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Resilient 3D hierarchical architected metamaterials

Meza, Lucas R. and Zelhofer, Alex J. and Clarke, Nigel and Mateos, Arturo J. and Kochmann, Dennis M. and Greer, Julia R. (2015) Resilient 3D hierarchical architected metamaterials. Proceedings of the National Academy of Sciences of the United States of America, 112 (37). pp. 11502-11507. ISSN 0027-8424. PMCID PMC4577192.

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Hierarchically designed structures with architectural features that span across multiple length scales are found in numerous hard biomaterials, like bone, wood, and glass sponge skeletons, as well as manmade structures, like the Eiffel Tower. It has been hypothesized that their mechanical robustness and damage tolerance stem from sophisticated ordering within the constituents, but the specific role of hierarchy remains to be fully described and understood. We apply the principles of hierarchical design to create structural metamaterials from three material systems: (i) polymer, (ii) hollow ceramic, and (iii) ceramic–polymer composites that are patterned into self-similar unit cells in a fractal-like geometry. In situ nanomechanical experiments revealed (i) a nearly theoretical scaling of structural strength and stiffness with relative density, which outperforms existing nonhierarchical nanolattices; (ii) recoverability, with hollow alumina samples recovering up to 98% of their original height after compression to ≥50% strain; (iii) suppression of brittle failure and structural instabilities in hollow ceramic hierarchical nanolattices; and (iv) a range of deformation mechanisms that can be tuned by changing the slenderness ratios of the beams. Additional levels of hierarchy beyond a second order did not increase the strength or stiffness, which suggests the existence of an optimal degree of hierarchy to amplify resilience. We developed a computational model that captures local stress distributions within the nanolattices under compression and explains some of the underlying deformation mechanisms as well as validates the measured effective stiffness to be interpreted as a metamaterial property.

Item Type:Article
Related URLs:
URLURL TypeDescription Information CentralArticle
Meza, Lucas R.0000-0003-0250-2621
Zelhofer, Alex J.0000-0002-8064-2876
Kochmann, Dennis M.0000-0002-9112-6615
Greer, Julia R.0000-0002-9675-1508
Additional Information:© 2015 National Academy of Sciences. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved August 11, 2015 (received for review May 8, 2015). Published ahead of print September 1, 2015. The authors thank the Kavli Nanoscience Institute at Caltech for the availability of critical cleanroom facilities. Part of this work was carried out in the Lewis Group facilities at Caltech. The authors acknowledge financial support from the Defense Advanced Research Projects Agency under Materials with Controlled Microstructural Architecture (MCMA) Program Contract W91CRB-10-0305 (managed by J. Goldwasser), Institute for Collaborative Biotechnologies Grant W911NF-09-0001 from the US Army Research Office, and National Science Foundation Grant CMMI‐1234364. Author contributions: L.R.M., N.C., D.M.K., and J.R.G. designed research; L.R.M., A.J.Z., N.C., and A.J.M. performed research; A.J.Z. and D.M.K. contributed new reagents/analytic tools; L.R.M. and A.J.Z. analyzed data; and L.R.M., A.J.Z., A.J.M., D.M.K., and J.R.G. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. This article contains supporting information online at
Group:Kavli Nanoscience Institute, GALCIT
Funding AgencyGrant Number
Army Research Office (ARO)W91CRB-10-0305
Army Research Office (ARO)W911NF-09-0001
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Subject Keywords:hierarchical; nanolattices; structural metamaterial; recoverable; damage tolerance
Issue or Number:37
PubMed Central ID:PMC4577192
Record Number:CaltechAUTHORS:20150909-102806332
Persistent URL:
Official Citation:Lucas R. Meza, Alex J. Zelhofer, Nigel Clarke, Arturo J. Mateos, Dennis M. Kochmann, and Julia R. Greer Resilient 3D hierarchical architected metamaterials PNAS 2015 112 (37) 11502-11507; published ahead of print September 1, 2015, doi:10.1073/pnas.1509120112
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60121
Deposited By: Tony Diaz
Deposited On:09 Sep 2015 21:01
Last Modified:04 Mar 2020 19:29

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