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An additive framework for kirigami design

Nature Computational Science volume 3, pages 443–454 (2023)Cite this article

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Abstract

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. Altogether, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kirigami art forms.

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Fig. 1: Marching construction for quad kirigami design.
Fig. 2: Encoding different desired properties in the design matrix.
Fig. 3: Linear and nonlinear inverse design of quad kirigami patterns using the proposed framework.
Fig. 4: Physical model fabrication for rigid-deployable kirigami fabricated via a 3D printing-based method and a cast silicone composite method.

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Data availability

Source data for Fig. 3c are available with this manuscript. Kirigami pattern files are available on Zenodo24.

Code availability

The kirigami design codes are available on Zenodo24.

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Acknowledgements

This work was supported in part by the National Science Foundation under grants nos. DMS-2002103 (G.P.T.C.), DMR 20-11754 (L.M.), DMREF 19-22321 (L.M.) and EFRI 18-30901 (L.M.), and the Simons Foundation (L.M.) and the Henri Seydoux Fund (L.M.).

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Author notes

  1. These authors contributed equally: Levi H. Dudte, Gary P. T. Choi.

Authors and Affiliations

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

    Levi H. Dudte, Kaitlyn P. Becker & L. Mahadevan

  2. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Gary P. T. Choi

  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Kaitlyn P. Becker

  4. Departments of Physics, and Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA

    L. Mahadevan

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  1. Levi H. Dudte
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  4. L. Mahadevan
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Contributions

L.H.D. and L.M. conceived the research. L.H.D., G.P.T.C., K.P.B. and L.M. designed the research. L.H.D. and G.P.T.C. derived the theoretical results, implemented the algorithms and conducted the numerical experiments. K.P.B. built the physical models. L.H.D., G.P.T.C., K.P.B. and L.M. analyzed the results and wrote the manuscript. L.M. supervised the research.

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Correspondence to L. Mahadevan.

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The authors declare no competing interests.

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Nature Computational Science thanks Xianqiao Wang, Alberto Corigliano and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Kaitlin McCardle, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Sections 1–4, Figs. 1–23 and discussion.

Source data

Source Data Fig. 3

Raw numerical source data for Fig. 3c.

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Dudte, L.H., Choi, G.P.T., Becker, K.P. et al. An additive framework for kirigami design. Nat Comput Sci 3, 443–454 (2023). https://doi.org/10.1038/s43588-023-00448-9

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