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Designing perturbative metamaterials from discrete models


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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Fig. 1: Design method concept.
Fig. 2: Veselago lens metamaterial example.
Fig. 3: Zero-group-velocity metamaterial.
Fig. 4: Topological insulator metamaterial.


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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.

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Authors and Affiliations



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.

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Correspondence to Marc Serra-Garcia.

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Matlack, K.H., Serra-Garcia, M., Palermo, A. et al. Designing perturbative metamaterials from discrete models. Nature Mater 17, 323–328 (2018).

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