Resilient 3D hierarchical architected metamaterials

Abstract

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.

Keywords: damage tolerance; hierarchical; nanolattices; recoverable; structural metamaterial.

Fig. 1.

Computer-aided design (CAD) and scanning electron microscopy (SEM) images of various hierarchical nanolattices show the versatility of the nanolattice fabrication technique. (A) CAD images illustrating the process of making a third-order hierarchical nanolattice. A zeroth-order repeating unit, an elliptical beam, is arranged into a first-order octahedron; it becomes the repeating unit for a second-order octahedron of octahedra, which is then arranged to create a third-order octahedron of octahedra of octahedra. (B, Upper, C, Upper, D, Upper, and E, Upper) CAD and (B, Lower, C, Lower, D, Lower, and E, Lower) SEM images of the various second-order samples. (Scale bars: 20 µm.) (F) SEM image of a second-order octahedron of octahedra lattice. (Scale bar: 50 µm.) (G) A zoomed-in image of the second-order octahedron of octahedra lattice showing the first-order repeating units that make up the structure. (Scale bar: 10 µm.) (H) SEM image of a third-order octahedron of octahedra of octahedra. (Scale bar: 25 µm.)

Fig. 2.

Compression experiments on second-order octahedron of octet half-cells with N = 15 and L = 8. (A) Image of the hollow 20-nm walled Al₂O₃ sample before compression. (B) Load displacement data that show compression to 50% strain. Inset corresponds to 50% strain. (C) Postdeformation image of the hollow sample. (D) Image of the composite polymer and 20-nm Al₂O₃ sample before compression. (E) Load displacement data that show compression to 65% strain. Inset corresponds to the sample after the occurrence of a strain burst. (F) Postdeformation image of the composite sample. (G) Image of the polymer sample before compression. (H) Load displacement data that show compression to 50% strain. Inset corresponds to 50% strain. (I) Postdeformation image of the polymer sample. (Scale bars: 20 µm.)

Fig. 3.

Compression experiments on third-order octahedron of octahedra of octahedra half-cells with N = 5 and L = 8. (A) Image of the hollow 20-nm walled Al₂O₃ sample before compression. (B) Load-displacement data that show cyclic compression to 50% strain. Insets correspond to 50% strain at various loading cycles. (C) Postcompression image of the hollow sample. (D) Image of the composite polymer and 20-nm Al₂O₃ sample before compression. (E) Load-displacement data that show compression to 65% strain. Inset corresponds to the sample after the occurrence of a strain burst. (F) Postdeformation image of the composite sample. (G) Image of the polymer sample before compression. (H) Load displacement data that show compression to 50% strain. Inset corresponds to 50% strain. (I) Postdeformation image of the polymer sample. (Scale bars: 50 µm.)

Fig. 4.

Model flowchart showing truss and refined model generation. (A) Representative lattice geometry section. (B) Creation of a truss model lattice. (C) Example compression of truss model half-cell nanolattices. Stress is normalized by the maximum compressive stress in the sample, and stresses $\left|\sigma \right|\le 15\%$ of the maximum stress have been grayed out to help illustrate the beams with high stresses. (D) Refined model creation process containing geometrically unique supernodes (SN) and superbeams (SB). (E) Example refined model half-cell nanolattice colored by unique geometry beam or node.

Fig. 5.

Comprehensive data plot of all tested hierarchical nanolattices. (A) Effective Young’s modulus of the hierarchical structures plotted against their relative density. Data are plotted for experimental (slope values are in bold) and refined node simulations (slope values are italicized) results. (B) Experimentally derived effective yield strength of the hierarchical nanolattices plotted against their relative density.