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Topological kinematics of origami metamaterials

Nature Physics volume 14, pages 811–815 (2018)Cite this article

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Abstract

A variety of electronic phases in solid-state systems can be understood by abstracting away microscopic details and refocusing on how Fermi surface topology interacts with band structure to define available electron states1. In fact, topological concepts are broadly applicable to non-electronic materials and can be used to understand a variety of seemingly unrelated phenomena2,3,4,5,6. Here, we apply topological principles to origami-inspired mechanical metamaterials7,8,9,10,11,12, and demonstrate how to guide bulk kinematics by tailoring the crease configuration-space topology. Specifically, we show that by simply changing the crease angles, we modify the configuration-space topology, and drive origami structures to dramatically change their kinematics from being smoothly and continuously deformable to mechanically bistable and rigid. In addition, we examine how a topologically disjointed configuration space can be used to constrain the locally accessible deformations of a single folded sheet. While analyses of origami structures are typically dependent on the energetics of constitutive relations11,12,13,14, the topological abstractions introduced here are a separate and independent consideration that we use to analyse, understand and design these metamaterials.

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Fig. 1: Distinguishing the roles of topological and energetic considerations in origami mechanics.
Fig. 2: Configuration-space topology of origami-inspired mechanical metamaterials is determined by the underlying crease pattern.
Fig. 3: Coupling configuration-space topology with vertex–vertex interactions.
Fig. 4: Decoupling configuration-space topology with vertex–vertex interactions.

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Acknowledgements

The authors thank A. Ruina, T. Healy, J. Jenkins, U. Nguyen, L. Freni and the Cohen laboratory for useful discussions. We also thank F. Parish for assistance with the laser cutter, and S. Waitukaitis, P. Dieleman and M. van Hecke for providing the photo in Fig. 1b. This work was supported by the National Science Foundation grant no. EFRI ODISSEI-1240441. I.C. received continuing support from DMREF-1435829. B.L. acknowledges the support of the National Science Foundation grant no. NSF CBET-1706511. C.D.S. acknowledges the kind hospitality of the Kavli Institute of Theoretical Physics in Santa Barbara, CA, funded by the National Science Foundation under grant no. NSF PHY-1125915.

Author information

Author notes

  1. These authors contributed equally: Bin Liu, Jesse L. Silverberg.

Authors and Affiliations

  1. Department of Physics, Cornell University, Ithaca, NY, USA

    Bin Liu, Jesse L. Silverberg & Itai Cohen

  2. School of Natural Sciences, University of California, Merced, Merced, CA, USA

    Bin Liu

  3. Wyss Institute for Biologically Inspired Engineering, Harvard University, Boston, MA, USA

    Jesse L. Silverberg

  4. Department of Systems Biology, Harvard Medical School, Boston, MA, USA

    Jesse L. Silverberg

  5. Department of Physics, University of Massachusetts Amherst, Amherst, MA, USA

    Arthur A. Evans & Christian D. Santangelo

  6. Lang Origami, Alamo, CA, USA

    Robert J. Lang

  7. Department of Mathematics, Western New England University, Springfield, MA, USA

    Thomas C. Hull

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Contributions

B.L. and J.L.S. designed the research; B.L. conducted the research; B.L., J.L.S., A.A.E., R.J.L., T.C.H. and I.C. interpreted the results; C.D.S., R.J.L., T.C.H. and I.C. supervised the research; B.L., J.L.S., C.D.S., R.J.L., T.C.H. and I.C. prepared the manuscript.

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Correspondence to Bin Liu.

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Supplementary Information, Supplementary Figures 1–5, Supplementary References 1–4

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Liu, B., Silverberg, J.L., Evans, A.A. et al. Topological kinematics of origami metamaterials. Nature Phys 14, 811–815 (2018). https://doi.org/10.1038/s41567-018-0150-8

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