arXiv subjects

Sébastien Guenneau

Publications and source records attributed to Sébastien Guenneau.

At least 37 records · Page 2Linked to original sources

arXiv2022

Mapping of Elastic Properties of Twisting Metamaterials onto Micropolar Continuum using Static Calculations

Recent developments in the engineering of metamaterials have brought forth a myriad of mesmerizing mechanical properties that do not exist in ordinary solids. Among these, twisting metamaterials, acoustical chirality, or Willis coupling are sample-size dependent. The purpose of this work is, first, to examine the mechanical performance of a new twisting cubic metamaterial. Then, we perform a comparative investigation of its twisting behavior using the finite element method on microstructure elements computation, an analytical model, and we compare them to Eringen micropolar continuum. Notably, the results of the three models are in good qualitative and quantitative agreements. Finally, a systematic comparison of dispersion relations was made for the continuum and for the microstructures with different sizes in unit cells as final proof of perfect mapping.

physics.app-ph↗

arXiv2022

Longitudinal-Twist Wave Converter based on Chiral Metamaterials

Advances in material architectures have enabled endowing materials with exotic attributes not commonly available in the conventional realm of mechanical engineering. Twisting, a mechanism whereby metamaterials are used to transform static axial load into twist motion, is of particular interest to this study. Herein, computations based on the finite element method, corroborated by an analytical approach derived from applying Lagrange's equations to a monoatomic spring-mass system, are employed to explore the longitudinal-twist (L-T) conversion exhibited by a chiral tetragonal-beam metamaterial. Firstly, we perform an eigenvalue analysis taking into account the polarization states to highlight the potential contribution of the longitudinal mode in the L-T conversion. We contrast the twisting behavior of the chiral cell with that of other homogeneous medium, octagonal-tube, and non-chiral cells. Moreover, we demonstrate the influence of the cell's chirality on the L-T conversion using both time-domain and frequency-domain studies. The findings indicate that at least a portion of the longitudinally propagating wave is transformed into twist throughout a broad frequency range and even quasi-totally converted at distinct frequencies.

physics.app-ph↗

arXiv2022

Neolithic stone settlements as locally resonant metasurfaces

We study the dynamic surface response of neolithic stone settlements obtained with seismic ambient noise techniques near the city of Carnac in French Brittany. Surprisingly, we find that menhirs (neolithic human size standing alone granite stones) with an aspect ratio between 1 and 2 periodically arranged atop a thin layer of sandy soil laid on a granite bedrock, exhibit fundamental resonances in the range of 10 to 25 Hz. We propose an analogic Kelvin-Voigt viscoelastic model that explains the origin of such low frequency resonances. We further explore low frequency filtering effect with full wave finite element simulations. Our numerical results confirm the bending nature of fundamental resonances of the menhirs and further suggest additional resonances of rotational and longitudinal nature in the frequency range 25 to 50 Hz. Our study thus paves the way for large scale seismic metasurfaces consisting of granite stones periodically arranged atop a thin layer of regolith over a bedrock, for ground vibration mitigation in earthquake engineering.

physics.geo-ph↗

arXiv2022

High-Quality Resonances in Quasi-Periodic Clusters of Scatterers for Flexural Waves

Multiple scattering theory is applied to the study of clusters of point-like scatterers attached to a thin elastic plate and arranged in quasi-periodic distributions. Two type of structures are specifically considered: the twisted bilayer and the quasi-periodic line. The former consists in a couple of two-dimensional lattices rotated a relative angle, so that the cluster forms a moiré pattern. The latter can be seen as a periodic one-dimensional lattice where an incommensurate modulation is superimposed. Multiple scattering theory allows for the fast an efficient calculation of the resonant modes of these structures as well as for their quality factor, which is thoroughly analyzed in this work. The results show that quasi-periodic structures present a large density of states with high quality factors, being therefore a promising way for the design of high quality wave-localization devices.

physics.class-ph↗

arXiv2022

Active exterior cloaking for the 2D Helmholtz equation with complex wavenumbers and application to thermal cloaking

We design sources for the two-dimensional Helmholtz equation that can cloak an object by cancelling out the incident field in a region, without the sources completely surrounding the object to hide. As in previous work for real positive wavenumbers, the sources are also determined by the Green identities. The novelty is that we prove that the same approach works for complex wavenumbers which makes it applicable to a variety of media, including media with dispersion, loss and gain. Furthermore, by deriving bounds on Graf's addition formulas with complex arguments, we obtain new estimates that allow to quantify the quality of the cloaking effect. We illustrate our results by applying them to achieve active exterior cloaking for the heat equation.

math.AP↗

arXiv2020

Acoustic topological circuitry in square and rectangular phononic crystals

We systematically engineer a series of square and rectangular phononic crystals to create experimental realisations of complex topological phononic circuits. The exotic topological transport observed is wholly reliant upon the underlying structure which must belong to either a square or rectangular lattice system and not to any hexagonal-based structure. The phononic system chosen consists of a periodic array of square steel bars which partitions acoustic waves in water over a broadband range of frequencies (~0.5 MHz). An ultrasonic transducer launches an acoustic pulse which propagates along a domain wall, before encountering a nodal point, from which the acoustic signal partitions towards three exit ports. Numerical simulations are performed to clearly illustrate the highly resolved edge states as well as corroborate our experimental findings. To achieve complete control over the flow of energy, power division and redirection devices are required. The tunability afforded by our designs, in conjunction with the topological robustness of the modes, will result in their assimilation into acoustical devices.

cond-mat.mes-hall↗

arXiv2020

Active Thermal Cloaking and Mimicking

We present an active cloaking method for the parabolic heat (and mass or light diffusion) equation that can hide both objects and sources. By active we mean that it relies on designing monopole and dipole heat source distributions on the boundary of the region to be cloaked. The same technique can be used to make a source or an object look like a different one to an observer outside the cloaked region, from the perspective of thermal measurements. Our results assume a homogeneous isotropic bulk medium and require knowledge of the source to cloak or mimic, but are in most cases independent of the object to cloak.

math.AP↗

arXiv2020

Designing thermal energy harvesting devices with natural materials through optimized microstructures

Metamaterial thermal energy devices obtained from transformation optics have recently attracted wide attention due to their vast potential in energy storage, thermal harvesting or heat manipulation. However, these devices usually require inhomogeneous and extreme material parameters which are difficult to realize in large-scale applications. Here, we demonstrate a general process to design thermal harvesting devices with available natural materials through optimized composite microstructures. We apply two-scale homogenization theory to obtain effective properties of the microstructures. Optimal Latin hypercube technique, combined with a genetic algorithm, is then implemented on the microstructures to achieve optimized design parameters. The optimized microstructures can accurately approximate the behavior of transformed materials. We design such devices and numerically characterize good thermal-energy harvesting performances. To validate the wide-range application of our approach, we illustrate other types of microstructures that mimic well the constitutive parameters. The approach we propose can be used to design novel thermal harvesting devices available with existing technology, and can also act as a beneficial vehicle to explore other transformation optics enabled designs.

physics.app-ph↗

arXiv2020

Hybrid topological guiding mechanisms for photonic crystal fibers

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.

physics.optics↗

arXiv2020

Experimental observations of topologically guided water waves within non-hexagonal structures

We investigate symmetry-protected topological water waves within a strategically engineered square lattice system. Thus far, symmetry-protected topological modes in hexagonal systems have primarily been studied in electromagnetism and acoustics, i.e. dispersionless media. Herein, we show experimentally how crucial geometrical properties of square structures allow for topological transport that is ordinarily forbidden within conventional hexagonal structures. We perform numerical simulations that take into account the inherent dispersion within water waves and devise a topological insulator that supports symmetry-protected transport along the domain walls. Our measurements, viewed with a high-speed camera under stroboscopic illumination, unambiguously demonstrate the valley-locked transport of water waves within a non-hexagonal structure. Due to the tunability of the energy's directionality by geometry, our results could be used for developing highly-efficient energy harvesters, filters and beam-splitters within dispersive media.

physics.flu-dyn↗

arXiv2020

Surface waves from flexural and compressional resonances of beams

We present a three-dimensional model describing the propagation of elastic waves in a soil substrate supporting an array of cylindrical beams experiencing flexural and compressional resonances. The resulting surface waves are of two types. In the sagittal plane, hybridized Rayleigh waves can propagate except within bandgaps resulting from a complex interplay between flexural and compressional resonances. We exhibit a wave decoupled from the hybridized Rayleigh wave which is the elastic analogue of electromagnetic spoof plasmon polaritons. This wave with displacements perpendicular to the sagittal plane is sensitive only to flexural resonances. Similar, yet quantitatively different, physics is demonstrated in a two-dimensional setting involving resonances of plates.

physics.comp-ph↗

arXiv2020

Effective model for elastic waves propagating in a substrate supporting a dense array of plates/beams with flexural resonances

We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with flexural resonances at low frequencies able to perturb significantly the propagation of waves in the ground. An effective model is obtained using asymptotic analysis and homogenization techniques, which can be expressed in terms of the ground alone with effective dynamic (frequency-dependent) boundary conditions of the Robin's type. For an incident plane wave at oblique incidence, the displacement fields and the reflection coefficients are obtained in closed forms and their validity is inspected by comparison with direct numerics in a two-dimensional setting.

physics.class-ph↗

arXiv2019

Homogenization of quasiperiodic structures and two-scale cut-and-projection convergence

Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses the cut-and-projection method that is used to characterize effective properties of quasiperiodic materials. Characterization of cut-and-projection convergence limits of partial differential operators is presented, and correctors are established. We provide the proofs of the results announced in (Wellander et al., 2018) and give further examples. Applications to problems of interest in physics include electrostatic, elastostatic and quasistatic magnetic cases.

math.AP↗

arXiv2019

Acoustic cloaking: geometric transform, homogenization and a genetic algorithm

A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows to perform cloaking. To approximate such complex metamaterials we apply results of the theory of homogenization and combine them with a genetic algorithm. To illustrate the power of our approach, we design three types of cloaks composed of isotropic concentric layers structured with three types of perforations: curved rectangles, split rings and crosses. These cloaks have parameters compatible with existing technology and they mimic the behavior of the transformed material. Numerical simulations have been performed to qualitatively and quantitatively study the cloaking efficiency of these metamaterials.

physics.comp-ph↗

arXiv2019

Role of nanophotonics in the birth of seismic megastructures

The discovery of photonic crystals thirty years ago, in conjunction with research advances in plasmonics and metamaterials, has inspired the concept of decameter scale metasurfaces, coined seismic metamaterials, for an enhanced control of surface (Love and Rayleigh) and bulk (shear and pressure) elastodynamic waves. The powerful mathematical tools of coordinate transforms, effective medium and Floquet-Bloch theories, which have revolutionized nanophotonics, can be translated in the language of civil engineering and geophysics. Experiments on seismic metamaterials made of buried elements in the soil demonstrate that the fore mentioned tools make possible a novel description of complex phenomena of soil-structure interaction during a seismic disturbance. But the concepts are already moving to more futuristic concepts and the same notions developed for structured soils are now used to examine the effects of buildings viewed as above surface resonators in megastructures such as metacities. But this perspective of the future should not make us forget the heritage of the ancient peoples. Indeed, we finally point out the striking similarity between an invisibility cloak design and the architecture of some ancient megastructures as antique Gallo-Roman theaters and amphitheatres.

physics.geo-ph↗

arXiv2019

The influence of building interactions on seismic and elastic surface waves

We outline some recent research advances on the control of elastic waves in thin and thick plates, that have occurred since the large scale experiment [Phys. Rev. Lett. 112, 133901, 2014] that demonstrated significant interaction of surface seismic waves with holes structuring sedimentary soils at the meter scale. We further investigate the seismic wave trajectories in soils structured with buildings. A significant substitution of soils by inclusions, acting as foundations, raises the question of the effective dynamic properties of these structured soils. Buildings, in the case of perfect elastic conditions for both soil and buildings, are shown to interact and strongly influence elastic surface waves; such site-city seismic interactions were pointed out in [Bulletin of Seismological Society of America 92, 794-811, 2002], and we investigate a variety of scenarios to illustrate the variety of behaviours possible.

physics.class-ph↗

arXiv2018

Electromagnetic waves in photonic crystals: laws of dispersion, causality and analytical properties

Photonic crystals are periodic structures which prevent light propagation along one or more directions in certain frequency intervals. Their band spectrum is usually analyzed using Floquet-Bloch decomposition. This spectrum is located on the real axis, and it enters the complex plane when absorption and dispersion is considered in the dielectric permittivity of material constituents. Here, we review fundamental definition and properties of dispersion law and group velocity in photonic crystals and we illustrate them with numerical examples.

physics.optics↗

arXiv2017

Emergence of Seismic Metamaterials: Current State and Future Perspectives

Following the advent of electromagnetic metamaterials at the turn of the century, researchers working in other areas of wave physics have translated concepts of electromagnetic metamaterials to acoustics, elastodynamics, as well as to heat, mass and light diffusion processes. In elastodynamics, seismic metamaterials have emerged in the last decade for soft soils structured at the meter scale, and have been tested thanks to full-scale experiments on holey soils five years ago. Born in the soil, seismic metamaterials grow simultaneously on the field of tuned-resonators buried in the soil, around building's foundations or near the soil-structure's interface, and on the field of above-surface resonators. In this perspective article, we quickly recall some research advances made in all these types of seismic metamaterials and we further dress an inventory of which material parameters can be achieved and which cannot, notably from the effective medium theory perspective. We finally envision perspectives on future developments of large scale auxetic metamaterials for building's foundations, forests of trees for seismic protection and metamaterial-like transformed urbanism at the city scale.

physics.app-ph↗