Beyond the Hexagon: Meso-structures in the Bee's Honeycomb for Bio-inspired Design

Abstract Perhaps no other biological structure has inspired as many engineering applications as the nest of the honeybee Apis mellifera. It is primarily just the hexagonal unit cell, with its material minimizing benefits, that has been abstracted as a design principle for bio-inspired structures. This is in part because of design constraints associated with manufacturing honeycomb panels, but also due to our limited understanding of the benefits of other design features of interest. The bee's honeycomb has several interesting meso-structural design elements, like the corner radius and the wall coping, which can be replicated using additive manufacturing processes. In this paper, we first identify and categorize these meso-scale design elements at four levels: (i) the unit cell shape, (ii) its size and distribution, (iii) the features that make up the unit cell and the parameters associated with them, and (iv) the integration of the cells into the build environment. Once identified, we attribute functional bases to each of these features, leveraging prior and ongoing studies in biology, as well as in materials science and mechanics. We then identify promising design principles for further advancing the engineering of honeycomb structures using additive manufacturing, as well as call out opportunities for future research. More generally, this paper argues for the importance of considering meso-structural design elements, beyond just unit cell selection, in the design of cellular materials.