Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Biomimetic 4D printing


Shape-morphing systems can be found in many areas, including smart textiles1, autonomous robotics2, biomedical devices3, drug delivery4 and tissue engineering5. The natural analogues of such systems are exemplified by nastic plant motions, where a variety of organs such as tendrils, bracts, leaves and flowers respond to environmental stimuli (such as humidity, light or touch) by varying internal turgor, which leads to dynamic conformations governed by the tissue composition and microstructural anisotropy of cell walls6,7,8,9,10. Inspired by these botanical systems, we printed composite hydrogel architectures that are encoded with localized, anisotropic swelling behaviour controlled by the alignment of cellulose fibrils along prescribed four-dimensional printing pathways. When combined with a minimal theoretical framework that allows us to solve the inverse problem of designing the alignment patterns for prescribed target shapes, we can programmably fabricate plant-inspired architectures that change shape on immersion in water, yielding complex three-dimensional morphologies.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: Programming localized anisotropy via biomimetic 4D printing.
Figure 2: Printing simple architectures with precise control over mean and Gaussian curvatures.
Figure 3: Complex flower morphologies generated by biomimetic 4D printing.
Figure 4: Predictive 4D printing of biomimetic architectures.


  1. Hu, J., Meng, H., Li, G. & Ibekwe, S. I. A review of stimuli-responsive polymers for smart textile applications. Smart Mater. Struct. 21, 053001 (2012).

    Article  Google Scholar 

  2. Felton, S., Tolley, M., Demaine, E., Rus, D. & Wood, R. A method for building self-folding machines. Science 345, 644–646 (2014).

    Article  CAS  Google Scholar 

  3. Randall, C. L., Gultepe, E. & Gracias, D. H. Self-folding devices and materials for biomedical applications. Trends Biotechnol. 30, 138–146 (2012).

    Article  CAS  Google Scholar 

  4. Fernandes, R. & Gracias, D. H. Self-folding polymeric containers for encapsulation and delivery of drugs. Adv. Drug Deliv. Rev. 64, 1579–1589 (2012).

    Article  CAS  Google Scholar 

  5. Kuribayashi-Shigetomi, K., Onoe, H. & Takeuchi, S. Cell origami: self-folding of three-dimensional cell-laden microstructures driven by cell traction force. PLoS ONE 7, e51085 (2012).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. Awell, B. J., Kriedemann, P. E. & Turnbull, C. G. N. Plants in Action (Macmillan Education AU, 1999).

    Google Scholar 

  8. Reyssat, E. & Mahadevan, L. Hygromorphs: from pine cones to biomimetic bilayers. J. R. Soc. Interface 6, 951–957 (2009).

    Article  CAS  Google Scholar 

  9. Armon, S., Efrati, E., Kupferman, R. & Sharon, E. Geometry and mechanics in the opening of chiral seed pods. Science 333, 1726–1730 (2011).

    Article  CAS  Google Scholar 

  10. Fratzl, P. & Burgert, I. Actuation systems in plants as prototypes for bioinspired devices. Phil. Trans. R. Soc. A 6, 1541–1557 (2009).

    Google Scholar 

  11. Ge, Q., Qi, H. J. & Dunn, M. L. Active materials by four-dimension printing. Appl. Phys. Lett. 103, 131901 (2013).

    Article  Google Scholar 

  12. Ratna, D. & Karger-Kocsis, J. Recent advances in shape memory polymers and composites: a review. J. Mater. Sci. 43, 254–260 (2008).

    Article  CAS  Google Scholar 

  13. Erb, R. M., Sander, J. S., Grisch, R. & Studart, A. E. R. Self-shaping composites with programmable bioinspired microstructures. Nature Commun. 4, 1712 (2012).

    Article  Google Scholar 

  14. Thérien-Aubin, H., Wu, Z. L., Nie, Z. & Kumacheva, E. Multiple shape transformations of composite hydrogel sheets. J. Am. Chem. Soc. 125, 4834–4839 (2013).

    Article  Google Scholar 

  15. Tibbits, S. 4D printing: multi-material shape change. Archit. Des. 84, 116–121 (2014).

    Google Scholar 

  16. Ionov, L. Bioinspired microorigami by self-folding polymer films. Macromol. Chem. Phys. 214, 1178–1183 (2012).

    Article  Google Scholar 

  17. Na, J. H. et al. Programming reversibly self-folding origami with micropatterned photo-crosslinkable polymer trilayers. Adv. Mat. 27, 79–85 (2015).

    Article  CAS  Google Scholar 

  18. Liu, Y., Boyles, J. K., Genzer, J. & Dickey, M. D. Self-folding of polymer sheets using local light absorption. Soft Matter 8, 1764–1769 (2012).

    Article  CAS  Google Scholar 

  19. Lewis, J. A. Direct ink writing of 3D functional materials. Adv. Funct. Mater. 16, 2193–2204 (2006).

    Article  CAS  Google Scholar 

  20. Oytun, F., Kahveci, M. U. & Yagci, Y. Sugar overcomes oxygen inhibition in photoinitiated free radical polymerization. J. Polym. Sci. A 51, 1685–1689 (2013).

    Article  CAS  Google Scholar 

  21. Josset, S. et al. Energy consumption of the nanofibrillation of bleached pulp, wheat straw and recycled newspaper through a grinding process. Nord. Pulp Paper Res. J. 29, 167–175 (2014).

    Article  CAS  Google Scholar 

  22. Haraguchi, K. & Takehisa, T. Nanocomposite hydrogels: a unique organic-inorganic network structure with extraordinary mechanical, optical, and swelling/de-swelling properties. Adv. Mater. 14, 1120–1124 (2002).

    Article  CAS  Google Scholar 

  23. Compton, B. G. & Lewis, J. A. 3D-printing of lightweight cellular composites. Adv. Mater. 26, 5930–5935 (2014).

    Article  CAS  Google Scholar 

  24. Smay, J. E., Cesarano, J. & Lewis, J. A. Colloidal inks for directed assembly of 3-D periodic structures. Langmuir 18, 5429–5437 (2002).

    Article  CAS  Google Scholar 

  25. Aharoni, H., Sharon, E. & Kupferman, R. Geometry of thin nematic elastomer sheets. Phys. Rev. Lett. 113, 257801 (2014).

    Article  Google Scholar 

  26. Timoshenko, S. Analysis of bi-metal thermostats. J. Opt. Soc. Am. 11, 233–255 (1925).

    Article  CAS  Google Scholar 

  27. Modes, C. D., Bhattacharya, K. & Warner, M. Gaussian curvature from flat elastic sheets. Proc. R. Soc. A 467, 1121–1140 (2011).

    Article  Google Scholar 

  28. Abraham, Y. et al. Titled cellulose arrangement as a novel mechanism for hygroscopic coiling in the stork’s bill awn. J. R. Soc. Interface 9, 640–647 (2012).

    Article  Google Scholar 

  29. Liang, H. & Mahadevan, L. The shape of a long leaf. Proc. Natl Acad. Sci. USA 106, 22049–22054 (2009).

    Article  CAS  Google Scholar 

  30. Liang, H. & Mahadevan, L. Growth, geometry, and mechanics of a blooming lily. Proc. Natl Acad. Sci. USA 108, 5516–5521 (2011).

    Article  CAS  Google Scholar 

  31. van Doorn, W. G. Flower opening and closure: a review. J. Exp. Bot. 54, 1801–1812 (2003).

    Article  CAS  Google Scholar 

  32. Haraguchi, K., Li, H.-J., Matsuda, K., Takehisa, T. & Elliott, E. Mechanism of forming organic/inorganic network structures during in-situ free-radical polymerization in PNIPA-clay nanocomposite hydrogels. Macromolecules 38, 3482–3490 (2005).

    Article  CAS  Google Scholar 

  33. Yong, X., Kuksenok, O. & Balazs, A. C. Modeling free radical polymerization using dissipative particle dynamics. Polymer 72, 217–225 (2015).

    Article  CAS  Google Scholar 

  34. Haraguchi, K., Murata, K. & Takehisa, T. Stimuli-responsive nanocomposite gels and soft nanocomposites consisting of inorganic clays and copolymers with different chemical affinities. Macromolecules 45, 385–391 (2012).

    Article  CAS  Google Scholar 

Download references


A.S.G. and J.A.L. were supported by the Army Research Office Award No. W911NF-13-0489. E.A.M. and L.M. werez supported by the NSF DMR 14-20570, Materials Research Science and Engineering Center, MRSEC and NSF DMREF 15-33985. We thank D. Stepp (ARO), A. Balazs (U. Pittsburgh), M. Brenner (Harvard) and B. Compton for useful discussions. We thank T. Zimmermann and the researchers at the Applied Wood Materials Laboratory at EMPA for providing samples of nanofibrillated cellulose. We also thank D. Kolesky for assistance with confocal imaging, D. Fitzgerald and J. Minardi for help with initial G-code programming, R. Valentin for permission to print a copy of his orchid photograph, and L. K. Sanders for help with photography and videography.

Author information

Authors and Affiliations



A.S.G., R.G.N. and J.A.L. developed the 4D printing concept. A.S.G. designed the ink composition, printed and prepared all samples, obtained photographic images, and characterized alignment, swelling, mechanical and rheological properties. E.A.M. and L.M. developed the theoretical model. E.A.M. rendered and calculated the desired shapes and print paths, and generated the G-code for printing. A.S.G., E.A.M., L.M. and J.A.L. wrote the manuscript. A.S.G. and E.A.M. developed the figures. All authors commented on the manuscript.

Corresponding authors

Correspondence to L. Mahadevan or Jennifer A. Lewis.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 23275 kb)

Supplementary Movie 1

Supplementary Movie 1 (MP4 1131 kb)

Supplementary Movie 2

Supplementary Movie 2 (MP4 302 kb)

Supplementary Movie 3

Supplementary Movie 3 (MP4 838 kb)

Supplementary Movie 4

Supplementary Movie 4 (MP4 538 kb)

Supplementary Movie 5

Supplementary Movie 5 (MP4 24818 kb)

Supplementary Movie 6

Supplementary Movie 6 (MP4 827 kb)

Supplementary Movie 7

Supplementary Movie 7 (MP4 6215 kb)

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sydney Gladman, A., Matsumoto, E., Nuzzo, R. et al. Biomimetic 4D printing. Nature Mater 15, 413–418 (2016).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing