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Motorizing fibres with geometric zero-energy modes


Responsive materials1,2,3 have been used to generate structures with built-in complex geometries4,5,6, linear actuators7,8,9 and microswimmers10,11,12. These results suggest that complex, fully functional machines composed solely from shape-changing materials might be possible13. Nonetheless, to accomplish rotary motion in these materials still relies on the classical wheel and axle motifs. Here we explore geometric zero-energy modes to elicit rotary motion in elastic materials in the absence of a rigid wheel travelling around an axle. We show that prestrained polymer fibres closed into rings exhibit self-actuation and continuous motion when placed between two heat baths due to elastic deformations that arise from rotational-symmetry breaking around the rod's axis. Our findings illustrate a simple but robust model to create active motion in mechanically prestrained objects.

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Fig. 1: Global ZEEMs in prestrained elastic objects.
Fig. 2: Self-organized driving of ZEEMs.
Fig. 3: The spiral fibre motor.
Fig. 4: Spontaneous symmetry breaking and self-propulsion of linear fibres.
Fig. 5: Fibre rotation and rolling motion.


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The authors acknowledge the Micro Nano Mechanics at ICS for providing the DMTA facility and thank A. Dutta for useful comments. This work was supported in part by the ANR grant Integrations.

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Authors and Affiliations



A.B., A.S.-F., L.J., V.L.H., P.M. and I.M.K. performed the experiments and analysed data, I.M.K. conceived the work, F.Z. and I.M.K. developed the theory, designed the experiments and wrote the paper, and all the authors commented on the article.

Corresponding authors

Correspondence to Falko Ziebert or Igor M. Kulić.

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The authors declare that they have no competing interests.

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Supplementary information

Supplementary Information

Supplementary Video Legends 1–7, Supplementary Methods, Supplementary Figures 1–13 and Supplementary References

Supplementary Video 1

Toroidal fibre motors

Supplementary Video 2

Spiral fibre motor

Supplementary Video 3

Self-propulsion of fibres

Supplementary Video 4

Annealing nylon-6 motors

Supplementary Video 5

Fibre animation

Supplementary Video 6

Ring self-healing

Supplementary Video 7

Thin filament loop

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Baumann, A., Sánchez-Ferrer, A., Jacomine, L. et al. Motorizing fibres with geometric zero-energy modes. Nature Mater 17, 523–527 (2018).

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