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Cited by 510

The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.

Sequential Self-Folding Structures by 3D Printed Digital Shape Memory Polymers

Open access
Mao, Yiqi, Yu, Kai, Isakov, Michael S., Wu, Jiangtao, Dunn, Martin L., Jerry Qi, H.·2015·Scientific Reports
DOI 10.1038/srep13616
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Abstract

Folding is ubiquitous in nature with examples ranging from the formation of cellular components to winged insects. It finds technological applications including packaging of solar cells and space structures, deployable biomedical devices and self-assembling robots and airbags. Here we demonstrate sequential self-folding structures realized by thermal activation of spatially-variable patterns that are 3D printed with digital shape memory polymers, which are digital materials with different shape memory behaviors. The time-dependent behavior of each polymer allows the temporal sequencing of activation when the structure is subjected to a uniform temperature. This is demonstrated via a series of 3D printed structures that respond rapidly to a thermal stimulus and self-fold to specified shapes in controlled shape changing sequences. Measurements of the spatial and temporal nature of self-folding structures are in good agreement with the companion finite element simulations. A simplified reduced-order model is also developed to rapidly and accurately describe the self-folding physics. An important aspect of self-folding is the management of self-collisions, where different portions of the folding structure contact and then block further folding. A metric is developed to predict collisions and is used together with the reduced-order model to design self-folding structures that lock themselves into stable desired configurations.

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Research works printed but not linked: 43

  1. Haas, F. & Wootton, R. J. Two basic mechanisms in insect wing folding. P Roy Soc B-Biol Sci 263, 1651–1658, 10.1098/Rspb.1996.0241 (1996). · doi:10.1098/rspb.1996.0241
  2. Kobayashi, H., Daimaruya, M. & Vincent, J. F. V. Effect of crease interval on unfolding manner of corrugated tree leaves. Jsme Int J C-Mech Sy 42, 759–767 (1999). · doi:10.1299/jsmec.42.759
  3. Kobayashi, H., Daimaruya, M. & Vincent, J. F. V. Folding/unfolding manner of tree leaves as a deployable structure. Iutam-Iass Symposium on Deployable Structures: Theory and Applications 80, 211–220 (2000).
  4. Kobayashi, H., Kresling, B. & Vincent, J. F. V. The geometry of unfolding tree leaves. P Roy Soc B-Biol Sci 265, 147–154 (1998). · DOI · Paper page
  5. Lang, R. J. The science of origami. Phys World 20, 30–31 (2007). · DOI · Paper page
  6. Guo, X. Y. et al. Two- and three-dimensional folding of thin film single-crystalline silicon for photovoltaic power applications. P Natl Acad Sci USA 106, 20149–20154, 10.1073/Pnas.0907390106 (2009). · DOI · Paper page
  7. Song, Z. et al. Origami lithium-ion batteries. Nat Commun 5, 10.1038/ncomms4140 (2014). · DOI · Paper page
  8. Wu, W. N. & You, Z. Modelling rigid origami with quaternions and dual quaternions. P Roy Soc a-Math Phy 466, 2155–2174, 10.1098/Rspa.2009.0625 (2010). · DOI
  9. Wu, W. N. & You, Z. A solution for folding rigid tall shopping bags. P Roy Soc a-Math Phy 467, 2561–2574, 10.1098/Rspa.2011.0120 (2011). · DOI
  10. Gracias, D. H. Stimuli responsive self-folding using thin polymer films. Current Opinion in Chemical Engineering 2, 112–119 (2013). · DOI · Paper page
  11. Randall, C. L., Gultepe, E. & Gracias, D. H. Self-folding devices and materials for biomedical applications. Trends Biotechnol 30, 138–146, 10.1016/J.Tibtech.2011.06.013 (2012). · DOI · Paper page
  12. Yoon, C. et al. Functional stimuli responsive hydrogel devices by self-folding. Smart Materials and Structures 23, Artn 094008 10.1088/0964-1726/23/9/094008 (2014). · DOI · Paper page
  13. Lv, C., Krishnaraju, D., Konjevod, G., Yu, H. & Jiang, H. Origami based Mechanical Metamaterials. Sci. Rep. 4, 5979 (2014). · DOI · Paper page
  14. Bassik, N., Stern, G. M. & Gracias, D. H. Microassembly based on hands free origami with bidirectional curvature Appl. Phys. Lett. 95 (2009). · DOI
  15. Guan, J., He, H., Hansford, D. J. & Lee, L. J. Self-folding of three-dimensional hydrogel microstructures. J. Phys. Chem. B 109, 23134–23137 (2005). · DOI · Paper page
  16. Judy, J. W. & Muller, R. S. Magnetically actuated,addressable microstructures. Journal of Microelectromechanical systems 6 (1997). · DOI · Paper page
  17. Hawkes, E. et al. Programmable matter by folding. Proc. Natl. Acad. Sci. 107, 12441–12445 (2010). · DOI · Paper page
  18. Cademartiri, L. & Bishop, K. J. M. Programmable self-assembly. Nature Materials 14, 2–9, 10.1038/nmat4184 (2015). · DOI · Paper page
  19. Ma, C. X. et al. Supramolecular Lego Assembly Towards Three-Dimensional Multi-Responsive Hydrogels. Advanced Materials 26, 5665-+, 10.1002/adma.201402026 (2014). · DOI
  20. Ge, Q., Dunn, C. K., Qi, H. J. & Dunn, M. L. Active Origami by 4D Printing. Smart Materials & Structures 23, 094007–094015 (2014). · DOI · Paper page
  21. Bakarich, S. E., Gorkin, I., Panhuis, M. & Spinks, G. M. 4D Printing with Mechanically Robust, Thermally Actuating Hydrogels. Macromolecular rapid communications 36, 1211–1217 (2015). · DOI · Paper page
  22. Pei, E. J. 4D Printing: dawn of an emerging technology cycle. Assembly Autom 34, 310–314, 10.1108/Aa-07-2014-062 (2014). · DOI · Paper page
  23. Raviv, D. et al. Active Printed Materials for Complex Self- Evolving Deformations. Scientific reports 4, ARTN 7422, 10.1038/srep07422 (2014). · DOI · Paper page
  24. Behl, M., Bellin, I., Kelch, S., Wagermaier, W. & Lendlein, A. One-Step Process for Creating Triple-Shape Capability of AB Polymer Networks. Advanced Functional Materials 19, 102–108, 10.1002/adfm.200800850 (2009). · DOI · Paper page
  25. Luo, X. F. & Mather, P. T. Triple-Shape Polymeric Composites (TSPCs). Adv Funct Mater 20, 2649–2656, 10.1002/Adfm.201000052 (2010). · DOI · Paper page
  26. Mohr, R. et al. Initiation of shape-memory effect by inductive heating of magnetic nanoparticles in thermoplastic polymers. P Natl Acad Sci USA 103, 3540–3545, 10.1073/Pnas.0600079103 (2006). · DOI · Paper page
  27. Buckley, P. R. et al. Inductively heated shape memory polymer for the magnetic actuation of medical devices. Ieee Transactions on Biomedical Engineering 53, 2075–2083, 10.1109/Tbme.2006.877113 (2006). · DOI · Paper page
  28. Schmidt, A. M. Electromagnetic activation of shape memory polymer networks containing magnetic nanoparticles. Macromol Rapid Comm 27, 1168–1172, 10.1002/marc.200600225 (2006). · DOI · Paper page
  29. Jiang, H. Y., Kelch, S. & Lendlein, A. Polymers move in response to light. Adv Mater 18, 1471–1475, 10.1002/adma.200502266 (2006). · DOI · Paper page
  30. Scott, T. F., Schneider, A. D., Cook, W. D. & Bowman, C. N. Photoinduced plasticity in cross-linked polymers. Science 308, 1615–1617, 10.1126/science.1110505 (2005). · DOI · Paper page
  31. Yakacki, C. M. et al. Unconstrained recovery characterization of shape-memory polymer networks for cardiovascular applications. Biomaterials 28, 2255–2263, 10.1016/J.Biomaterials.2007.01.030 (2007). · DOI · Paper page
  32. Lendlein, A. & Kelch, S. Shape-memory polymers as stimuli-sensitive implant materials. Clinical Hemorheology and Microcirculation 32, 105–116 (2005).
  33. Francis, W. H. et al. in 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference. AIAA 2007–2164.
  34. Liu, Y., Miskiewicz, M., Escuti, M. J., Genzer, J. & Dickey, M. D. Three-dimensional folding of pre-strained polymer sheets via absorption of laser light. Journal of Applied Physics 115, Artn 204911, 10.1063/1.4880160 (2014). · DOI
  35. Felton, S., Tolley, M., Demaine, E., Rus, D. & Wood, R. Applied origami. A method for building self-folding machines. Science 345, 644–646, 10.1126/science.1252610 (2014). · DOI · Paper page
  36. Felton, S. M. et al. Self-folding with shape memory composites. Soft Matter 9, 7688–7694, 10.1039/C3sm51003d (2013). · DOI · Paper page
  37. Yu, K., Ge, Q. & Qi, H. J. Reduced time as a unified parameter determining fixity and free recovery of shape memory polymers. Nat.Commun. 5, 3066, 10.1038/ncomms4066 (2014). · DOI · Paper page
  38. Diani, J., Gilormini, P., Fredy, C. & Rousseau, I. Predicting thermal shape memory of crosslinked polymer networks from linear viscoelasticity. International Journal of Solids and Structures 49, 793–799, 10.1016/J.Ijsolstr.2011.11.019 (2012). · DOI · Paper page
  39. Yu, K., Westbrook, K. K., Kao, P. H., Leng, J. & Qi, H. J. Design considerations for shape memory polymer composites with magnetic particles. J Compos Mater 47, 51–63, 10.1177/0021998312447647 (2013). · DOI
  40. Shan, S. et al. Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves. Adv Funct Mater 24, 4935–4942, 10.1002/adfm.201400665 (2014). · DOI · Paper page
  41. Castro, F., Westbrook, K., Long, K., Shandas, R. & Qi, H. Effects of thermal rates on the thermomechanical behaviors of amorphous shape memory polymers. Mechanics of Time-Dependent Materials 14, 219–241, 10.1007/s11043-010-9109-6 (2010). · DOI
  42. Ferry, J. D. Viscoelastic properties of polymers. 3d edn, (Wiley, 1980).
  43. Young, R. J. & Lovell, P. A. Introduction to polymers. 3rd edn, (CRC Press, 2011). · doi:10.1201/9781439894156 · Paper page

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Metadata

Authors
Mao, Y., Yu, K., Isakov, M. S., Wu, J., Dunn, M. L., & Jerry Qi, H.
Venue
Scientific Reports
Publisher
Springer Science and Business Media LLC
Published
2015-09-08
Volume
5
Issue
1
Pages
13616-13616
ISSN
2045-2322 (ISSN-L)
DOI
10.1038/srep13616
OpenAlex
W2414330814
Cited by
510
References
10
FWCI
41.52
Type
journal article
Language
en
Open access
gold
Licence

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CoChat. (2026). Citation check: Sequential Self-Folding Structures by 3D Printed Digital Shape Memory Polymers. https://app.cochat.ai/papers/10.1038/srep13616
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Mao, Y., Yu, K., Isakov, M. S., Wu, J., Dunn, M. L., & Jerry Qi, H. (2015). Sequential Self-Folding Structures by 3D Printed Digital Shape Memory Polymers. Scientific Reports. https://doi.org/10.1038/srep13616

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