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Reprogrammable snapping morphogenesis in ribbon-cluster meta-units using stored elastic energy

Nature Materials volume 24, pages 1793–1801 (2025) Cite this article

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Abstract

Snapping, driven by stored elastic energy, enables versatile and rapid shape changes in nature; yet replicating such autonomous, reprogrammable morphogenesis in free-standing volumetric structures remains elusive. Here we report a lantern-shaped ribbon-cluster meta-unit that harnesses programmable and reprogrammable elastic energy to achieve over 13 distinct volumetric snapping morphologies from a single unit. Governed by three Euler angles, the meta-unit post-fabrication offers a tunable mechanical design space spanning up to quadrastable states. Unlike single-ribbon or mechanism-based designs, our system autonomously selects snapping pathways via nastic coupling between multiple ribbons, enabling the inverse design of complex snapping morphologies. We harness magnetically actuated bud-to-bloom and tristable morphogenesis to enable fast, non-invasive grasping and remote flow regulation in confined environments. These results establish a general framework for architected materials with programmable shape, stability and function, offering potential applications in soft robotics, deployable devices and mechanical logic.

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Fig. 1: Design and snapping morphogenesis of a ribbon-cluster meta-unit.
The alternative text for this image may have been generated using AI.
Fig. 2: Snapping transition through the configuration and elastic energy yielded by β.
The alternative text for this image may have been generated using AI.
Fig. 3: A snapping morphogenesis system by tuning the flipping angle α of one unit.
The alternative text for this image may have been generated using AI.
Fig. 4: Instabilities phase diagram of all units.
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Fig. 5: Magnetically actuated snapping morphogenesis and its applications in non-invasive manipulation and flow regulation.
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Data availability

All data generated or analysed during this study are included in the Article and its Supplementary Information. Source data are provided with this paper.

References

  1. Forterre, Y., Skotheim, J. M., Dumais, J. & Mahadevan, L. How the Venus flytrap snaps. Nature 433, 421–425 (2005).

    CAS  PubMed  Google Scholar 

  2. Vincent, O. et al. Ultra-fast underwater suction traps. Proc. R. Soc. B 278, 2909–2914 (2011).

    PubMed  PubMed Central  Google Scholar 

  3. Aubin, C. A. et al. Towards enduring autonomous robots via embodied energy. Nature 602, 393–402 (2022).

    CAS  PubMed  Google Scholar 

  4. Xia, N. et al. Dynamic morphological transformations in soft architected materials via buckling instability encoded heterogeneous magnetization. Nat. Commun. 13, 7514 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. Bertoldi, K., Vitelli, V., Christensen, J. & van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 17066 (2017).

    CAS  Google Scholar 

  6. Kim, Y., van den Berg, J. & Crosby, A. J. Autonomous snapping and jumping polymer gels. Nat. Mater. 20, 1695–1701 (2021).

    CAS  PubMed  Google Scholar 

  7. Hwang, M. & Arrieta, A. F. Solitary waves in bistable lattices with stiffness grading: augmenting propagation control. Phys. Rev. E 98, 042205 (2018).

    CAS  Google Scholar 

  8. Melancon, D., Gorissen, B., Garcia-Mora, C. J., Hoberman, C. & Bertoldi, K. Multistable inflatable origami structures at the metre scale. Nature 592, 545–550 (2021).

    CAS  PubMed  Google Scholar 

  9. Chen, T., Pauly, M. & Reis, P. M. A reprogrammable mechanical metamaterial with stable memory. Nature 589, 386–390 (2021).

    CAS  PubMed  Google Scholar 

  10. Jiang, Y., Korpas, L. M. & Raney, J. R. Bifurcation-based embodied logic and autonomous actuation. Nat. Commun. 10, 128 (2019).

    PubMed  PubMed Central  Google Scholar 

  11. Chi, Y. et al. Bistable and multistable actuators for soft robots: structures, materials, and functionalities. Adv. Mater. 34, 2110384 (2022).

    CAS  Google Scholar 

  12. Tang, Y. et al. Leveraging elastic instabilities for amplified performance: spine-inspired high-speed and high-force soft robots. Sci. Adv. 6, eaaz6912 (2020).

    PubMed  PubMed Central  Google Scholar 

  13. Zhai, Z., Wang, Y., Lin, K., Wu, L. & Jiang, H. In situ stiffness manipulation using elegant curved origami. Sci. Adv. 6, eabe2000 (2020).

    PubMed  PubMed Central  Google Scholar 

  14. Shah, D. et al. Shape changing robots: bioinspiration, simulation, and physical realization. Adv. Mater. 33, e2002882 (2021).

    PubMed  Google Scholar 

  15. Ramachandran, V., Bartlett, M. D., Wissman, J. & Majidi, C. Elastic instabilities of a ferroelastomer beam for soft reconfigurable electronics. Extreme Mech. Lett. 9, 282–290 (2016).

    Google Scholar 

  16. Rafsanjani, A., Akbarzadeh, A. & Pasini, D. Snapping mechanical metamaterials under tension. Adv. Mater. 27, 5931–5935 (2015).

    CAS  PubMed  Google Scholar 

  17. Zhao, Y. et al. Twisting for soft intelligent autonomous robot in unstructured environments. Proc. Natl Acad. Sci. USA 119, e2200265119 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  18. Sano, T. G. & Wada, H. Twist-induced snapping in a bent elastic rod and ribbon. Phys. Rev. Lett. 122, 114301 (2019).

    CAS  PubMed  Google Scholar 

  19. Zhang, X. et al. Kirigami-based metastructures with programmable multistability. Proc. Natl Acad. Sci. USA 119, e2117649119 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  20. Zhang, H., Wu, J., Fang, D. & Zhang, Y. Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation. Sci. Adv. 7, eabf1966 (2021).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. Liu, K., Pratapa, P. P., Misseroni, D., Tachi, T. & Paulino, G. H. Triclinic metamaterials by tristable origami with reprogrammable frustration. Adv. Mater. 34, 2107998 (2022).

    CAS  Google Scholar 

  22. Chen, T., Panetta, J., Schnaubelt, M. & Pauly, M. Bistable auxetic surface structures. ACM Trans. Graph. 40, 39 (2021).

    Google Scholar 

  23. Stein-Montalvo, L. et al. Efficient snap-through of spherical caps by applying a localized curvature stimulus. Eur. Phys. J. E 45, 3 (2022).

    CAS  PubMed  Google Scholar 

  24. Zheng, Y., Lai, Y., Hu, Y. & Cai, S. Rayleigh–Taylor instability in a confined elastic soft cylinder. J. Mech. Phys. Solids 131, 221–229 (2019).

    Google Scholar 

  25. He, Q., Zheng, Y., Wang, Z., He, X. & Cai, S. Anomalous inflation of a nematic balloon. J. Mech. Phys. Solids 142, 104013 (2020).

    Google Scholar 

  26. Yasuda, H., Tachi, T., Lee, M. & Yang, J. Origami-based tunable truss structures for non-volatile mechanical memory operation. Nat. Commun. 8, 962 (2017).

    PubMed  PubMed Central  Google Scholar 

  27. Novelino, L. S., Ze, Q., Wu, S., Paulino, G. H. & Zhao, R. Untethered control of functional origami microrobots with distributed actuation. Proc. Natl Acad. Sci. USA 117, 24096–24101 (2020).

    CAS  PubMed  PubMed Central  Google Scholar 

  28. Yu, T., Marmo, F., Cesarano, P. & Adriaenssens, S. Continuous modeling of creased annuli with tunable bistable and looping behaviors. Proc. Natl Acad. Sci. USA 120, e2209048120 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. Lu, L., Dai, J., Leanza, S., Zhao, R. R. & Hutchinson, J. W. Multiple equilibrium states of a curved-sided hexagram: part I—stability of states. J. Mech. Phys. Solids 180, 105406 (2023).

    Google Scholar 

  30. Lu, L., Leanza, S., Dai, J., Hutchinson, J. W. & Zhao, R. R. Multistability of segmented rings by programming natural curvature. Proc. Natl Acad. Sci. USA 121, e2405744121 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. Smith, M. L., Yanega, G. M. & Ruina, A. Elastic instability model of rapid beak closure in hummingbirds. J. Theor. Biol. 282, 41–51 (2011).

    CAS  PubMed  Google Scholar 

  32. Gomez, M., Moulton, D. E. & Vella, D. Critical slowing down in purely elastic ‘snap-through’ instabilities. Nat. Phys. 13, 142–145 (2017).

    CAS  Google Scholar 

  33. Huang, W., Yu, T., Vella, D., Hsia, K. J. & Liu, M. Exploiting dynamic bifurcation in elastic ribbons for mode skipping and selection. J. Mech. Phys. Solids 190, 105721 (2024).

    Google Scholar 

  34. Yang, S. et al. ‘Cut-and-paste’ manufacture of multiparametric epidermal sensor systems. Adv. Mater. 27, 6423–6430 (2015).

    CAS  PubMed  Google Scholar 

  35. Timoshenko, S. & Gere, J. M. Theory of Elastic Stability 2nd edn (McGraw-Hill, 1961).

  36. Efrati, E., Pocivavsek, L., Meza, R., Lee, K. Y. & Witten, T. Confined disclinations: exterior versus material constraints in developable thin elastic sheets. Phys. Rev. E 91, 022404 (2014).

    Google Scholar 

  37. Sadik, S. & Dias, M. On local kirigami mechanics I: isometric conical solutions. J. Mech. Phys. Solids 151, 104370 (2021).

    Google Scholar 

  38. Frenzel, T., Kadic, M. & Wegener, M. Three-dimensional mechanical metamaterials with a twist. Science 358, 1072–1074 (2017).

    CAS  PubMed  Google Scholar 

  39. Sinatra, N. et al. Ultragentle manipulation of delicate structures using a soft robotic gripper. Sci. Robot. 4, eaax5425 (2019).

    PubMed  Google Scholar 

  40. Hong, Y. et al. Boundary curvature guided programmable shape-morphing kirigami sheets. Nat. Commun. 13, 530 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  41. Yang, Y., Vella, K. & Holmes, D. Grasping with kirigami shells. Sci. Robot. 6, eabd6426 (2021).

    PubMed  Google Scholar 

  42. Kang, G. et al. Grasping through dynamic weaving with entangled closed loops. Nat. Commun. 14, 4633 (2023).

    CAS  PubMed  PubMed Central  Google Scholar 

  43. Kim, Y., Parada, G. A., Liu, S. & Zhao, X. Ferromagnetic soft continuum robots. Sci. Robot. 4, eaax7329 (2019).

    PubMed  Google Scholar 

  44. Rothemund, P. et al. A soft, bistable valve for autonomous control of soft actuators. Sci. Robot. 3, eaar7986 (2018).

    PubMed  Google Scholar 

Download references

Acknowledgements

J.Y. acknowledges funding support from the National Science Foundation under award numbers CMMI-2005374, 2369274 and 2445551.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC, USA

    Yaoye Hong, Caizhi Zhou, Haitao Qing, Yinding Chi & Jie Yin

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  1. Yaoye Hong
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  2. Caizhi Zhou
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  3. Haitao Qing
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  4. Yinding Chi
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  5. Jie Yin
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Contributions

Y.H. and J.Y. designed the research. Y.H. designed the snapping system and conducted the theoretical modelling. Y.H. and C.Z. conducted the modelling and experimental exploration of the phase diagram, as well as finite element simulation. Y.C. fabricated the magnetic polymers. Y.H. and Y.C. conducted the experimental demonstration and mechanical testing. H.Q. and C.Z. conducted the experimental demonstrations of mechanical valves and deployment. All authors analysed the data. J.Y. supervised the overall research. Y.H. and J.Y. wrote the paper, and all the co-authors revised the paper.

Corresponding author

Correspondence to Jie Yin.

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Nature Materials thanks Yang Li, Jinkyu Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Schematics of three Euler angles.

a, The prescribed angle β denotes the angle between the parallel cuts (black lines) and the vertical axis in the parallelogram-shaped 2D precursor. Pasting the 2D precursor forms a curved-lantern configuration. b, Schematics show the isometric-view and top-view of a single ribbon within a 3D unit. The twisting angle γ is the angle between the central line and the line connecting the ribbon’s top end to the boundary cylindrical strip’s center. c, Schematics show how the flipping angle α can be changed by flipping the top or bottom boundary either outside or inside. Red symbols “0”, “+”, and “–” denote the three flipping states of each boundary: no flipping, inside-out flipping, and outside-in flipping, respectively. States “0”, “+”, and “-” correspond to α = 0, 180o, and −180o, respectively. Blue and green colors represent the two faces of the precursor.

Extended Data Fig. 2 Assembly of multiple units for enriched snapping morphogenesis.

a-b, Parallel connection of two stable units (β = 45o) with opposite chirality (a) for a mono-stable Matryoshka-doll-like structure under compression (b). LH and RH denote the left-handed and right-handed chirality. c-d, Serial connection of two stable units (β = 45o) with opposite chirality (c) for bi-stable switch upon twisting under fixed compression distance (d). e-f, Parallelly connection of two stable un-flipped and flipped units (β = 45o, e) for bi-stable switch under compression (f). g, Serial connection of two flipped tri-stable units (configuration ⑤) for multi-stable switch under remote rotating magnetic field. The cyan ellipses represent magnetic polymer plates attached to each unit’s top boundary strip. “0” and “1” denote vase and sandglass shapes, respectively. h-i, Serial connection of two bi-stable spherical-bud configurations (β = 60o) and a tri-stable sandglass-shaped configuration (⑧, β = 60o, h) for multi-stable switch (i). Scale bars, 10 mm.

Supplementary information

Supplementary Information (download PDF )

Supplementary Figs. 1–14 and Notes 1–9.

Supplementary Video 1 (download MP4 )

Schematics of pasting 2D precursors with different angle β (0° and 60°) to generate different 3D units. Compressing-driven snapping in the 3D unit with β = 60°.

Supplementary Video 2 (download MP4 )

Schematics of flipping the boundary strip (that is, changing the angle α) of the same unit (β = 60°) to tune the stored configuration and elastic energy.

Supplementary Video 3 (download MP4 )

Snapping morphogenesis of one unit (β = 60°) after flipping, actuated by compressing or twisting.

Supplementary Video 4 (download MP4 )

Schematics of the phase diagram of the (0, 0) state.

Supplementary Video 5 (download MP4 )

Schematics of the phase diagram of the (+, -) flipping state.

Supplementary Video 6 (download MP4 )

Schematics of the phase diagram of the (0, +) flipping state.

Supplementary Video 7 (download MP4 )

Schematics of the phase diagram of the (+,+) flipping state.

Supplementary Video 8 (download MP4 )

Snapping blossom actuated by a rotating magnetic field and its application as a noninvasive and fast gripper for a confined space.

Supplementary Video 9 (download MP4 )

Demonstrations of remote flow control and deployment in confined spaces.

Supplementary Video 10 (download MP4 )

Schematic illustration and demonstration of enriched snapping morphogenesis through parallel or serial connections of units.

Source data

Source Data Fig. 1 (download XLSX )

Statistical source data.

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Statistical source data.

Source Data Fig. 3 (download XLSX )

Statistical source data.

Source Data Fig. 4 (download XLSX )

Statistical source data.

Source Data Fig. 5 (download XLSX )

Statistical source data.

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Hong, Y., Zhou, C., Qing, H. et al. Reprogrammable snapping morphogenesis in ribbon-cluster meta-units using stored elastic energy. Nat. Mater. 24, 1793–1801 (2025). https://doi.org/10.1038/s41563-025-02370-z

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