Metamaterial-like transformed urbanism

  • Stéphane BrûléEmail author
  • Bogdan Ungureanu
  • Younes Achaoui
  • André Diatta
  • Ronald Aznavourian
  • Tryfon Antonakakis
  • Richard Craster
  • Stefan Enoch
  • Sébastien Guenneau
Technical Note


Viewed from the sky, the urban fabric pattern appears similar to the geometry of structured devices called metamaterials; these were developed by Physicists to interact with waves that have wavelengths in the range from nanometers to meters (from electromagnetic to seismic metamaterials). Visionary research in the late 1980s based on the interaction of big cities with seismic signals and more recent studies on seismic metamaterials, made of holes or vertical inclusions in the soil, has generated interest in exploring the multiple interaction effects of seismic waves in the ground and the local resonances of both buried pillars and buildings. Here, we use techniques from transformational optics and theoretically validate, by numerical experiments, that a district of buildings could be considered as a set of above-ground resonators, purely elastic, interacting with an incident seismic signal. We hope that our proposal will contribute to all theoretical and experimental efforts in design of cities of the future, from a metamaterial standpoint.


Metamaterial Urban fabric Metacity Transformational physics Homogenization 


  1. 1.
    Achaoui Y, Ungureanu B, Enoch S, Brûlé S, Guenneau S (2016) Seismic waves damping with arrays of inertial resonators. Extreme Mech Lett, 8:30–37Google Scholar
  2. 2.
    Auriault JL, Boutin C, Geindreau C (2009) Homogénéisation de phénomènes couplés en milieux hétérogènes, Mécanique et Ingénierie des Matériaux, Hermes, LavoisierGoogle Scholar
  3. 3.
    Aznavourian R, Puvirajesinghe T, Brûlé S, Enoch S, Guenneau S (2016) Bio-inspired seismic metamaterials with transformed elastic crystals. J Phys Condens Matter (provisionally accepted)Google Scholar
  4. 4.
    Bielak J (1975) Dynamic behaviour of structures with embedded foundations. Earthq Eng Struct Dyn 3:259–274CrossRefGoogle Scholar
  5. 5.
    Boutin C, Roussillon P (2004) Assessment of the urbanization effect on seismic response. Bull Seismol Soc Am 94(1):251–268CrossRefGoogle Scholar
  6. 6.
    Boutin C, Roussillon P (2006) Wave propagation in presence of oscillators on the free surface. Int J Eng Sci 4:180–204CrossRefGoogle Scholar
  7. 7.
    Brûlé S, Javelaud EH, Enoch S, Guenneau S (2017a) Flat lens for seismic waves. Sci Rep (in progress)Google Scholar
  8. 8.
    Brûlé S, Enoch S, Guenneau S, Craster RV (2017b) Seismic metamaterials: controlling surface Rayleigh waves using analogies with electromagnetic metamaterials. In: Handbook of metamaterials. World Scientific (in press)Google Scholar
  9. 9.
    Brûlé S, Duquesnoy S (2016) Change of ground type by means of dynamic compaction: consequences on the calculation of seismic loadings. Innov Infrastruct Solut 1:39. doi: 10.1007/s41062-016-0037-4 CrossRefGoogle Scholar
  10. 10.
    Brûlé S, Enoch S, Guenneau S (2017). Structured soils under dynamic loading: The metamaterials in Geotechnics. Revue Française de Géotechnique (in press)Google Scholar
  11. 11.
    Brûlé S, Javelaud EH, Enoch S, Guenneau S (2014) Experiments on seismic metamaterials: molding surface waves. Phys Rev Lett 112:133901CrossRefGoogle Scholar
  12. 12.
    Clouteau D, Aubry D (2001) Modification of the ground motion in dense urban areas. J Comput Acoust 9(4):1659–1675CrossRefGoogle Scholar
  13. 13.
    Colombi A, Roux P, Guenneau S, Rupin M (2015) Directional cloaking of flexural waves in a plate with a locally resonant metamaterial. J Acoust Soc Am 137(4):1783–1789CrossRefGoogle Scholar
  14. 14.
    Colombi A, Roux P, Guenneau S, Guéguen P, Craster RV (2016) Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances. Sci Rep 6:19238CrossRefGoogle Scholar
  15. 15.
    Diatta A, Guenneau S (2014) Controlling solid elastic waves with spherical cloaks. Appl Phys Lett 105(2):021901CrossRefGoogle Scholar
  16. 16.
    Diatta A, Achaoui Y, Brûlé S, Enoch S, Guenneau S (2016) Control of Rayleigh-like waves in thick plate Willis metamaterials. AIP Adv 6(12):121707CrossRefGoogle Scholar
  17. 17.
    Dupont G, Kimmoun O, Molin B, Guenneau S, Enoch S (2015) Numerical and experimental study of an invisibility carpet in a water channel. Phys Rev E 91:023010CrossRefGoogle Scholar
  18. 18.
    Farhat M, Enoch S, Guenneau S, Movchan AB (2008) Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys Rev Lett 101:1345011CrossRefGoogle Scholar
  19. 19.
    Farhat M, Guenneau S, Enoch S, Movchan AB (2009) Cloaking bending waves propagating in thin elastic plates. Phys Rev B 79(3):033102CrossRefGoogle Scholar
  20. 20.
    Guéguen P, Bard PY, Semblat JF (2000) From soil-structure interaction to site-city interaction. In: 12th World conference on earthquake engineering, Auckland, New ZealandGoogle Scholar
  21. 21.
    Guéguen Ph, Bard P-Y, Chàvez-Garcia FJ (2002) Site-city seismic interaction in Mexico City-like environments: an analytical study. Bull Seismol Soc Am 92(2):794–811CrossRefGoogle Scholar
  22. 22.
    Ghergu M, Ionescu IR (2009) Structure–soil–structure coupling in seismic excitation and city effect. Int J Eng Sci 47:342–354CrossRefGoogle Scholar
  23. 23.
    Guillier B, Machane D, Oubaiche EH, Chatelain J-L, Ait Meziane Y, Ben Salem R Dunand F, Guéguen P, Hadid M, Hellel M, Kiboua A, Laouami N, Mezouer N, Nour A, Remas A (2004) Résultats préliminaires sur les fréquences fondamentales et les amplifications de sols, obtenus par l'étude du bruit de fond, sur la ville de boumerdes-algérie. Mém Serv. Géol. Alg. 12:103–114Google Scholar
  24. 24.
    Housner GW (1954) Effect of foundation compliance on earthquake stresses in multistory buildings. Bull Seismol Soc Am 44:551–569Google Scholar
  25. 25.
    Housner GW (1957) Interaction of building and ground during an earthquake. Bull Seismol Soc Am 47:179–186Google Scholar
  26. 26.
    Hu X, Chan CT (2005) Refraction of water waves by periodic cylinder arrays. Phys Rev Lett 95:154501CrossRefGoogle Scholar
  27. 27.
    Li J, Pendry JB (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101(20):203901CrossRefGoogle Scholar
  28. 28.
    Iorch IV, Muskhin IS, Shadrivov IV, Belov PA, Kivshar YS (2013) Hyperbolic metamaterials based on multilayer graphene structures. Phys Rev B 87:075416-6Google Scholar
  29. 29.
    Kadic M, Bückmann T, Schittny R, Wegener M (2013) Metamaterials beyond electromagnetism. Rep Prog Phys 76:26501CrossRefGoogle Scholar
  30. 30.
    Kim SH, Das MP (2012) Seismic waveguide of metamaterials. Mod Phys Lett B 26:1250105CrossRefGoogle Scholar
  31. 31.
    Krodel S, Thome N, Daraio C (2015) Wide band-gap seismic metastructures, Ex Mech Letters 4:111–117Google Scholar
  32. 32.
    Kushwaha MS, Halevi P, Dobrzynski L, Djafari-Rouhani B (1993) Accoustic band structure of periodic elastic composites. Phys Rev Lett 71:2022–2025CrossRefGoogle Scholar
  33. 33.
    Kushwaha MS (1997) Stop-bands for periodic metallic rods—sculptures that can filter the noise. Appl Phys Lett 70(24):3218–3220CrossRefGoogle Scholar
  34. 34.
    Lakes R (1987) Foam structures with a negative Poisson’s ratio. Science 235(4792):1038–1040CrossRefGoogle Scholar
  35. 35.
    Ledoux CN (1804) L’Architecture considérée sous le rapport de l’Art, des Mœurs et de la Législation, Tome 1, Imprimerie Perronneau, ParisGoogle Scholar
  36. 36.
    Leonhardt U (2006) Optical conformal mapping. Science 312(5781):1777–1780CrossRefGoogle Scholar
  37. 37.
    Ramakrishna SA (2005) Physics of negative refractive index materials. Rep Prog Phys 68(2):449CrossRefGoogle Scholar
  38. 38.
    Sánchez-Pérez JV, Caballero D, Mártinez-Sala R, Rubio C, Sánchez-Dehesa J, Meseguer F, Llinares J, Gálvez F (1998) Sound attenuation by a two-dimensional array of rigid cylinders. Phys Rev Lett 80:5325CrossRefGoogle Scholar
  39. 39.
    Pendry JB, Holden AJ, Robbins DJ, Stewart WJ (1999) Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech 47(11):2075–2084CrossRefGoogle Scholar
  40. 40.
    Pendry JB (2000) Negative refraction makes a perfect lens. Phys Rev Lett 85:3966–3969CrossRefGoogle Scholar
  41. 41.
    Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312(5781):1780–1782CrossRefGoogle Scholar
  42. 42.
    Perrault M, Guéguen P (2015) Correlation between ground motion and building response using Californian earthquake records. Earthq Spectra 31(4):2027–2046CrossRefGoogle Scholar
  43. 43.
    Renger J, Kadic M, Dupont G, Aćimović SS, Guenneau S, Quidant R, Enoch S (2010) Hidden progress: broadband plasmonic invisibility. Opt Express 18(15):15757–15768CrossRefGoogle Scholar
  44. 44.
    Semblat JF, Pecker A (2009) Waves and vibrations in soils: earthquakes, traffic, shocks, construction works. IUSS Press, PaviaGoogle Scholar
  45. 45.
    Sheng P (2014) Viewpoint: a step towards a seismic cloak. Physics 7:34CrossRefGoogle Scholar
  46. 46.
    Spiliopoulos KV, Anagnospoulos SA (1992) Earthquake induced pounding in adjacent building. In: Earthquake engineering, 10th World conference, 1992, Balkema, RotterdamGoogle Scholar
  47. 47.
    Trifunac MD (1972) Interaction of a shear wall with the soil for incident plane SH waves. Bull Seismol Soc Am 62:63–83Google Scholar
  48. 48.
    Ungureanu B, Achaoui Y, Enoch S, Brûlé S, Guenneau S (2016) Auxetic-like metamaterials as novel earthquake protections. EPJ Appl Metamat 2015(2):17Google Scholar
  49. 49.
    Walser RM (2001) Electromagnetic metamaterials. In: Paper presented at the International Society for Optical Engineering (SPIE), San Diego, USA, 4467, 1–165Google Scholar
  50. 50.
    Wirgin A, Bard P-Y (1996) Effects of buildings on the duration and amplitude of ground motion in Mexico City. Bull Seismol Soc Am 86(3):914–920Google Scholar
  51. 51.
    Wong HL, Trifunac MD, Westermo B (1977) Effects of surface and subsurface irregularities on the amplitude of monochromatic waves. Bull Seismol Soc Am 67:353–368Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Stéphane Brûlé
    • 1
    Email author
  • Bogdan Ungureanu
    • 1
  • Younes Achaoui
    • 1
  • André Diatta
    • 1
  • Ronald Aznavourian
    • 1
  • Tryfon Antonakakis
    • 2
  • Richard Craster
    • 3
  • Stefan Enoch
    • 1
  • Sébastien Guenneau
    • 1
  1. 1.CNRS, Centrale Marseille, Institut FresnelAix-Marseille UniversityMarseilleFrance
  2. 2.Multiwave Technologies AGGenevaSwitzerland
  3. 3.Department of MathematicsImperial College LondonLondonUK

Personalised recommendations