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Critical slowing down in purely elastic ‘snap-through’ instabilities

Nature Physics volume 13, pages 142–145 (2017)Cite this article

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Abstract

Many elastic structures have two possible equilibrium states1: from umbrellas that become inverted in a sudden gust of wind, to nanoelectromechanical switches2,3, origami patterns4,5 and the hopper popper, which jumps after being turned inside-out6. These systems typically transition from one state to the other via a rapid ‘snap-through’. Snap-through allows plants to gradually store elastic energy, before releasing it suddenly to generate rapid motions7,8, as in the Venus flytrap9. Similarly, the beak of the hummingbird snaps through to catch insects mid-flight10, while technological applications are increasingly exploiting snap-through instabilities11,12,13. In all of these scenarios, it is the ability to repeatedly generate fast motions that gives snap-through its utility. However, estimates of the speed of snap-through suggest that it should occur more quickly than is usually observed. Here, we study the dynamics of snap-through in detail, showing that, even without dissipation, the dynamics slow down close to the snap-through transition. This is reminiscent of the slowing down observed in critical phenomena, and provides a handheld demonstration of such phenomena, as well as a new tool for tuning dynamic responses in applications of elastic bistability.

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Figure 1: Exploring ‘snap-through’ instabilities in a simple elastic system.
Figure 2: Investigating the snapping dynamics of an elastic arch.
Figure 3: Midpoint trajectories during snapping for different end-shortenings just beyond the snapping transition.
Figure 4: Slowing down of snapping dynamics near the loss of bistability.

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Acknowledgements

We are grateful to J.-B. Gorce for early experiments in a related system and to J. Dawes, S. Neukirch and J.-C. Tan for discussions. The research leading to these results has received funding from the European Research Council under the European Union’s Horizon 2020 Programme/ERC Grant Agreement no. 637334 (DV) and the EPSRC (MG).

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Woodstock Rd, Oxford OX2 6GG, UK

    Michael Gomez, Derek E. Moulton & Dominic Vella

Authors
  1. Michael Gomez
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  2. Derek E. Moulton
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  3. Dominic Vella
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Contributions

D.V. designed the research. M.G. performed experiments. M.G., D.E.M. and D.V. performed the analysis and wrote the paper.

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Correspondence to Dominic Vella.

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The authors declare no competing financial interests.

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Gomez, M., Moulton, D. & Vella, D. Critical slowing down in purely elastic ‘snap-through’ instabilities. Nature Phys 13, 142–145 (2017). https://doi.org/10.1038/nphys3915

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