Multiscale metallic metamaterials

An Addendum to this article was published on 27 March 2017

This article has been updated


Materials with three-dimensional micro- and nanoarchitectures exhibit many beneficial mechanical, energy conversion and optical properties. However, these three-dimensional microarchitectures are significantly limited by their scalability. Efforts have only been successful only in demonstrating overall structure sizes of hundreds of micrometres, or contain size-scale gaps of several orders of magnitude. This results in degraded mechanical properties at the macroscale. Here we demonstrate hierarchical metamaterials with disparate three-dimensional features spanning seven orders of magnitude, from nanometres to centimetres. At the macroscale they achieve high tensile elasticity (>20%) not found in their brittle-like metallic constituents, and a near-constant specific strength. Creation of these materials is enabled by a high-resolution, large-area additive manufacturing technique with scalability not achievable by two-photon polymerization or traditional stereolithography. With overall part sizes approaching tens of centimetres, these unique nanostructured metamaterials might find use in a broad array of applications.

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Figure 1: Nickel alloy hierarchical metamaterial and critical features across seven orders of magnitude in length scale.
Figure 2: Hybrid hierarchical metamaterials from combinations of microarchitectures.
Figure 3: Tunable compressive response of fractal-like metamaterial.
Figure 4: Uniaxial tensile responses of hybrid hierarchical metamaterials.

Change history

  • 07 March 2017

    In the version of this Article originally published, Fig. 3e used data from ref. 3 that has since been corrected. The Al2O3 nanolattice dataset has been corrected to reflect this. In addition, the Al2O3 hollowtube dataset from ref. 14 has been added to the plot. These changes do not affect the data or findings of the present study.


  1. 1

    Bauer, J., Schroer, A., Schwaiger, R. & Kraft, O. Approaching theoretical strength in glassy carbon nanolattices. Nature Mater. 15, 438–443 (2016).

    CAS  Article  Google Scholar 

  2. 2

    Jang, D., Meza, L. R., Greer, F. & Greer, J. R. Fabrication and deformation of three-dimensional hollow ceramic nanostructures. Nature Mater. 12, 893–898 (2013).

    CAS  Article  Google Scholar 

  3. 3

    Meza, L. R., Das, S. & Greer, J. R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345, 1322–1326 (2014).

    CAS  Article  Google Scholar 

  4. 4

    Zheng, X. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373–1377 (2014).

    CAS  Article  Google Scholar 

  5. 5

    Zhang, H. G., Yu, X. D. & Braun, P. V. Three-dimensional bicontinuous ultrafast-charge and -discharge bulk battery electrodes. Nature Nanotech. 6, 277–281 (2011).

    CAS  Article  Google Scholar 

  6. 6

    Bonaccorso, F. et al. Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage. Science 347, (2015).

    Article  Google Scholar 

  7. 7

    Soukoulis, C. M. & Wegener, M. Past achievements and future challenges in the development of three-dimensional photonic metamaterials. Nature Photon. 5, 523–530 (2011).

    CAS  Article  Google Scholar 

  8. 8

    Vignolini, S. et al. A 3D optical metamaterial made by self-assembly. Adv. Mater. 24, Op23–Op27 (2012).

    CAS  Article  Google Scholar 

  9. 9

    Zheng, X. Y. et al. Design and optimization of a light-emitting diode projection micro-stereolithography three-dimensional manufacturing system. Rev. Sci. Instrum. 83, 125001 (2012).

    Article  Google Scholar 

  10. 10

    Bauer, J., Hengsbach, S., Tesari, I., Schwaiger, R. & Kraft, O. High-strength cellular ceramic composites with 3D microarchitecture. Proc. Natl Acad. Sci. USA 111, 2453–2458 (2014).

    CAS  Article  Google Scholar 

  11. 11

    Zheng, X. et al. Proc. IEEE 27th Int. Conf. Micro Electro Mechanical Systems (MEMS) 510–513 (IEEE, 2014).

    Google Scholar 

  12. 12

    Bauer, J. et al. Push-to-pull tensile testing of ultra-strong nanoscale ceramic–polymer composites made by additive manufacturing. Extreme Mech. Lett. 3, 105–112 (2015).

    Article  Google Scholar 

  13. 13

    Buckmann, T., Kadic, M., Schittny, R. & Wegener, M. Mechanical cloak design by direct lattice transformation. Proc. Natl Acad. Sci. USA 112, 4930–4934 (2015).

    Article  Google Scholar 

  14. 14

    Meza, L. R. et al. Resilient 3D hierarchical architected metamaterials. Proc. Natl Acad. Sci. USA 112, 11502–11507 (2015).

    CAS  Article  Google Scholar 

  15. 15

    Gansel, J. K. et al. Gold Helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).

    CAS  Article  Google Scholar 

  16. 16

    Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).

    CAS  Article  Google Scholar 

  17. 17

    Ferreira, A. & Peres, N. M. R. Complete light absorption in graphene-metamaterial corrugated structures. Phys. Rev. B 86, 205401 (2012).

    Article  Google Scholar 

  18. 18

    Sun, K. et al. 3D printing of interdigitated Li-ion microbattery architectures. Adv. Mater. 25, 4539–4543 (2013).

    CAS  Article  Google Scholar 

  19. 19

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

    CAS  Article  Google Scholar 

  20. 20

    Ahn, B. Y. et al. Omnidirectional printing of flexible, stretchable, and spanning silver microelectrodes. Science 323, 1590–1593 (2009).

    CAS  Article  Google Scholar 

  21. 21

    Schaedler, T. A. et al. Ultralight metallic microlattices. Science 334, 962–965 (2011).

    CAS  Article  Google Scholar 

  22. 22

    Qiu, L., Liu, J. Z., Chang, S. L. Y., Wu, Y. Z. & Li, D. Biomimetic superelastic graphene-based cellular monoliths. Nature Commun. 3, 1241 (2012).

    Article  Google Scholar 

  23. 23

    Maloney, K. J. et al. Microlattices as architected thin films: analysis of mechanical properties and high strain elastic recovery. APL Mater. 1, 022106 (2013).

    Article  Google Scholar 

  24. 24

    Rayneau-Kirkhope, D., Mao, Y. & Farr, R. Ultralight fractal structures from hollow tubes. Phys. Rev. Lett. 109, 204301 (2012).

    Article  Google Scholar 

  25. 25

    Biener, M. M. et al. Ultra-strong and low-density nanotubular bulk materials with tunable feature sizes. Adv. Mater. 26, 4808–4813 (2014).

    CAS  Article  Google Scholar 

  26. 26

    Tillotson, T. M. & Hrubesh, L. W. Transparent ultralow-density silica aerogels prepared by a 2-step sol-gel process. J. Non-Cryst. Solids 145, 44–50 (1992).

    CAS  Article  Google Scholar 

  27. 27

    Kucheyev, S. O. et al. Super-compressibility of ultralow-density nanoporous silica. Adv. Mater. 24, 776–780 (2012).

    CAS  Article  Google Scholar 

  28. 28

    Torrents, A., Schaedler, T. A., Jacobsen, A. J., Carter, W. B. & Valdevit, L. Characterization of nickel-based microlattice materials with structural hierarchy from the nanometer to the millimeter scale. Acta Mater. 60, 3511–3523 (2012).

    CAS  Article  Google Scholar 

  29. 29

    Kim, S. H., Kim, H. & Kim, N. J. Brittle intermetallic compound makes ultrastrong low-density steel with large ductility. Nature 518, 77–79 (2015).

    CAS  Article  Google Scholar 

  30. 30

    Ashby, M. F. The properties of foams and lattices. Phil. Trans. R. Soc. A 364, 15–30 (2006).

    CAS  Article  Google Scholar 

  31. 31

    Lakes, R. Materials with structural hierarchy. Nature 361, 511–515 (1993).

    Article  Google Scholar 

  32. 32

    Kooistra, G. W., Deshpande, V. & Wadley, H. N. G. Hierarchical corrugated core sandwich panel concepts. J. Appl. Mech. 74, 259–268 (2005).

    Article  Google Scholar 

  33. 33

    Oftadeh, R., Haghpanah, B., Vella, D., Boudaoud, A. & Vaziri, A. Optimal fractal-like hierarchical honeycombs. Phys. Rev. Lett. 113, 104301 (2014).

    Article  Google Scholar 

  34. 34

    Rayneau-Kirkhope, D., Mao, Y. & Farr, R. Optimization of fractal space frames under gentle compressive load. Phys. Rev. E. 87, 063204 (2013).

    Article  Google Scholar 

  35. 35

    Rho, J. Y., Kuhn-Spearing, L. & Zioupos, P. Mechanical properties and the hierarchical structure of bone. Med. Eng. Phys. 20, 92–102 (1998).

    CAS  Article  Google Scholar 

  36. 36

    Ritchie, R. O. The conflicts between strength and toughness. Nature Mater. 10, 817–822 (2011).

    CAS  Article  Google Scholar 

  37. 37

    Hall, G. S. Chemist’s wood. Nature 310, 521 (1984).

    Article  Google Scholar 

  38. 38

    Wang, L. H. et al. In situ atomic-scale observation of continuous and reversible lattice deformation beyond the elastic limit. Nature Commun. 4, 2413 (2013).

    Article  Google Scholar 

  39. 39

    Rys, J. et al. Fabrication and deformation of metallic glass micro-lattices. Adv. Eng. Mater. 16, 889–896 (2014).

    CAS  Article  Google Scholar 

  40. 40

    Keong, K. G., Sha, W. & Malinov, S. Crystallisation kinetics and phase transformation behaviour of electroless nickel–phosphorus deposits with high phosphorus content. J. Alloys Compd. 334, 192–199 (2002).

    CAS  Article  Google Scholar 

  41. 41

    Dong, L., Deshpande, V. & Wadley, H. Mechanical response of Ti-6Al-4V octet-truss lattice structures. Int. J. Solids Struct. 60–61, 107–124 (2015).

    Article  Google Scholar 

  42. 42

    Valdevit, L., Godfrey, S. W., Schaedler, T. A., Jacobsen, A. J. & Carter, W. B. Compressive strength of hollow microlattices: experimental characterization, modeling, and optimal design. J. Mater. Res. 28, 2461–2473 (2013).

    CAS  Article  Google Scholar 

  43. 43

    Sun, H., Xu, Z. & Gao, C. Multifunctional, ultra-flyweight, synergistically assembled carbon aerogels. Adv. Mater. 25, 2554–2560 (2013).

    CAS  Article  Google Scholar 

  44. 44

    Kato, K. et al. Cytocompatibility and mechanical properties of novel porous 316 L stainless steel. Mater. Sci. Eng. C 33, 2736–2743 (2013).

    CAS  Article  Google Scholar 

  45. 45

    Olurin, O. B., Fleck, N. A. & Ashby, M. F. Deformation and fracture of aluminium foams. Mater. Sci. Eng. A 291, 136–146 (2000).

    Article  Google Scholar 

  46. 46

    Andrews, E., Sanders, W. & Gibson, L. J. Compressive and tensile behaviour of aluminum foams. Mater. Sci. Eng. A 270, 113–124 (1999).

    Article  Google Scholar 

  47. 47

    Kashef, S. et al. Fracture toughness of titanium foams for medical applications. Mater. Sci. Eng. A 527, 7689–7693 (2010).

    Article  Google Scholar 

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This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Funding support from DOE LDRD LabWide 15-LW-083, Virginia Tech Startup support and SCHEV fund from the State of Virginia and DARPA MCMA (Materials with Controlled Microstructural Architecture, Program Manager J. Goldwasser) is gratefully acknowledged. The authors wish to acknowledge Y. Wang and M. Messner for useful input (LLNL-JRNL-677190). Large-area projection microstereolithography has been submitted and is pending a US patent.

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X.Z. conceived and directed the research; X.Z. and W.S. designed structures; X.Z. designed the experiments. J.J., B.M., H.C. and X.Z. manufactured samples; W.S., H.C., D.C. and N.R. performed measurements; X.Z. and T.W. performed analytical and numerical analysis. J.Y. performed ex situ measurements on nickel–phosphorus; W.S., N.R., H.C. and X.Z. analysed data; X.Z. wrote the paper. X.Z. and C.M.S. supervised research. All authors contributed to interpreting the data, preparing and editing the manuscript.

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Correspondence to Xiaoyu Zheng.

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Zheng, X., Smith, W., Jackson, J. et al. Multiscale metallic metamaterials. Nature Mater 15, 1100–1106 (2016).

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