The DOI matches its Crossref record; 20 of the 20 references it cites were found in a registry or an index.
Resilient 3D hierarchical architected metamaterials
Open accessAbstract
Significance: Fractal-like architectures exist in natural materials, like shells and bone, and have drawn considerable interest because of their mechanical robustness and damage tolerance. Developing hierarchically designed metamaterials remains a highly sought after task impaired mainly by limitations in fabrication techniques. We created 3D hierarchical nanolattices with individual beams comprised of multiple self-similar unit cells spanning length scales over four orders of magnitude in fractal-like geometries. We show, through a combination of experiments and computations, that introducing hierarchy into the architecture of 3D structural metamaterials enables the attainment of a unique combination of properties: ultralightweight, recoverability, and a near-linear scaling of stiffness and strength with density.
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Cites
The Fractal Geometry of Nature
Mandelbrot, B. B., & Wheeler, J. A. (1983) · American Journal of Physics · doi:10.1119/1.13295 · Cited by 21,832
The Fractal Geometry of Nature
Mandelbrot, B. B., & Longley, P. (1982) · CERN Document Server (European Organization for Nuclear Research) · Cited by 7,293
Nature’s hierarchical materials
Fratzl, P., & Weinkamer, R. (2007) · Progress in Materials Science · doi:10.1016/j.pmatsci.2007.06.001 · Cited by 2,800
Ultralight, ultrastiff mechanical metamaterials
Zheng, X., Lee, H., Weisgraber, T. H., Shusteff, M., DeOtte, J., Duoss, E. B., Kuntz, J. D., Biener, M. M., Ge, Q., Jackson, J. A., et al. (2014) · Science · doi:10.1126/science.1252291 · Cited by 2,308
Ultralight Metallic Microlattices
Schaedler, T. A., Jacobsen, A. J., Torrents, A., Sorensen, A. E., Lian, J., Greer, J. R., Valdevit, L., & Carter, W. B. (2011) · Science · doi:10.1126/science.1211649 · Cited by 1,784
Self-citationEffective properties of the octet-truss lattice material
Deshpande, V. S., Fleck, N. A., & Ashby, M. F. (2001) · Journal of the Mechanics and Physics of Solids · doi:10.1016/s0022-5096(01)00010-2 · Cited by 1,741
Strong, lightweight, and recoverable three-dimensional ceramic nanolattices
Meza, L. R., Das, S., & Greer, J. R. (2014) · Science · doi:10.1126/science.1255908 · Cited by 1,498
Self-citationMaterials with structural hierarchy
Lakes, R. (1993) · Nature · doi:10.1038/361511a0 · Cited by 1,402
Structural Biological Materials: Critical Mechanics-Materials Connections
Meyers, M. A., McKittrick, J., & Chen, P.-Y. (2013) · Science · doi:10.1126/science.1220854 · Cited by 1,171
Skeleton of Euplectella sp.: Structural Hierarchy from the Nanoscale to the Macroscale
Aizenberg, J., Weaver, J. C., Thanawala, M. S., Sundar, V. C., Morse, D. E., & Fratzl, P. (2005) · Science · doi:10.1126/science.1112255 · Cited by 1,144
Cited by
Printing soft matter in three dimensions
Truby, R. L., & Lewis, J. A. (2016) · Nature · doi:10.1038/nature21003 · Cited by 1,622
Mechanical Metamaterials and Their Engineering Applications
Surjadi, J. U., Gao, L., Du, H., Li, X., Xiong, X., Fang, N. X., & Lu, Y. (2019) · Advanced Engineering Materials · doi:10.1002/adem.201800864 · Cited by 982
Multiscale metallic metamaterials
Zheng, X., Smith, W., Jackson, J., Moran, B., Cui, H., Chen, D., Ye, J., Fang, N., Rodriguez, N., Weisgraber, T., et al. (2016) · Nature Materials · doi:10.1038/nmat4694 · Cited by 870
Architected Cellular Materials
Schaedler, T. A., & Carter, W. B. (2016) · Annual Review of Materials Research · doi:10.1146/annurev-matsci-070115-031624 · Cited by 786
Additive manufacturing of structural materials
Liu, G., Zhang, X., Chen, X., He, Y., Cheng, L., Huo, M., Yin, J., Hao, F., Chen, S., Wang, P., et al. (2021) · Materials Science and Engineering: R: Reports · doi:10.1016/j.mser.2020.100596 · Cited by 707
Metadata
- Authors
- Meza, L. R., Zelhofer, A. J., Clarke, N., Mateos, A. J., Kochmann, D. M., & Greer, J. R.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2015-09
- Volume
- 112
- Issue
- 37
- Pages
- 11502-11507
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W1917020151
- Cited by
- 706
- References
- 20
- FWCI
- 45.11
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Meza, L. R., Zelhofer, A. J., Clarke, N., Mateos, A. J., Kochmann, D. M., & Greer, J. R. (2015). Resilient 3D hierarchical architected metamaterials. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.1509120112
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
