Self-similar hierarchical honeycombs

Abstract

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.

Dynamic compressive response of additively manufactured AlSi10Mg alloy hierarchical honeycomb structures

“…With increasing hierarchical level, there is a transition of in-plane failure mode from elastic buckling to plastic buckling [10]. However, increases in the in-plane collapse strength were only seen to be significant for the first, second and third levels of hierarchy; higher hierarchical level did not significantly increase performance [7].…”

“…For example, the two-scale and three-scale hierarchical honeycombs were 2.0 and 3.5 times, respectively, stiffer than the standard hexagonal honeycomb with identical relative density [8]. Hierarchical honeycombs also have higher in-plane collapse strength than standard hexagonal honeycombs with identical relative density [7]. With increasing hierarchical level, there is a transition of in-plane failure mode from elastic buckling to plastic buckling [10].…”

“…The out-of-plane stiffness and strength of periodic honeycombs are much greater than those along the in-plane directions [4,7,11]. For example, the out-of-plane compressive strength of aluminium hexagonal honeycomb is 2 times greater than the in-plane compressive strength [11].…”

“…owing to structural buckling [6]. 3 Periodic, hierarchical honeycombs have recently emerged by combining in-plane geometrical elements at different length scales, see [4,7,8] and Fig. 1.…”

Intrinsic half-metallicity in fractal carbon nitride honeycomb lattices

“…More generalized two-dimensional (2D) honeycomb frameworks are predicted to have relatively high stiffness for their low density 12 . In-plane stiffness and strength can be greatly improved in these cellular solids compared to the corresponding regular honeycombs 13,14 . This process can be repeated to create frameworks of higher fractal hierarchy (see Fig.…”