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Damage-tolerant architected materials inspired by crystal microstructure

A Publisher Correction to this article was published on 28 February 2019

This article has been updated


Architected materials that consist of periodic arrangements of nodes and struts are lightweight and can exhibit combinations of properties (such as negative Poisson ratios) that do not occur in conventional solids. Architected materials reported previously are usually constructed from identical ‘unit cells’ arranged so that they all have the same orientation. As a result, when loaded beyond the yield point, localized bands of high stress emerge, causing catastrophic collapse of the mechanical strength of the material. This ‘post-yielding collapse’ is analogous to the rapid decreases in stress associated with dislocation slip in metallic single crystals. Here we use the hardening mechanisms found in crystalline materials to develop architected materials that are robust and damage-tolerant, by mimicking the microscale structure of crystalline materials—such as grain boundaries, precipitates and phases. The crystal-inspired mesoscale structures  in our architected materials are as important for their mechanical properties as are crystallographic microstructures in metallic alloys. Our approach combines the hardening principles of metallurgy and architected materials, enabling the design of materials with desired properties.

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Fig. 1: Lattice structures and deformation behaviour.
Fig. 2: Role of lattice orientation in the deformation behaviour of crystals and architected lattices.
Fig. 3: Precipitation and multiphase hardening in architected materials.
Fig. 4: Lightweight and damage-tolerant architected materials inspired by crystal microstructure.

Data availability

The datasets generated and analysed during this study are available from the corresponding author on reasonable request.

Change history

  • 28 February 2019

    In Fig. 4a of this Article, owing to an error in the production process, the scale bar inadvertently read 1 mm instead of 1 m. This error has been corrected online.


  1. Cottrell, A. Dislocations and Plastic Flow in Crystals (Clarendon Press, New York, 1953).

    MATH  Google Scholar 

  2. Argon, A. Strengthening Mechanisms in Crystal Plasticity (Oxford Univ. Press, New York, 2007).

    Book  Google Scholar 

  3. Dimiduk, D. M., Uchic, M. D. & Parthasarathy, T. A. Size-affected single-slip behavior of pure nickel microcrystals. Acta Mater. 53, 4065–4077 (2005).

    Article  CAS  Google Scholar 

  4. Csikor, F. F., Motz, C., Weygand, D., Zaiser, M. & Zapperi, S. Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318, 251–254 (2007).

    Article  ADS  CAS  Google Scholar 

  5. Pham, M. S., Holdsworth, S. R., Janssens, K. G. F. & Mazza, E. Cyclic deformation response of AISI 316L at room temperature: mechanical behaviour, microstructural evolution, physically-based evolutionary constitutive modelling. Int. J. Plasticity 47, 143–164 (2013).

    Article  CAS  Google Scholar 

  6. Imrich, P. J., Kirchlechner, C., Motz, C. & Dehm, G. Differences in deformation behavior of bicrystalline Cu micropillars containing a twin boundary or a large-angle grain boundary. Acta Mater. 73, 240–250 (2014).

    Article  CAS  Google Scholar 

  7. Hall, E. O. The deformation and ageing of mild steel: III. Discussion of Results. Proc. Phys. Soc. B 64, 747–753 (1951).

    Article  ADS  Google Scholar 

  8. Petch, N. J. The cleavage strength of polycrystals. J. Iron Steel Inst. 174, 25–28 (1953).

    CAS  Google Scholar 

  9. Subedi, S., Beyerlein, I. J., LeSar, R. & Rollett, A. D. Strength of nanoscale metallic multilayers. Scr. Mater. 145, 132–136 (2018).

    Article  CAS  Google Scholar 

  10. Wegst, U. G. K., Bai, H., Saiz, E., Tomsia, A. P. & Ritchie, R. O. Bioinspired structural materials. Nat. Mater. 14, 23–36 (2015).

    Article  ADS  CAS  Google Scholar 

  11. Barthelat, F. Architectured materials in engineering and biology: fabrication, structure, mechanics and performance. Int. Mater. Rev. 60, 413–430 (2015).

    Article  CAS  Google Scholar 

  12. Chen, P.-Y., McKittrick, J. & Meyers, M. A. Biological materials: functional adaptations and bioinspired designs. Prog. Mater. Sci. 57, 1492–1704 (2012).

    Article  CAS  Google Scholar 

  13. Gu, G. X., Libonati, F., Wettermark, S. D. & Buehler, M. J. Printing nature: unraveling the role of nacre’s mineral bridges. J. Mech. Behav. Biomed. Mater. 76, 135–144 (2017).

    Article  CAS  Google Scholar 

  14. Gibson, L. J. & Ashby, M. F. Cellular Solids: Structure and Properties (Cambridge Univ. Press, Cambridge, 1997).

    Book  Google Scholar 

  15. Schaedler, T. A. & Carter, W. B. Architected cellular materials. Annu. Rev. Mater. Res. 46, 187–210 (2016).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  17. Lakes, R. Foam structures with a negative Poisson’s ratio. Science 235, 1038–1040 (1987).

    Article  ADS  CAS  Google Scholar 

  18. Andreassen, E., Lazarov, B. S. & Sigmund, O. Design of manufacturable 3D extremal elastic microstructure. Mech. Mater. 69, 1–10 (2014).

    Article  Google Scholar 

  19. Qin, Z., Jung, G. S., Kang, M. J. & Buehler, M. J. The mechanics and design of a lightweight three-dimensional graphene assembly. Sci. Adv. 3, e1601536 (2017).

    Article  ADS  Google Scholar 

  20. Zheng, X. et al. Multiscale metallic metamaterials. Nat. Mater. 15, 1100–1106 (2016); addendum 16, 497 (2017).

    Article  ADS  CAS  Google Scholar 

  21. Qiu, C. et al. Influence of processing conditions on strut structure and compressive properties of cellular lattice structures fabricated by selective laser melting. Mater. Sci. Eng. A 628, 188–197 (2015); corrigendum 638, 228–231 (2015).

    Article  CAS  Google Scholar 

  22. Maskery, I. et al. A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting. Mater. Sci. Eng. A 670, 264–274 (2016).

    Article  CAS  Google Scholar 

  23. Bouaziz, O., Brechet, Y. & Embury, J. D. Heterogeneous and architectured materials: a possible strategy for design of structural materials. Adv. Eng. Mater. 10, 24–36 (2008).

    Article  CAS  Google Scholar 

  24. Li, L. L. et al. Microcompression and cyclic deformation behaviors of coaxial copper bicrystals with a single twin boundary. Scr. Mater. 69, 199–202 (2013).

    Article  CAS  Google Scholar 

  25. Armstrong, R., Codd, I., Douthwaite, R. M. & Petch, N. J. The plastic deformation of polycrystalline aggregates. Philos. Mag. 7, 45–58 (1962).

    Article  ADS  CAS  Google Scholar 

  26. Kimura, Y., Inoue, T., Yin, F. & Tsuzaki, K. Inverse temperature dependence of toughness in an ultrafine grain-structure steel. Science 320, 1057–1060 (2008).

    Article  ADS  CAS  Google Scholar 

  27. Hirth, J. P. The influence of grain boundaries on mechanical properties. Metall. Trans. 3, 3047–3067 (1972).

    Article  CAS  Google Scholar 

  28. Suresh, S. & Ritchie, R. O. Propagation of short fatigue cracks. Int. Mater. Rev. 29, 445–475 (1984).

    Article  Google Scholar 

  29. Pham, M. S. & Holdsworth, S. R. Role of microstructural condition on fatigue damage development of AISI 316L at 20 and 300 °C. Int. J. Fatigue 51, 36–48 (2013).

    Article  CAS  Google Scholar 

  30. Kobayashi, S., Nakamura, M., Tsurekawa, S. & Watanabe, T. Effect of grain boundary microstructure on fatigue crack propagation in austenitic stainless steel. J. Mater. Sci. 46, 4254–4260 (2011).

    Article  ADS  CAS  Google Scholar 

  31. Pham, M.-S. & Holdsworth, S. Evolution of relationships between dislocation microstructures and internal stresses of AISI 316L during cyclic loading at 293 K and 573 K (20 °C and 300 °C). Metall. Mater. Trans. A 45, 738–751 (2014).

    Article  CAS  Google Scholar 

  32. Reed, R. C. The Superalloys: Fundamentals and Applications Ch. 2 (Cambridge Univ. Press, Cambridge, 2006).

    Book  Google Scholar 

  33. Orowan, E. Discussion on internal stresses. In Symp. Internal Stresses in Metals and Alloys 451–453 (Inst. of Metals, 1948).

  34. Hirsch, P. B. & Humpreys, F. J. The deformation of single crystals of copper and copper-zinc alloys containing alumina particles - I. Macroscopic properties and workhardening theory. Proc. R. Soc. Lond. A 318, 45–72 (1970).

    Article  ADS  CAS  Google Scholar 

  35. Porter, D. A. & Easterling, K. E. Phase Transformations in Metals and Alloys (CRC Press, Boca Raton, 2009).

  36. Kresling, B. in Deployable Structures and Biological Morphology (eds Furuya, H. et al.) 188–195 (Internet-First Univ. Press, Ithaca, 2008).

  37. Zhao, H. et al. Atomic-scale understanding of stress-induced phase transformation in cold-rolled Hf. Acta Mater. 131, 271–279 (2017).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  39. Restrepo, D., Mankame, N. D. & Zavattieri, P. D. Phase transforming cellular materials. Extreme Mech. Lett. 4, 52–60 (2015).

    Article  Google Scholar 

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M.-S.P. thanks A. Rollett, F. Dunne, C. Gourlay and S. Holdsworth for discussions, T. Walton and P. Hooper for fabricating some lattices, A. Piglione for providing an SEM image of γ/γ′ microstructure, and an Engineering Alloys Fellowship awarded by the Department of Materials, Imperial College London. M.-S.P. also thanks M. M. Attallah and D. M. Dimiduk for providing the original versions of Fig. 1b, f. I.T. is grateful for funding through EPSRC grants EP/P006566/1 and EP/L02513/1, and the Royal Academy of Engineering.

Reviewer information

Nature thanks C. Niordson, N. Pugno and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

Authors and Affiliations



M.-S.P. developed the idea and directed the research. C.L. carried out the computer-aided design, fabrication, mechanical tests and post analyses. J.L. performed the FEM. I.T. discussed and contributed to the development of the concept. All the authors participated in analysing and interpreting the data. The manuscript was written and approved by all authors.

Corresponding author

Correspondence to Minh-Son Pham.

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Competing interests

A patent developed on the basis of the approach proposed in this study has been filed, managed by Imperial Innovations.

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Extended data figures and tables

Extended Data Fig. 1 Mimicking a crystal lattice.

a, Unit cell of the fcc lattice. b, A macro-lattice cube consisting of 8 × 8 × 8 macro-unit cells. ce, The rotation sequence to form a twin meta-grain.

Extended Data Fig. 2 Different numbers of meta-grains within the same global volume (40 mm × 40 mm × 40 mm).

a, A single meta-grain. b, c, Two twinned meta-grains, with (b) and without (c) the outer frame. dh, Four (d), eight (e), 16 (f), 18 (g) and 27 (h) meta-grains. The locations of the boundaries are highlighted.

Extended Data Fig. 3 Repeatability of the mechanical behaviour of architected materials.

ac, Materials consisting of two (a), eight (b) and 16 (c) meta-grains.

Extended Data Fig. 4 Effect of meta-grain size on mechanical strength.

a, Stress–strain curves of architected materials consisting of different numbers of meta-grains. b, The flow stress σf of architected materials containing meta-grains at a given nominal strain of 40% increases as the size of the meta-grains decreases.

Extended Data Fig. 5 Mimicking crystalline grains separated by incoherent high-angle boundaries.

a, Model of eight meta-grains. b, c, The orientations of lattices (with respect to the global X, Y and Z co-ordinates) in the four meta-grains in the top (b) and bottom (c) layers.

Extended Data Fig. 6 Deformation behaviour of an architected material containing eight meta-grains separated by incoherent high-angle boundaries.

a, b, Macro-lattice fabricated from 316L stainless steel (a) and an elasto-plastic polymer (b). c, d, Stress–strain constitutive behaviour of the macro-lattices fabricated from the steel (c) and polymer (d).

Extended Data Fig. 7 Mimicking precipitates.

a, Meta-precipitate lattice (orange) embedded in the matrix. b, Cubic morphology and locations of meta-precipitates inside the fcc meta-phase. c, fcc unit cell of the matrix. d, Face-centred tetragonal unit cell of the meta-precipitate.

Extended Data Fig. 8 Repeatability of the mechanical behaviour of an architected material.

This material contains 25 meta-precipitates.

Extended Data Fig. 9 Mimicking multiple phases.

a, Single fcc-phase meta-grain. b, Single bcc-phase meta-grain. c, A cube of meta-polygrains (left panel) consisting of two meta-phases: fcc (top and bottom layers; middle panel) and bcc (middle layer; right panel).

Extended Data Fig. 10 Kresling lattice.

a, Unit cell. b, hcp-inspired meta-phase.

Extended Data Fig. 11 Helical movement changes the stack sequence of nodes.

Red lines represent the helical movements of basal nodes; for clarity, only the movement of basal nodes on the top plane are shown.

Extended Data Table 1 Mechanical properties of base materials

Supplementary information

Video 1

Finite-element method simulation of an architected material containing two twinned meta-grains mimicking twinned bi-crystals. Colour represents the degrees of true strain during compression

Video 2

Experimental record of the deformation behaviour of an architected hexagonal lattice during a compression loading–unloading cycle

Video 3

Finite-element method simulation of the deformation behaviour of an architected hexagonal lattice during a compression loading–unloading cycle. Colour represents the degrees of true strain during deformation

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Pham, MS., Liu, C., Todd, I. et al. Damage-tolerant architected materials inspired by crystal microstructure. Nature 565, 305–311 (2019).

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