Shape-morphing structures are at the core of future applications in aeronautics1, minimally invasive surgery2, tissue engineering3 and smart materials4. However, current engineering technologies, based on inhomogeneous actuation across the thickness of slender structures, are intrinsically limited to one-directional bending5. Here, we describe a strategy where mesostructured elastomer plates undergo fast, controllable and complex shape transformations under applied pressure. Similar to pioneering techniques based on soft hydrogel swelling6,7,8,9,10, these pneumatic shape-morphing elastomers, termed here as ‘baromorphs’, are inspired by the morphogenesis of biological structures11,12,13,14,15. Geometric restrictions are overcome by controlling precisely the local growth rate and direction through a specific network of airways embedded inside the rubber plate. We show how arbitrary three-dimensional shapes can be programmed using an analytic theoretical model, propose a direct geometric solution to the inverse problem, and illustrate the versatility of the technique with a collection of configurations.
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The data supporting the findings of this study are available within the paper and its Supplementary Information files and from the corresponding author upon reasonable request.
Ajaj, R. M., Beaverstock, C. S. & Friswell, M. I. Morphing aircraft: the need for a new design philosophy. Aerospace Sci. Technol. 49, 154–166 (2016).
Cianchetti, M. et al. Soft robotics technologies to address shortcomings in today’s minimally invasive surgery: The stiff-flop approach. Soft Robotics 1, 122–131 (2014).
Gao, B. et al. 4D bioprinting for biomedical applications. Trends Biotechnol. 34, 746–756 (2016).
McEvoy, M. A. & Correll, N. Materials that couple sensing, actuation, computation, and communication. Science 347, 1261689 (2015).
Shepherd, R. F. et al. Multigait soft robot. Proc. Natl Acad. Sci. USA 108, 20400–20403 (2011).
Klein, Y., Efrati, E. & Sharon, E. Shaping of elastic sheets by prescription of non-Euclidean metrics. Science 315, 1116–1120 (2007).
Kim, J., Hanna, J. A., Byun, M., Santangelo, C. D. & Hayward, R. C. Designing responsive buckled surfaces by halftone gel lithography. Science 335, 1201–1205 (2012).
Aharoni, H., Sharon, E. & Kupferman, R. Geometry of thin nematic elastomer sheets. Phys. Rev. Lett. 113, 257801 (2014).
Erb, R. M., Sander, J. S., Grisch, R. & Studart, A. R. Self-shaping composites with programmable bioinspired microstructures. Nat. Commun. 4, 1712 (2013).
Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nat. Mater. 15, 416–418 (2016).
Dervaux, J. & Ben Amar, M. Morphogenesis of growing soft tissues. Phys. Rev. Lett. 101, 068101 (2008).
Rebocho, A. B., Kennaway, J. R., Bangham, J. A. & Coen, E. Formation and shaping of the antirrhinum flower through modulation of the cup boundary gene. Curr. Biol. 27, 2610–2622 (2017).
Nath, U., Crawford, B., Carpenter, R. & Coen, E. Genetic control of surface curvature. Science 299, 1404–1407 (2003).
Fratzl, P., Elbaum, R. & Burgert, I. Cellulose fibrils direct plant organ movements. Faraday Discuss. 139, 275–282 (2008).
Armon, S., Efrati, E., Kupferman, R. & Sharon, E. Geometry and mechanics in the opening of chiral seed pods. Science 333, 1726–1730 (2011).
Reyssat, E. & Mahadevan, L. Hygromorphs: from pine cones to biomimetic bilayers. J. R. Soc. Interface 6, 951–957 (2009).
Pezzulla, M., Smith, G. P., Nardinocchi, P. & Holmes, D. P. Geometry and mechanics of thin growing bilayers. Soft Matter 12, 4435–4442 (2016).
Huang, L. et al. Ultrafast digital printing toward 4D shape changing materials. Adv. Mater. 29, 1605390 (2017).
Gorissen, B. et al. Elastic inflatable actuators for soft robotic applications. Adv. Mater. 29, 1604977 (2017).
Pikul, J. H. et al. Stretchable surfaces with programmable 3D texture morphing for synthetic camouflaging skins. Science 358, 210–214 (2017).
Bertoldi, K., Vitelli, V., Christensen, J. & van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 17066 (2017).
Timoshenko, S. & Woinowsky-Krieger, S. Theory of Plates and Shells 2nd edn (McGraw-Hill, New York, 1959).
Serikawa, K. A. & Mandoli, D. F. An analysis of morphogenesis of the reproductive whorl of Acetabularia acetabulum. Planta 207, 96–104 (1998).
Dias, M. A., Hanna, J. A. & Santangelo, C. D. Programmed buckling by controlled lateral swelling in a thin elastic sheet. Phys. Rev. E 84, 036603 (2011).
Efrati, E., Sharon, E. & Kupferman, R. Elastic theory of unconstrained non-Euclidean plates. J. Mech. Phys. Solids 57, 762–775 (2009).
Mosadegh, B. et al. Pneumatic networks for soft robotics that actuate rapidly. Adv. Funct. Mater. 24, 2163–2170 (2014).
Dumais, J. & Forterre, Y. ‘Vegetable dynamicks’: the role of water in plant movements. Annu. Rev. Fluid. Mech. 44, 453–478 (2012).
Aharoni, H., Xia, Y., Zhang, X., Kamien, R. & Yang, S. Universal inverse design of surfaces with thin nematic elastomer sheets. Proc. Natl Acad. Sci. USA 115, 7206–7211 (2018).
Konakovic, M. et al. Beyond developable: computational design and fabrication with auxetic materials. ACM Trans. Graph. 35, 1–11 (2016).
van Rees, W. M., Vouga, E. & Mahadevan, L. Growth patterns for shape-shifting elastic bilayers. Proc. Natl Acad. Sci. USA 114, 11597–11602 (2017).
Hild, F. & Roux, S. Digital image correlation: from displacement measurement to identification of elastic properties—a review. Strain 42, 69–80 (2006).
Cobelli, P. J., Maurel, A., Pagneux, V. & Petitjeans, P. Global measurement of water waves by Fourier transform profilometry. Exp. Fluids 46, 1037–1047 (2009).
der Jeught, S. V., Soons, J. A. M. & Dirckx, J. J. J. Real-time microscopic phase-shifting profilometry. Appl. Opt. 54, 4953–4959 (2015).
Ghiglia, D. C. & Romero, L. A. Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods. J. Opt. Soc. Am. A 11, 107–117 (1994).
This work received support from the Institut Pierre-Gilles de Gennes (Équipement d’excellence, ‘investissements d’avenir’, ANR-10-EQPX-34) and from ANR SMART. The authors thank C. Blanquart for developing the 3D scanning technique and M. Lebihain from the Institut Jean Le Rond d’Alembert for technical support with 3D printing of the moulds.
The authors declare no competing interests.
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Supplementary Video Legends 1–10, Supplementary Notes, Supplementary Figures 1–9
Dynamical behaviour of a baromorph under inflation and deflation
Parallel actuation of three baromorphs with the same design, at different scales
Bowl-shaped baromorph fitting a spherical cap
Large angle cone with a centred hole
A helicoid baromorph
Face programmed with the geometric inverse recipe
A mask baromorph
Actuation of a double layer baromorph
Actuation of an isotropic baromorph
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Siéfert, E., Reyssat, E., Bico, J. et al. Bio-inspired pneumatic shape-morphing elastomers. Nature Mater 18, 24–28 (2019). https://doi.org/10.1038/s41563-018-0219-x
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