Resilient 3D hierarchical architected metamaterials

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. 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.