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.H ierarchy is ubiquitous in the natural world; characterizing it, understanding its origins, and discovering its role in enhancing material properties are essential to designing new advanced materials (1-4). Natural structural materials, like Euplectella sponges, radiolarians, and bone, are exceptionally resilient against extreme mechanical environments and seem to draw their robustness from intricate mechanical networks that contain multiple levels of hierarchy (3-7). Hierarchical engineered structures are used in modern architecture, with notable examples being the Eiffel tower and the Garabit viaduct (8); today, hierarchy is seen commonly in construction cranes and building scaffolding. Both natural and engineered structures use the concept of hierarchical design to minimize material use while optimizing structural integrity.The hierarchical scale of a material is defined by its order, which represents the number of distinct structural length scales (2). Design principles and theories describing hierarchical structural materials exist (2, 9), and macroscopic second-and thirdorder 2D cellular solids, like honeycombs (10, 11) and corrugated core sandwich panels (12)(13)(14), have been designed and tested experimentally. Theories that describe the design and optimization of 3D hierarchical trusses have been proposed (15-18)...
Auxetic behavior (i.e., a negative value of Poisson's ratio) has been reported for a variety of cellular networks including truss structures. Commonly, this implies that the geometric arrangement of truss members within a periodic unit cell is designed to achieve the negative Poisson effect, e.g., in the reentrant honeycomb configuration. Here, we show that elastic periodic truss lattices can be tuned to display auxeticity by controlling the ratio of bending to stretching stiffness. If the nodal stiffness (or the bending stiffness) is low compared to the stretching stiffness of individual truss members, then the lattice is expected to exhibit a positive Poisson's ratio, showing lateral expansion upon uniaxial compression. In contrast, if the nodal or bending stiffness is high (and buckling is prevented), the lattice may reveal auxetic behavior, contracting laterally under uniaxial compression. This effect is demonstrated in two dimensions for the examples of square and triangular lattices, and it is confirmed both analytically in the limit of small strains as well as numerically for finite elastic deformation. Under large deformation, instability additionally gives rise to auxetic behavior due to truss buckling.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.