Letter | Published:

Combinatorial design of textured mechanical metamaterials

Nature volume 535, pages 529532 (28 July 2016) | Download Citation

Abstract

The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features1,2,3,4,5,6,7,8,9,10,11. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks—voxels—that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.

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Acknowledgements

We are grateful to J. Mesman for technical support. We thank R. Golkov, Y. Kamir, G. Kosa, K. Kuipers, F. Leoni, W. Noorduin and V. Vitelli for discussions. We acknowledge funding from the Netherlands Organisation for Scientific Research through grants VICI No. NWO-680-47-609 (M.v.H. and C.C.) and VENI No. NWO-680-47-445 (C.C.) and from the Israel Science Foundation through grant numbers 617/12 and 1730/12 (E.T and Y.S.).

Author information

Affiliations

  1. Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, PO box 9504, 2300 RA Leiden, The Netherlands

    • Corentin Coulais
    • , Koen de Reus
    •  & Martin van Hecke
  2. FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands

    • Corentin Coulais
    •  & Martin van Hecke
  3. School of Mechanical Engineering and The Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 69978, Israel

    • Eial Teomy
    •  & Yair Shokef

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Contributions

C.C. and M.v.H. conceived the main concepts. C.C., E.T., Y.S. and M.v.H. formulated the spin problem. E.T. and Y.S. solved the spin problem. C.C and K.d.R. performed the experiments and simulations with inputs from E.T., Y.S. and M.v.H. C.C. and M.v.H wrote the manuscript with contributions from all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Corentin Coulais.

Extended data

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains Supplementary Text and Data, Supplementary Figures 1-14 and Supplementary Table 1.

Videos

  1. 1.

    5x5x5 metacube, uniaxially compressed along its minor axis by flat clamps.

    As discussed in the main text, it exhibits a pattern transformation, where its building blocks suddenly morph in to alternated bricks of elongated and flattened shape.

  2. 2.

    10x10x10 metacube decorated with square pedestals, which is uniaxially compressed along its minor axis by clamps textured in a checker board pattern (seemethods).

    As discussed in the main text, its surface texture morphs into an exactingly designed ”smiley” pattern.

  3. 3.

    The opposite face of the same 10x10x10 metacube during a similar experiment.

    As discussed in the methods, its surface texture morphs into the inverted ”smiley” pattern.

  4. 4.

    A side face of the same 10x10x10 metacube during a similar experiment.

    As discussed in the methods, its surface texture morphs into a checkerboard pattern.

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DOI

https://doi.org/10.1038/nature18960

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