Designing perturbative metamaterials from discrete models

  • Nature Materialsvolume 17pages323328 (2018)
  • doi:10.1038/s41563-017-0003-3
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Identifying material geometries that lead to metamaterials with desired functionalities presents a challenge for the field. Discrete, or reduced-order, models provide a concise description of complex phenomena, such as negative refraction, or topological surface states; therefore, the combination of geometric building blocks to replicate discrete models presenting the desired features represents a promising approach. However, there is no reliable way to solve such an inverse problem. Here, we introduce ‘perturbative metamaterials’, a class of metamaterials consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model with individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing two-dimensional elastic metamaterials that realize Veselago lenses, zero-dispersion bands and topological surface phonons. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal and photonic metamaterials composed of weakly interacting unit cells.

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This work was partially supported by the ETH Postdoctoral Fellowship to K.H.M., and by the Swiss National Science Foundation. The authors would like to thank R. Süsstrunk and O. Bilal for discussions.

Author information

Author notes

  1. Kathryn H. Matlack and Marc Serra Garcia contributed equally to this work.


  1. Department of Mechanical and Process Engineering, ETH Zürich, Zürich, Switzerland

    • Kathryn H. Matlack
    • , Marc Serra-Garcia
    •  & Chiara Daraio
  2. Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland

    • Kathryn H. Matlack
    •  & Sebastian D. Huber
  3. Department of Civil, Chemical, Environmental and Materials Engineering – DICAM, University of Bologna, Bologna, Italy

    • Antonio Palermo
  4. California Institute of Technology, Pasadena, California, USA

    • Chiara Daraio


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K.H.M. and M.S.G. performed the optimization and simulation of the materials. K.H.M. wrote the manuscript. M.S.G. proposed the reduction approach and optimization algorithm. A.P. designed and performed the dynamic condensation. S.H. selected and interpreted the reduced-order models. C.D. provided guidance during all stages of the project. All authors contributed to the discussion and interpretation of the results, and to the editing of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Marc Serra-Garcia.

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