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Optimal fractal-like hierarchical honeycombs

Abstract : Hexagonal honeycomb structures are known for their high strength and low weight. We construct a new class of fractal-appearing cellular metamaterials by replacing each three-edge vertex of a base hexagonal network with a smaller hexagon and iterating this process. The mechanical properties of the structure after different orders of the iteration are optimized. We find that the optimal structure (with highest in-plane stiffness for a given weight ratio) is self-similar but requires higher order hierarchy as the density vanishes. These results offer insights into how incorporating hierarchy in the material structure can create low-density metamaterials with desired properties and function.
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Ramin Oftadeh, Babak Haghpanah, Dominic Vella, Arezki Boudaoud, Ashkan Vaziri. Optimal fractal-like hierarchical honeycombs. Physical Review Letters, American Physical Society, 2014, 113 (10), ⟨10.1103/PhysRevLett.113.104301⟩. ⟨hal-02634452⟩



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