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.

Honeycomb phononic crystals with self-similar hierarchy

“…This geometrical change results in an increase in multiple scattering of the propagating waves at the cell walls and consequently opening up the Bragg-type band gaps [31]. The alterations of the band structure indicate a hierarchy-dependent transition, which parallels the effect of hierarchy on mechanical behavior in other contexts [10][11][12][13][14].…”

“…Examples include collagen [1], bone [2,3], tooth [2], tendon [3], wood [3,4], nacre [5], gecko foot pads [6], Asteriscus plant [7], Euplectella sponge [8], and water-repellent biological systems [9]. The purely structural role of hierarchy in boosting mechanical performance is now well known [10][11][12][13][14]. In addition to hierarchy, periodic organizations aimed at influencing the wave-propagation behavior, for instance in structural colorations, can also be found in nature [15][16][17].…”

3D printed polyurethane honeycombs for repeated tailored energy absorption

“…3D printing provides a geometric design freedom unrivalled by traditional manufacturing methods, coupled with the increased accessibility of this technology in recent years, this has allowed the creation of honeycombs with dual-material structures [5], structural hierarchy [6][7][8] and graded density [9]; these topological complexities all have the potential to enhance and tailor the energy absorbing capabilities of honeycombs. Much of the work in this field has focused on exploring the behaviour of rigid 3D printed honeycombs [6][7][8][9]; such structures subject to large compressive loads would fail by crushing and brittle fracture, preventing energy recovery or reuse. In order to utilise the advances in our understanding of honeycomb design in applications such as vibration isolation and personal protection equipment, it is necessary that the next generation of honeycomb structures be 3D printed from highly elastic, hard wearing materials.…”

Dynamic compressive response of additively manufactured AlSi10Mg alloy hierarchical honeycomb structures

“…1. Oftadeh et al [9] investigated the in-plane mechanical behaviour of hierarchical honeycombs with various hierarchical levels.…”