example of such application, we demonstrate how an assembly of elastic slabs that is designed with two degenerate shear states according to our scheme, can be used for mass sensing with enhanced sensitivity by exploiting the unique topology near the exceptional point of degeneracy.

cond-mat.soft↗

arXiv2019

Symmetry Breaking Creates Electro-Momentum Coupling in Piezoelectric Metamaterials

Metamaterials posses microstructure designed to acquire properties not found in nature. An epitome in acoustics and solid mechanics is Willis coupling, which refers to the particle velocity-stress coupling, and of great significance since it controls mechanical waves. We here reveal new couplings, analogous to Willis coupling, when considering patterns of materials that mechanically interact with magnetic, electric or thermal fields. To this end, we develop a rigorous homogenization method for the effective properties of such responsive metamaterials. As an example, we apply the scheme to piezoelectric materials, and unveil coupling of the velocity and electric fields. Hence, Willis-like couplings in responsive metamaterials open new avenues for active wave control by modulation of external stimuli.

physics.app-ph↗

arXiv2019

Anomalous energy transport in laminates with exceptional points

Recent interest in metamaterials has led to a renewed study of wave mechanics in different branches of physics. Elastodynamics involves a special intricacy, owing to a coupling between the volumetric and shear parts of the elastic waves. Through a study of in-plane waves traversing periodic laminates, we here show that this coupling can result with unusual energy transport. We find that the corresponding frequency spectrum contains modes which simultaneously attenuate and propagate, and demonstrate that these modes coalesce to purely propagating modes at exceptional points, a property that was recently reported in parity-time symmetric systems. We show that the laminate exhibits metamaterial features near these points, such as negative refraction, and beam steering and splitting. While negative refraction in laminates has been demonstrated before by considering pure shear waves impinging an interface with multiple layers, here we realize it for coupled waves impinging a simple single-layer interface. This feature, together with the appearance of exceptional points, are absent from the model problem of anti-plane shear waves which have no volumetric part, and hence from the mathematically identical electromagnetic waves. Our work further paves the way for applications such as asymmetric mode switches, by encircling exceptional points in a tangible, purely elastic apparatus.

physics.app-ph↗

arXiv2019

Smooth waves and shocks of finite amplitude in soft materials

Recently developed soft materials exhibit nonlinear wave propagation with potential applications for energy trapping, shock mitigation and wave focusing. We address finitely deformed materials subjected to combined transverse and axial impacts, and study the resultant nonlinear waves. We determine the dependency of the induced motion on the impact, pre-deformation and the employed constitutive models. We analyze the neo-Hookean constitutive model and show it cannot capture shear shocks and tensile-induced shocks, in contrast with experimental results on soft materials. We find that the Gent constitutive model predicts that compressive impact may not be sufficient to induce a quasi-pressure shock---yet it may induce a quasi-shear shock, where tensile impact can trigger quasi-pressure shock ---and may simultaneously trigger a quasi-shear shock, in agreement with experimental data. We show that the tensile impact must be greater than a calculated threshold value to induce shock, and demonstrate that this threshold is lowered by application of pre-shear.

cond-mat.soft↗

arXiv2018

On the band gap universality multiphase laminates and its applications

\citet{Shmuel2016JMPS} discovered that all infinite band structures of waves at normal incidence in two-phase laminates are encapsulated in a compact universal manifold. We show that manifolds of higher dimensionality encapsulate the band structures of all multiphase laminates. We use these manifolds to determine the density of gaps in the spectrum, and prove it is invariant with respect to certain properties. We further demonstrate that these manifolds are useful for formulating optimization problems on the gaps width, for which we develop a simple bound. Using our theory, we numerically study the dependency of the gaps density and width on the impedance and number of phases. Finally, we show that in certain settings, our analysis applies to non-linear multiphase laminates, whose band diagram is tunable by finite pre-deformations. Through simple examples, we demonstrate how the universality of our representation is useful for characterizing this tunability in multiphase laminates.

cond-mat.mtrl-sci↗

arXiv2018

Dynamic homogenization of composite and locally resonant flexural systems

Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion relations of infinitely periodic flexural systems. Our scheme evades the need to calculate field variables at each point, yet capable of recovering them, if wanted. Through reflected energy analysis in scattering problems, we quantify the applicability of the homogenized approximation. We show that at low frequencies, our model replicates the transmission characteristics of semi-infinite and finite periodic media. We quantify the decline in the approximation as frequency increases, having certain characteristics sensitive to microscale details. We observe that the homogenized model captures the dynamic response of locally resonant media more accurately and across a wider range of frequencies than the dynamic response of media without local resonance.

physics.app-ph↗

arXiv2015

Universality and optimality of band-gaps in laminated media

We find that the frequency spectra of layered phononic and photonic composites admit a universal struc- ture, independent of the geometry of the periodic-cell and the specific physical properties. We show that this representation extends to highly deformable and multi-physical materials of tunable spectra. The structure is employed to establish universal properties of the corresponding band-gaps, and to rigorously determine their sta- tistical and optimal characteristics. Specifically, we investigate the density of the gaps, their maximal width and expected value. As a result, rules for tailoring the laminate according to desired spectra properties follow. Our representation further facilitates characterizing the tunability of the band-structure of soft and multi-physical materials.

cond-mat.mtrl-sci↗

arXiv2012

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular the the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity. Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.

cond-mat.soft↗

arXiv2011

The Rayleigh-Lamb wave propagation in dielectric elastomer layers subjected to large deformations

The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of mechanically traction-free layer, which is an extension of the Rayleigh-Lamb problem in the purely elastic case. Two other loading configurations are accounted for too. Subsequently, numerical examples for the dispersion relations are evaluated for a dielectric solid governed by an augmented neo-Hookean strain energy. It is found that the the phase speeds and frequencies strongly depend on the electric excitation and pre-stretch. These findings lend themselves at the possibility of controlling the propagation velocity as well as filtering particular frequencies with suitable choices of the electric bias field.

cond-mat.soft↗