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Shape-morphing metamaterials

Nature Reviews Materials volume 10, pages 783–798 (2025)Cite this article

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Abstract

Mechanical metamaterials use geometric design to achieve unconventional properties, such as high strength at low density, efficient waveguiding and complex shape morphing. The ability to control changes in shape builds on the complex relationship between geometry and nonlinear mechanics, and opens new possibilities for disruptive technologies across diverse fields, including wearable devices, medical technology, robotics and beyond. In this Review, we examine the current state of the field of shape-morphing metamaterials and propose a unified classification system for the mechanisms involved, as well as the design principles underlying them. Specifically, we explore two main categories of unit cells — those that exploit structural anisotropy and those that exploit internal rotations — and two potential approaches to tessellating these cells, based on kinematic compatibility or geometric frustration. We conclude by discussing the available design tools and highlighting emerging challenges in the development of shape-morphing metamaterials.

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Fig. 1: Unit cells based on anisotropic mechanisms.
Fig. 2: Unit cells based on internal rotations.
Fig. 3: Bistable unit cells.
Fig. 4: Kinematically compatible metamaterials designed via periodic tiling of structural units.
Fig. 5: Kinematically compatible metamaterials designed via non-periodic tiling of structural units.
Fig. 6: Kinematically incompatible metamaterials designed via periodic tiling of structural units.
Fig. 7: Kinematically incompatible metamaterials made from non-periodic arrangements of structural units.

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Acknowledgements

K.K.D. acknowledges the support of the Polish National Science Centre (NCN) (project no. 2022/47/D/ST5/00280) and the Polish Ministry of Science programme ‘Regional Excellence Initiative’ (project no. RID/SP/0050/2024/1). C.C. acknowledges funding from the European Research Council under grant agreement no. 852587 and from the Netherlands Organisation for Scientific Research (NWO) under grant agreement VIDI 2131313. M.K. acknowledges French ANR support via OPTOBOTs (ANR-21-CE33-0003), PNanoBot (ANR-21-CE33-0015) and the French–Swiss SMYLE network. K.B. acknowledges support from the Simons Collaboration on Extreme Wave Phenomena Based on Symmetries.

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Authors and Affiliations

  1. Institute of Physics, University of Zielona Gora, Zielona Gora, Poland

    Krzysztof K. Dudek

  2. Université Marie et Louis Pasteur, Institut FEMTO-ST, Besançon, France

    Muamer Kadic

  3. Institute of Physics, Universiteit van Amsterdam, Amsterdam, Netherlands

    Corentin Coulais

  4. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Katia Bertoldi

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  2. Muamer Kadic
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C.C., K.B. and K.K.D. wrote the first draft. K.K.D., C.C. and M.K. prepared the figures based on the concept proposed by K.B. and C.C. All authors reviewed and/or edited the article before submission and contributed to the discussion.

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Correspondence to Muamer Kadic.

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Dudek, K.K., Kadic, M., Coulais, C. et al. Shape-morphing metamaterials. Nat Rev Mater 10, 783–798 (2025). https://doi.org/10.1038/s41578-025-00828-9

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