Mechanically robust lattices inspired by deep-sea glass sponges


The predominantly deep-sea hexactinellid sponges are known for their ability to construct remarkably complex skeletons from amorphous hydrated silica. The skeletal system of one such species of sponge, Euplectella aspergillum, consists of a square-grid-like architecture overlaid with a double set of diagonal bracings, creating a chequerboard-like pattern of open and closed cells. Here, using a combination of finite element simulations and mechanical tests on 3D-printed specimens of different lattice geometries, we show that the sponge’s diagonal reinforcement strategy achieves the highest buckling resistance for a given amount of material. Furthermore, using an evolutionary optimization algorithm, we show that our sponge-inspired lattice geometry approaches the optimum material distribution for the design space considered. Our results demonstrate that lessons learned from the study of sponge skeletal systems can be exploited for the realization of square lattice geometries that are geometrically optimized to avoid global structural buckling, with implications for improved material use in modern infrastructural applications.

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Fig. 1: Representative skeletal system of the hexactinellid sponge Euplectella aspergillum.
Fig. 2: Experimental and numerical results.
Fig. 3: Numerical results describing structural response to varying loading angle.
Fig. 4: Optimization results and experimental validation.
Fig. 5: Numerical and experimental results of slender structures undergoing 3-point bending tests.

Data availability

Raw data for the plots are available on GitHub at Additional data that support the findings of this study are available from the corresponding authors on request.

Code availability

All codes necessary to reproduce results in main paper are available on GitHub at


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This work was supported by NSF-GRFP Fellowship Grant Number DGE-1144152 (M.C.F.), a GEM Consortium Fellowship (M.C.F.) and the Harvard Graduate Prize Fellowship (M.C.F.), and was partially supported by the NSF through the Harvard University Materials Research Science and Engineering Center Grant Number DMR-2011754 and NSF DMREF Grant Number DMR-1922321. We also thank J. R. Rice, J. W. Hutchinson, F. H. Abernathy, J. Vlassak, S. Gerasimidis and C. Rycroft for discussions.

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All authors secured research funding. K.B. and J.C.W. supervised the research. M.C.F. and J.C.W. generated models and performed mechanical testing and finite element simulations. M.C.F., K.B. and J.C.W. analysed the data. All authors wrote the paper.

Corresponding authors

Correspondence to James C. Weaver or Katia Bertoldi.

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Competing interests

The authors would like to disclose a submitted patent application on related geometric features reported in this manuscript. United States Patent and Trademark Office (USPTO) (RO/US) application number: 002806-094100WOPT filed in 2019. Patent applicant: President and Fellows of Harvard College. Inventors: Matheus C. Fernandes, James C. Weaver, and Katia Bertoldi. The authors declare no further competing interests.

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Supplementary Figs. 1–27, Tables 1–3 and Sections 1–5.

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Fernandes, M.C., Aizenberg, J., Weaver, J.C. et al. Mechanically robust lattices inspired by deep-sea glass sponges. Nat. Mater. 20, 237–241 (2021).

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