Comptes Rendus
Past, present and future of seismic metamaterials: experiments on soil dynamics, cloaking, large scale analogue computer and space–time modulations
Comptes Rendus. Physique, Volume 21 (2020) no. 7-8, pp. 767-785.

Some properties of electromagnetic metamaterials have been translated, using some wave analogies, to surface seismic wave control in sedimentary soils structured at the meter scale. Two large scale experiments performed in 2012 near the French cities of Grenoble [] and Lyon [] have confirmed the usefulness of this methodology and its potential influence on soil-structure interaction. We present here a new perspective on the in-situ experiment near Lyon, which unveils energy corridors in the seismic lens. We further introduce a concept of time-modulated seismic metamaterial underpined by an effective model based on Willis’s equations. As a first application, we propose that ambient seismic noise time-modulates structured soils that can be viewed as moving media. In the same spirit, a design of an analogous seismic computer is proposed making use of ambient seismic noise. We recall that ancient Roman theaters and forests of trees are two examples of large scale structures that behave in a way similar to electromagnetic metamaterials: invisibility cloaks and rainbows, respectively. Seismic metamaterials can thus not only be implemented for shielding, lensing and cloaking of potentially deleterious Rayleigh waves, but they also have potential applications in energy harvesting and analogous computations using ambient seismic noise, and this opens new vistas in seismic energy harvesting and conversion through the use of natural or artificial soil structuring.

Certaines propriétés des métamatériaux électromagnétiques ont été traduites, en utilisant certaines analogies d’ondes, en contrôle des ondes sismiques de surface dans des sols sédimentaires structurés à l’échelle du mètre. Deux expériences à grande échelle réalisées en 2012 près des villes françaises de Grenoble [] et Lyon [] ont confirmé l’utilité de cette méthodologie et son influence potentielle sur l’interaction sol-structure. Nous présentons ici une nouvelle perspective sur l’expérience in-situ menée près de Lyon, qui dévoile des couloirs d’énergie dans la lentille sismique. Nous introduisons en outre un concept de métamatériau sismique modulé dans le temps sous-tendu par un modèle effectif s’appuyant sur les équations de Willis. Dans une première application, nous proposons que le bruit sismique ambiant module dans le temps les sols structurés pouvant être considérés comme des milieux en mouvement. Dans le même esprit, il est proposé de concevoir un calculateur analogique sismique utilisant le bruit sismique ambiant. Nous rappelons que les anciens théâtres romains et les forêts d’arbres sont deux exemples de structures à grande échelle qui se comportent de manière similaire aux métamatériaux électromagnétiques : capes d’invisibilité et rainbows (anglicisme d’arcs-en-ciel), respectivement. Les métamatériaux sismiques peuvent donc non seulement être mis en œuvre pour des murailles, lentilles et capes pour ondes de Rayleigh potentiellement délétères, mais ils ont également des applications potentielles dans la récupération d’énergie et des ordinateurs analogiques utilisant le bruit sismique ambiant, ce qui ouvre de nouvelles perspectives dans la récupération et la conversion d’énergie sismique grâce à l’exploitation de structuration naturelle ou artificielle des sols.

Published online:
DOI: 10.5802/crphys.39
Keywords: Seismic metamaterial, Transformational physics, Time-modulated medium, Homogenization, Analogue computer, Ambient seismic energy
Mot clés : Métamatériaux sismiques, Physique transformationnelle, Milieux modulés en temps, Homogénéisation, Calculateur analogique, Energie sismique ambiante

Stéphane Brûlé 1; Sébastien Guenneau 2

1 Aix Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
2 UMI 2004 Abraham de Moivre-CNRS, Imperial College London, London SW7 2AZ, UK
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRPHYS_2020__21_7-8_767_0,
     author = {St\'ephane Br\^ul\'e and S\'ebastien Guenneau},
     title = {Past, present and future of seismic metamaterials: experiments on soil dynamics, cloaking, large scale analogue computer and space{\textendash}time modulations},
     journal = {Comptes Rendus. Physique},
     pages = {767--785},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {21},
     number = {7-8},
     year = {2020},
     doi = {10.5802/crphys.39},
     language = {en},
}
TY  - JOUR
AU  - Stéphane Brûlé
AU  - Sébastien Guenneau
TI  - Past, present and future of seismic metamaterials: experiments on soil dynamics, cloaking, large scale analogue computer and space–time modulations
JO  - Comptes Rendus. Physique
PY  - 2020
SP  - 767
EP  - 785
VL  - 21
IS  - 7-8
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.39
LA  - en
ID  - CRPHYS_2020__21_7-8_767_0
ER  - 
%0 Journal Article
%A Stéphane Brûlé
%A Sébastien Guenneau
%T Past, present and future of seismic metamaterials: experiments on soil dynamics, cloaking, large scale analogue computer and space–time modulations
%J Comptes Rendus. Physique
%D 2020
%P 767-785
%V 21
%N 7-8
%I Académie des sciences, Paris
%R 10.5802/crphys.39
%G en
%F CRPHYS_2020__21_7-8_767_0
Stéphane Brûlé; Sébastien Guenneau. Past, present and future of seismic metamaterials: experiments on soil dynamics, cloaking, large scale analogue computer and space–time modulations. Comptes Rendus. Physique, Volume 21 (2020) no. 7-8, pp. 767-785. doi : 10.5802/crphys.39. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.39/

[1] S. Brûlé; E. Javelaud; S. Enoch; S. Guenneau Experiments on seismic metamaterials: molding surface waves, Phys. Rev. Lett., Volume 112 (2014), 133901 | DOI

[2] S. Brûlé; E. Javelaud; S. Enoch; S. Guenneau Flat lens for seismic waves, Sci. Rep., Volume 7 (2017), 18066

[3] S. Brûlé; C. Deprez; C. Fernandez; M. Givry; K. Manchuel; G. Mendoza; B. Richard; C. Taylor Report of the post-seismic mission on the mexico earthquake of september 19th, 20017 (2017) (Technical report)

[4] S. Brûlé; S. Enoch; S. Guenneau Role of nanophotonics in the birth of seismic megastructures, Nanophotonics, Volume 8 (2019), pp. 1591-1605 | DOI

[5] H. Nassar; X. Xu; A. Norris; G. Huang Modulated phononic crystals: non-reciprocal wave propagation and willis materials, J. Mech. Phys. Solids, Volume 101 (2017), pp. 10-29 | DOI | MR

[6] J. Willis Variational principles for dynamic problems in inhomogeneous elastic media, Wave Motion, Volume 3 (1981), pp. 1-11 | DOI | Zbl

[7] Y. Liu; S. Guenneau; B. Gralak Artificial dispersion via high-order homogenization: magnetoelectric coupling and magnetism from dielectric layers, Proc. R. Soc. Lond. A, Volume 469 (2013), 20130240 | MR | Zbl

[8] P. Huidobro; E. Galiffi; S. Guenneau; R. Craster; J. Pendry Fresnel drag in space-time modulated metamaterials, Proc. Natl Acad. Sci. USA, Volume 116 (2019), pp. 24943-24948 | DOI

[9] A. Silva; F. Monticone; G. Castaldi; V. Galdi; A. Alu; N. Engheta Performing mathematical operations with metamaterials, Science, Volume 343 (2014), pp. 160-163 | DOI | MR | Zbl

[10] N. Estakhri; B. Edwards; N. Engheta Inverse-designed metastructures that solve equations, Science, Volume 22 (2019), pp. 1333-1338 | DOI | MR | Zbl

[11] S. Brûlé; S. Enoch; S. Guenneau Sols structurés sous sollicitation dynamique : des métamatériaux en géotechnique, Rev. Fr. Geotech., Volume 151 (2017), p. 4 | DOI

[12] G. Dupont; O. Kimmoun; B. Molin; S. Guenneau; S. Enoch Numerical and experimental study of an invisibility carpet in a water channel, Phys. Rev. E, Volume 91 (2015), 023010 | DOI

[13] M. Farhat; S. Enoch; S. Guenneau; A. Movchan Broadband cylindrical acoustic cloak for linear surface waves in a fluid, Phys. Rev. Lett., Volume 101 (2008), 134501 | DOI

[14] S. Brûlé; S. Enoch; S. Guenneau Emergence of seismic metamaterials: current state and future perspectives, Phys. Lett. A, Volume 384 (2020), 126034 | DOI

[15] J. Xu; X. Jiang; N. Fang; E. Georget; R. Abdeddaim; J. Geffrin; M. Farhat; P. Sabouroux; S. Enoch; S. Guenneau Molding acoustic, electromagnetic and water waves with a single cloak, Sci. Rep., Volume 5 (2015), 10678

[16] M. Farhat; S. Guenneau; S. Enoch Broadband cloaking of bending waves via homogenization of multiply perforated radially symmetric and isotropic thin elastic plates, Phys. Rev. B, Volume 85 (2012), 020301 | DOI

[17] N. Stephen On energy harvesting from ambient noise, J. Sound Vib., Volume 293 (2006), pp. 413-425 | DOI

[18] S. Brûlé; S. Enoch; S. Guenneau Experimental evidence of auxetic features in seismic metamaterials: Ellipticity of seismic rayleigh waves for subsurface architectured ground with holes (2018) (https://arxiv.org/abs/1809.05841)

[19] S. Brûlé; S. Enoch; S. Guenneau On the possibility of seismic rogue waves in very soft soils, 2020 (https://arxiv.org/abs/2004.07037)

[20] B. Ungureanu; S. Guenneau; Y. Achaoui; A. Diatta; M. Farhat; H. Hutridurga; R. Craster; S. Enoch; S. Brûlé The influence of building interactions on seismic and elastic body waves, EPJ Appl. Metamater., Volume 6 (2019), p. 18 | DOI

[21] A. Colombi; P. Roux; S. Guenneau; P. Gueguen; R. Craster Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances, Sci. Rep., Volume 6 (2016), 19238 | DOI

[22] A. Colombi; D. Colquitt; P. Roux; S. Guenneau; R. Craster A seismic metamaterial: the resonant metawedge, Sci. Rep., Volume 6 (2016), 27717 | DOI

[23] K. Tsakmakidis; A. Boardman; O. Hess Trapped rainbow storage of light in metamaterials, Nature, Volume 450 (2007), p. 397 | DOI

[24] A. Maurel; J. Marigo; K. Pham; S. Guenneau Conversion of love waves in a forest of trees, Phys. Rev. B, Volume 98 (2018), 134311 | DOI

[25] J. D. Ponti; A. Colombi; R. Ardito; F. Braghin; A. Corigliano; R. Craster Graded metasurface for enhanced sensing and energy harvesting, New J. Phys., Volume 22 (2020), 013013

[26] P. Vitruvius Ten Books on Architecture. Vol. 15, Cambridge University Press, New York, 1999

[27] A. B. Clymer The mechanical analog computers of Hannibal Ford and William Newell, IEEE Ann. Hist. Comput., Volume 15 (1993), pp. 19-34 | DOI

[28] K. Lurie An Introduction to the Mathematical Theory of Dynamic Materials, Springer, New York, 2007 | Zbl

[29] A. Fresnel Lettre d’augustin fresnel a francois arago sur l’influence du mouvement terrestre dans quelques phenomenes d’optique, Ann. Chem. Phys., Volume 9 (1818), pp. 57-67

[30] H. Fizeau Sur les hypotheses relatives a l’ether lumineux, C. R. Acad. Sci., Volume 33 (1851), pp. 349-355

[31] T. Devaux; V. Tournat; O. Richoux; V. Pagneux Asymmetric acoustic propagation of wave packets via the self-demodulation effect, Phys. Rev. Lett., Volume 115 (2015), 234301 | DOI

[32] M. Kadic; T. Buckmann; R. Schittny; M. Wegener Metamaterials beyond electromagnetism, Rep. Prog. Phys., Volume 76 (2013), 126501 | DOI

[33] B. Ungureanu; Y. Achaoui; S. Enoch; S. Brûlé; S. Guenneau Auxetic-like metamaterials as novel earthquake protections, EPJ Appl. Metamater., Volume 2015 (2016), p. 17

[34] R. Aznavourian; T. Puvirajesinghe; S. Brûlé; S. Enoch; S. Guenneau Spanning the scales of mechanical metamaterials using time domain simulations in transformed crystals, graphene flakes and structured soils, J. Phys. Condens. Matter, Volume 29 (2017), 433004 | DOI

[35] F. Meseguer; M. Holgado; D. Caballero; N. Benaches; J. Sanchez-Dehesa; C. Lopez; J. Llinares Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-bandgap, Phys. Rev. B, Volume 59 (1999), 12169 | DOI

[36] Y. Achaoui; A. Khelif; S. Benchabane; L. Robert; V. Laude Experimental observation of locally-resonant and bragg band gaps for surface guided waves in a phononic crystal of pillars, Phys. Rev. B, Volume 83 (2011), 104201 | DOI

[37] M. Miniaci; A. Krushynska; F. Bosia; N. Pugno Large scale mechanical metamaterials as seismic shields, New J. Phys., Volume 18 (2016), 083041 | DOI

[38] Y. Achaoui; T. Antonakakis; S. Brûlé; R. Craster; S. Enoch; S. Guenneau Clamped seismic metamaterials: ultra-low frequency stop bands, New J. Phys., Volume 19 (2017), 063022 | DOI

[39] A. Palermo; S. Krödel; K. H. Matlack; R. Zaccherini; V. K. Dertimanis; E. N. Chatzi; A. Marzani; C. Daraio Hybridization of guided surface acoustic modes in unconsolidated granular media by a resonant metasurface, Phys. Rev. Appl., Volume 9 (2018), 054026 | DOI

[40] M. Lott; P. Roux; S. Garambois; P. Gueguen; A. Colombi Evidence of metamaterial physics at the geophysics scale: the metaforet experiment, Geophys. J. Int., Volume 220 (2020), pp. 1330-1339

[41] D. Mu; H. Shu; L. Zhao; S. An A review of research on seismic metamaterials, Adv. Eng. Mater., Volume 22 (2020), e1901148

[42] H. Wong; M. Trifunac; B. Westermo Effects of surface and subsurface irregularities on the amplitude of monochromatic waves, Bull. Seismol. Soc. Am., Volume 67 (1977), pp. 353-368

[43] A. Diatta; Y. Achaoui; S. Brûlé; S. Enoch; S. Guenneau Control of Rayleigh-like waves in thick plate willis metamaterials, AIP Adv., Volume 6 (2016), 121707 | DOI

[44] S. Brûlé; B. Ungureanu; Y. Achaoui; R. Aznavourian; T. Antonakakis; R. Craster; S. Enoch; S. Guenneau Metamaterial-like transformed urbanism, Innov. Infrastruct. Solut., Volume 2 (2017), p. 20 | DOI

[45] A. Wirgin; P. Bard Effects of buildings on the duration and amplitude of ground motion in mexico city, Bull. Seismol. Soc. Am., Volume 86 (1996), pp. 914-920

[46] J. Semblat; A. Duval; P. Dangla Numerical analysis of seismic wave amplification in nice (france) and comparisons with experiments, Soil Dyn. Earthq. Eng., Volume 19 (2000), pp. 347-362 | DOI

[47] D. Clouteau; D. Aubry Modification of the ground motion in dense urban areas, J. Comput. Acoust., Volume 9 (2001), pp. 1659-1675 | DOI

[48] P. Gueguen; P. Bard; F. Chavez-Garcia Site-city seismic interaction in mexico city-like environments: an analytical study, Bull. Seismol. Soc. Am., Volume 92 (2002), pp. 794-811 | DOI

[49] C. Boutin; P. Roussillon Assessment of the urbanization effect on seismic response, Bull. Seismol. Soc. Am., Volume 94 (2004), pp. 251-268 | DOI

[50] M. Kham; J. Semblat; P. Bard; P. Dangla Seismic site-city interaction: main governing phenomena through simplified numerical models, Bull. Seismol. Soc. Am., Volume 96 (2006), pp. 1934-1951 | DOI

[51] B. Gutenberg; C. Richter Magnitude and energy of earthquakes, Ann. Geofis., Volume 9 (1956), pp. 1-15

Cited by Sources:

Comments - Policy