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.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)...

Reexamining the mechanical property space of three-dimensional lattice architectures

“…These materials are 3D assemblies of beams with micro-and nanoscale constituent dimensions, and it is the confluence of nanometer-sized dimensions and architecture that gives rise to their unique properties [1][2][3]15,[18][19][20][21][22][23][24][25][26]. The theoretical maximum Young's modulus ‫)ܧ(‬ and yield strength (ߪ ௬ ) of a lightweight porous material are set by the Voigt bound, which are functions of the relative density (ߩ̅ ) as ‫ܧ‬ = ‫ܧ‬ ௦ ߩ̅ and ߪ ௬ = ߪ ௬௦ ߩ̅ .…”

“…A large body of theoretical and experimental work has been dedicated to creating new lattice architectures and investigating their properties [1,15,18,19,23,[30][31][32][33][34]. Most analytical models for the mechanical behavior of both 2D and 3D lattices are derived using beam theory, and these models generally predict that strength and modulus follow a power law scaling with relative density as ‫ܧ‬ = ‫ܧܤ‬ ௦ ߩ̅ ,…”

“…Experimental and theoretical work on lattices have shown mixed results on the exact role of topology in governing strength and modulus scaling; a wide range of reported strength and stiffness power law scaling relationships exists, even for topologically identical systems, and no experimentally realized M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 3 lightweight lattice matches the performance predicted by the Gurtner-Durand bound [1,2,18,[21][22][23]37,38].…”

“…The solid unit cell simulations were performed using C3D10 10-node quadratic tetrahedral elements, and the hollow simulations used S3R 3-node shell elements to represent the discretized unit cells. An isotropic linear elastic material model was used for both solid and hollow structure simulations, and stiffnesses for the constituent polymer and Al 2 O 3 were obtained from literature [23,40]. Solid unit cell simulations had between 25,000 -250,000 elements and hollow unit cell simulations had between 25,000 -100,000 elements; the exact number of elements varied depending on the unit cell and structural parameters used.…”

Ultra-efficient wound composite truss structures

“…Truss structures and space frames have been created at nearly all size scales, from the micrometer [3] scale all the way up to to 400 m long Ikitsuki truss bridge in Japan (the world's longest) and the world's largest indoor theme park, Ferrari World, who's elegant space frame structure encloses an incredible 86,000 m 2 .…”