Self-similar hierarchical honeycombs

Hierarchical structures are observed in nature, and can be shown to offer superior efficiency. However, the potential advantages of structural hierarchy are not well understood. We extensively explored a bending-dominated model material (i.e. transversely loaded hexagonal honeycomb) which is susceptible to improvement by simple iterative refinement that replaces each three-edge structural node with a smaller hexagon. Using a blend of analytical and numerical techniques, both elastic and plastic properties were explored over a range of loadings and iteration parameters. A wide variety of specific stiffness and specific strengths (up to fourfold increase) were achieved. The results offer insights into the potential value of iterative structural refinement for creating low-density materials with desired properties and function.