Skip to main content

Metamaterial-like transformed urbanism

Innovative Infrastructure Solutions volume 2, Article number: 20 (2017) Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

References

  1. Achaoui Y, Ungureanu B, Enoch S, Brûlé S, Guenneau S (2016) Seismic waves damping with arrays of inertial resonators. Extreme Mech Lett, 8:30–37

  2. Auriault JL, Boutin C, Geindreau C (2009) Homogénéisation de phénomènes couplés en milieux hétérogènes, Mécanique et Ingénierie des Matériaux, Hermes, Lavoisier

  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)

  4. Bielak J (1975) Dynamic behaviour of structures with embedded foundations. Earthq Eng Struct Dyn 3:259–274

    Article  Google Scholar 

  5. Boutin C, Roussillon P (2004) Assessment of the urbanization effect on seismic response. Bull Seismol Soc Am 94(1):251–268

    Article  Google Scholar 

  6. Boutin C, Roussillon P (2006) Wave propagation in presence of oscillators on the free surface. Int J Eng Sci 4:180–204

    Article  Google Scholar 

  7. Brûlé S, Javelaud EH, Enoch S, Guenneau S (2017a) Flat lens for seismic waves. Sci Rep (in progress)

  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)

  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

    Article  Google Scholar 

  10. Brûlé S, Enoch S, Guenneau S (2017). Structured soils under dynamic loading: The metamaterials in Geotechnics. Revue Française de Géotechnique (in press)

  11. Brûlé S, Javelaud EH, Enoch S, Guenneau S (2014) Experiments on seismic metamaterials: molding surface waves. Phys Rev Lett 112:133901

    Article  Google Scholar 

  12. Clouteau D, Aubry D (2001) Modification of the ground motion in dense urban areas. J Comput Acoust 9(4):1659–1675

    Article  Google Scholar 

  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):1783–1789

    Article  Google Scholar 

  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 6:19238

    Article  Google Scholar 

  15. Diatta A, Guenneau S (2014) Controlling solid elastic waves with spherical cloaks. Appl Phys Lett 105(2):021901

    Article  Google Scholar 

  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):121707

    Article  Google Scholar 

  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 91:023010

    Article  Google Scholar 

  18. Farhat M, Enoch S, Guenneau S, Movchan AB (2008) Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys Rev Lett 101:1345011

    Article  Google Scholar 

  19. Farhat M, Guenneau S, Enoch S, Movchan AB (2009) Cloaking bending waves propagating in thin elastic plates. Phys Rev B 79(3):033102

    Article  Google Scholar 

  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 Zealand

  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):794–811

    Article  Google Scholar 

  22. Ghergu M, Ionescu IR (2009) Structure–soil–structure coupling in seismic excitation and city effect. Int J Eng Sci 47:342–354

    Article  Google Scholar 

  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. 12:103–114

  24. Housner GW (1954) Effect of foundation compliance on earthquake stresses in multistory buildings. Bull Seismol Soc Am 44:551–569

    Google Scholar 

  25. Housner GW (1957) Interaction of building and ground during an earthquake. Bull Seismol Soc Am 47:179–186

    Google Scholar 

  26. Hu X, Chan CT (2005) Refraction of water waves by periodic cylinder arrays. Phys Rev Lett 95:154501

    Article  Google Scholar 

  27. Li J, Pendry JB (2008) Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett 101(20):203901

    Article  Google Scholar 

  28. Iorch IV, Muskhin IS, Shadrivov IV, Belov PA, Kivshar YS (2013) Hyperbolic metamaterials based on multilayer graphene structures. Phys Rev B 87:075416-6

    Google Scholar 

  29. Kadic M, Bückmann T, Schittny R, Wegener M (2013) Metamaterials beyond electromagnetism. Rep Prog Phys 76:26501

    Article  Google Scholar 

  30. Kim SH, Das MP (2012) Seismic waveguide of metamaterials. Mod Phys Lett B 26:1250105

    Article  Google Scholar 

  31. Krodel S, Thome N, Daraio C (2015) Wide band-gap seismic metastructures, Ex Mech Letters 4:111–117

  32. Kushwaha MS, Halevi P, Dobrzynski L, Djafari-Rouhani B (1993) Accoustic band structure of periodic elastic composites. Phys Rev Lett 71:2022–2025

    Article  Google Scholar 

  33. Kushwaha MS (1997) Stop-bands for periodic metallic rods—sculptures that can filter the noise. Appl Phys Lett 70(24):3218–3220

    Article  Google Scholar 

  34. Lakes R (1987) Foam structures with a negative Poisson’s ratio. Science 235(4792):1038–1040

    Article  Google Scholar 

  35. Ledoux CN (1804) L’Architecture considérée sous le rapport de l’Art, des Mœurs et de la Législation, Tome 1, Imprimerie Perronneau, Paris

  36. Leonhardt U (2006) Optical conformal mapping. Science 312(5781):1777–1780

    Article  Google Scholar 

  37. Ramakrishna SA (2005) Physics of negative refractive index materials. Rep Prog Phys 68(2):449

    Article  Google Scholar 

  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 80:5325

    Article  Google Scholar 

  39. Pendry JB, Holden AJ, Robbins DJ, Stewart WJ (1999) Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech 47(11):2075–2084

    Article  Google Scholar 

  40. Pendry JB (2000) Negative refraction makes a perfect lens. Phys Rev Lett 85:3966–3969

    Article  Google Scholar 

  41. Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312(5781):1780–1782

    Article  Google Scholar 

  42. Perrault M, Guéguen P (2015) Correlation between ground motion and building response using Californian earthquake records. Earthq Spectra 31(4):2027–2046

    Article  Google Scholar 

  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):15757–15768

    Article  Google Scholar 

  44. Semblat JF, Pecker A (2009) Waves and vibrations in soils: earthquakes, traffic, shocks, construction works. IUSS Press, Pavia

    Google Scholar 

  45. Sheng P (2014) Viewpoint: a step towards a seismic cloak. Physics 7:34

    Article  Google Scholar 

  46. Spiliopoulos KV, Anagnospoulos SA (1992) Earthquake induced pounding in adjacent building. In: Earthquake engineering, 10th World conference, 1992, Balkema, Rotterdam

  47. Trifunac MD (1972) Interaction of a shear wall with the soil for incident plane SH waves. Bull Seismol Soc Am 62:63–83

    Google Scholar 

  48. Ungureanu B, Achaoui Y, Enoch S, Brûlé S, Guenneau S (2016) Auxetic-like metamaterials as novel earthquake protections. EPJ Appl Metamat 2015(2):17

    Google Scholar 

  49. Walser RM (2001) Electromagnetic metamaterials. In: Paper presented at the International Society for Optical Engineering (SPIE), San Diego, USA, 4467, 1–165

  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):914–920

    Google Scholar 

  51. Wong HL, Trifunac MD, Westermo B (1977) Effects of surface and subsurface irregularities on the amplitude of monochromatic waves. Bull Seismol Soc Am 67:353–368

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS, Centrale Marseille, Institut Fresnel, Aix-Marseille University, Marseille, France

    Stéphane Brûlé, Bogdan Ungureanu, Younes Achaoui, André Diatta, Ronald Aznavourian, Stefan Enoch & Sébastien Guenneau

  2. Multiwave Technologies AG, Geneva, Switzerland

    Tryfon Antonakakis

  3. Department of Mathematics, Imperial College London, London, UK

    Richard Craster

Authors
  1. Stéphane Brûlé
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bogdan Ungureanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Younes Achaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. André Diatta
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ronald Aznavourian
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Tryfon Antonakakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Richard Craster
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Stefan Enoch
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Sébastien Guenneau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stéphane Brûlé.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Brûlé, S., Ungureanu, B., Achaoui, Y. et al. Metamaterial-like transformed urbanism. Innov. Infrastruct. Solut. 2, 20 (2017). https://doi.org/10.1007/s41062-017-0063-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41062-017-0063-x

Keywords

  • Metamaterial
  • Urban fabric
  • Metacity
  • Transformational physics
  • Homogenization