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Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics


Three-dimensional (3D) structures capable of reversible transformations in their geometrical layouts have important applications across a broad range of areas. Most morphable 3D systems rely on concepts inspired by origami/kirigami or techniques of 3D printing with responsive materials. The development of schemes that can simultaneously apply across a wide range of size scales and with classes of advanced materials found in state-of-the-art microsystem technologies remains challenging. Here, we introduce a set of concepts for morphable 3D mesostructures in diverse materials and fully formed planar devices spanning length scales from micrometres to millimetres. The approaches rely on elastomer platforms deformed in different time sequences to elastically alter the 3D geometries of supported mesostructures via nonlinear mechanical buckling. Over 20 examples have been experimentally and theoretically investigated, including mesostructures that can be reshaped between different geometries as well as those that can morph into three or more distinct states. An adaptive radiofrequency circuit and a concealable electromagnetic device provide examples of functionally reconfigurable microelectronic devices.

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Fig. 1: Morphable 3D mesostructures, integrated circuits and optoelectronic devices by loading-path controlled mechanical assembly.
Fig. 2: Probabilistic energy analysis and design rationale for morphable 3D mesostructures.
Fig. 3: A broad set of 3D mesostructures morphable by loading path strategies.
Fig. 4: Morphable 3D mesostructures with multiple (≥3) stable states accessed through complex paths of sequential release.
Fig. 5: Applications of 3D morphable mesostructures as switchable radiofrequency (RF) electronic components.


  1. 1.

    Miura, K. Method of packaging and deployment of large membranes in space. The Institute of Space and Astronautical Science Report 618, 1–9 (1985).

  2. 2.

    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  Google Scholar 

  3. 3.

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

    Article  Google Scholar 

  4. 4.

    Bishop, D., Pardo, F., Bolle, C., Giles, R. & Aksyuk, V. Silicon micro-machines for fun and profit. J. Low Temp. Phys. 169, 386–399 (2012).

    Article  Google Scholar 

  5. 5.

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

    Article  Google Scholar 

  6. 6.

    Ko, H. & Javey, A. Smart actuators and adhesives for reconfigurable matter. Acc. Chem. Res. 50, 691–702 (2017).

    Article  Google Scholar 

  7. 7.

    Kwok, S. W. et al. Magnetic assembly of soft robots with hard components. Adv. Funct. Mater. 24, 2180–2187 (2014).

    Article  Google Scholar 

  8. 8.

    Silverberg, J. L. et al. Using origami design principles to fold reprogrammable mechanical metamaterials. Science 345, 647–650 (2014).

    Article  Google Scholar 

  9. 9.

    Overvelde, J. T. B. et al. A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom. Nat. Commun. 7, 10929 (2016).

    Article  Google Scholar 

  10. 10.

    Overvelde, J. T. B., Weaver, J. C., Hoberman, C. & Bertoldi, K. Rational design of reconfigurable prismatic architected materials. Nature 541, 347–352 (2017).

    Article  Google Scholar 

  11. 11.

    Shan, S. et al. Multistable architected materials for trapping elastic strain energy. Adv. Mater. 27, 4296–4301 (2015).

    Article  Google Scholar 

  12. 12.

    Li, X. Y. & Gao, H. J. Smaller and stronger. Nat. Mater. 15, 373–374 (2016).

    Article  Google Scholar 

  13. 13.

    Silverberg, J. L. et al. Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat. Mater. 14, 389–393 (2015).

    Article  Google Scholar 

  14. 14.

    Yang, N. & Silverberg, J. L. Decoupling local mechanics from large-scale structure in modular metamaterials. Proc. Natl Acad. Sci. USA 114, 3590–3595 (2017).

    Article  Google Scholar 

  15. 15.

    Castle, T. et al. Making the cut: lattice kirigami rules. Phys. Rev. Lett. 113, 245502 (2014).

    Article  Google Scholar 

  16. 16.

    Castle, T., Sussman, D. M., Tanis, M. & Kamien, R. D. Additive lattice kirigami. Sci. Adv. 2, e1601258 (2016).

    Article  Google Scholar 

  17. 17.

    Sussman, D. M. et al. Algorithmic lattice kirigami: a route to pluripotent materials. Proc. Natl Acad. Sci. USA 112, 7449–7453 (2015).

    Article  Google Scholar 

  18. 18.

    Dudte, L. H., Vouga, E., Tachi, T. & Mahadevan, L. Programming curvature using origami tessellations. Nat. Mater. 15, 583–588 (2016).

    Article  Google Scholar 

  19. 19.

    Lv, C., Krishnaraju, D., Konjevod, G., Yu, H. Y. & Jiang, H. Q. Origami based mechanical metamaterials. Sci. Rep. 4, 5979 (2014).

    Article  Google Scholar 

  20. 20.

    Schenk, M. & Guest, S. D. Geometry of Miura-folded metamaterials. Proc. Natl Acad. Sci. USA 110, 3276–3281 (2013).

    Article  Google Scholar 

  21. 21.

    Waitukaitis, S., Menaut, R., Chen, B. G. G. & van Hecke, M. Origami multistability: from single vertices to metasheets. Phys. Rev. Lett. 114, 055503 (2015).

    Article  Google Scholar 

  22. 22.

    Wei, Z. Y., Guo, Z. V., Dudte, L., Liang, H. Y. & Mahadevan, L. Geometric mechanics of periodic pleated origami. Phys. Rev. Lett. 110, 215501 (2013).

    Article  Google Scholar 

  23. 23.

    Al-Mulla, T., & Buehler, M. J. Folding creases through bending. Nat. Mater. 14, 366–368 (2015).

    Article  Google Scholar 

  24. 24.

    Reis, P. M., Jimenez, F. L. & Marthelot, J. Transforming architectures inspired by origami. Proc. Natl Acad. Sci. USA 112, 12234–12235 (2015).

    Article  Google Scholar 

  25. 25.

    Cheung, K. C., Tachi, T., Calisch, S. & Miura, K. Origami interleaved tube cellular materials. Smart Mater. Struct. 23, 094012 (2014).

    Article  Google Scholar 

  26. 26.

    Filipov, E. T., Paulino, G. H. & Tachi, T.Origami tubes with reconfigurable polygonal cross-sections. Proc. R. Soc. A 472, 20150607 (2016).

    Article  Google Scholar 

  27. 27.

    Filipov, E. T., Tachi, T. & Paulino, G. H. Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials. Proc. Natl Acad. Sci. USA 112, 12321–12326 (2015).

    Article  Google Scholar 

  28. 28.

    Babaee, S., Overvelde, J. T. B., Chen, E. R., Tournat, V. & Bertoldi, K. Reconfigurable origami-inspired acoustic waveguides. Sci. Adv. 2, e1601019 (2016).

    Article  Google Scholar 

  29. 29.

    Rogers, J., Huang, Y. G., Schmidt, O. G. & Gracias, D. H. Origami MEMS and NEMS. MRS Bull. 41, 123–129 (2016).

    Article  Google Scholar 

  30. 30.

    Shenoy, V. B. & Gracias, D. H. Self-folding thin-film materials: from nanopolyhedra to graphene origami. MRS Bull. 37, 847–854 (2012).

    Article  Google Scholar 

  31. 31.

    Leong, T. G. et al. Tetherless thermobiochemically actuated microgrippers. Proc. Natl Acad. Sci. USA. 106, 703–708 (2009).

    Article  Google Scholar 

  32. 32.

    Reis, P. M. A perspective on the revival of structural (in)stability with novel opportunities for function: from Buckliphobia to Buckliphilia. J. Appl. Mech. 82, 111001 (2015).

    Article  Google Scholar 

  33. 33.

    Ge, Q., Dunn, C. K., Qi, H. J. & Dunn, M. L. Active origami by 4D printing. Smart Mater. Struct. 23, 094007 (2014).

    Article  Google Scholar 

  34. 34.

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

    Article  Google Scholar 

  35. 35.

    Ding, Z. et al. Direct 4D printing via active composite materials. Sci. Adv. 3, e1602890 (2017).

    Article  Google Scholar 

  36. 36.

    Gladman, A. S., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nat. Mater. 15, 413–418 (2016).

    Article  Google Scholar 

  37. 37.

    Raviv, D. et al. Active printed materials for complex self-evolving deformations. Sci. Rep. 4, 7422 (2014).

    Article  Google Scholar 

  38. 38.

    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).

    Article  Google Scholar 

  39. 39.

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

    Article  Google Scholar 

  40. 40.

    Zhang, Y. H. et al. Printing, folding and assembly methods for forming 3D mesostructures in advanced materials. Nat. Rev. Mater. 2, 17019 (2017).

    Article  Google Scholar 

  41. 41.

    Liu, Y., Genzer, J. & Dickey, M. D. ‘2D or not 2D’: shape-programming polymer sheets. Prog. Polym. Sci. 52, 79–106 (2016).

    Article  Google Scholar 

  42. 42.

    Liu, Y., Shaw, B., Dickey, M. D. & Genzer, J. Sequential self-folding of polymer sheets. Sci. Adv. 3, e1602417 (2017).

    Article  Google Scholar 

  43. 43.

    Xu, S. et al. Assembly of micro/nanomaterials into complex, three-dimensional architectures by compressive buckling. Science 347, 154–159 (2015).

    Article  Google Scholar 

  44. 44.

    Zhang, Y. H. et al. A mechanically driven form of kirigami as a route to 3D mesostructures in micro/nanomembranes. Proc. Natl Acad. Sci. USA 112, 11757–11764 (2015).

    Article  Google Scholar 

  45. 45.

    Yan, Z. et al. Mechanical assembly of complex, 3D mesostructures from releasable multilayers of advanced materials. Sci. Adv. 2, e1601014 (2016).

    Article  Google Scholar 

  46. 46.

    Yan, Z. et al. Controlled mechanical buckling for origami-inspired construction of 3D microstructures in advanced materials. Adv. Funct. Mater. 26, 2629–2639 (2016).

    Article  Google Scholar 

  47. 47.

    Nan, K. et al. Engineered elastomer substrates for guided assembly of complex 3D mesostructures by spatially nonuniform compressive buckling. Adv. Funct. Mater. 27, 1604281 (2017).

    Article  Google Scholar 

  48. 48.

    Kim, J. et al. Battery-free, stretchable optoelectronic systems for wireless optical characterization of the skin. Sci. Adv. 2, e1600418 (2016).

    Article  Google Scholar 

  49. 49.

    Kong, Y. L. et al. 3D printed quantum dot light-emitting diodes. Nano Lett. 14, 7017–7023 (2014).

    Article  Google Scholar 

  50. 50.

    Fenno, L., Yizhar, O. & Deisseroth, K. The development and application of optogenetics. Annu. Rev. Neurosci. 34, 389–412 (2011).

    Article  Google Scholar 

  51. 51.

    Kim, T. I. et al. Injectable, cellular-scale optoelectronics with applications for wireless optogenetics. Science 340, 211–216 (2013).

    Article  Google Scholar 

  52. 52.

    Kim, S. et al. Microstructured elastomeric surfaces with reversible adhesion and examples of their use in deterministic assembly by transfer printing. Proc. Natl Acad. Sci. USA 107, 17095–17100 (2010).

    Article  Google Scholar 

  53. 53.

    Meitl, M. A. et al. Transfer printing by kinetic control of adhesion to an elastomeric stamp. Nat. Mater. 5, 33–38 (2006).

    Article  Google Scholar 

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J.A.R. and X.L. acknowledge support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences (DE-FG02-07ER46471). Y.Z. acknowledges support from the National Natural Science Foundation of China (11672152), the National Basic Research Program of China (2015CB351900), the Thousand Young Talents Program of China and the Tsinghua National Laboratory for Information Science and Technology. Y.H. acknowledges the support from the NSF (CMMI1300846, CMMI1400169 and CMMI1534120) and the NIH (R01EB019337). J.W.L. acknowledges support from National Research Foundation of Korea (NRF-2017M3A7B4049466). K.N. acknowledges the support from the Frederick Seitz Materials Research Laboratory Central Research Facilities, University of Illinois, where the majority of the experimental work was carried out.

Author information




J.A.R., Yihui Z. and Y.H. designed and supervised the research; Yihui Z. and H.F. led the structural designs, mechanics modelling, electromagnetic modelling, and design of conceivable electromagnetic device, with assistance from K.B., F.L., Y.L., D.F. and Y.H.; H.F. led the submillimetre-scale experimental work, with assistance from K.B. and X.C.; K.N. led the micro-fabrication work, with assistance from W.B., C.Z., J.W, Y.L., M.H., Z.Y., H.L., Yijie Z., Yutong Z., J.Z. and J.W.L.; W.H., K.N. and W.B. led the design and experimental characterizations of 3D radiofrequency demonstrations, with assistance from M.L. and X.L.; K.N., H.F. and L.L. led the design and experimental realizations of 3D active device demonstrations, with assistance from W.B., C.Z., Y.L. and J.Z.; H.F., K.N., W.B., Y.H., Yihui Z., and J.A.R. wrote the text and designed the figures. All authors commented on the paper.

Corresponding authors

Correspondence to Yonggang Huang, Yihui Zhang or John A. Rogers.

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The authors declare no competing financial interests.

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Supplementary information

Supplementary Information

Supplementary Notes 1–4; Supplementary Figures 1–25


Supplementary Video 1

A morphable mesostructure that can be reconfigured between an ‘octopus’ and a ‘spider’.

Supplementary Video 2

A morphable mesostructure that can be reconfigured among four stable shapes.

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Fu, H., Nan, K., Bai, W. et al. Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nature Mater 17, 268–276 (2018).

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