Resilient 3D hierarchical architected metamaterials

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

Auxeticity in truss networks and the role of bending versus stretching deformation

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

Auxeticity in truss networks and the role of bending versus stretching deformation

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