A simplified thermomechanical approach to visualize hexagonal honeycomb construction

Abstract

The construction of honeycombs astonished human being from ancient time due to their perfect geometrical structure. How the hexagonal cells are constructed from fresh circular cells during the cell building process is a matter of long debate. Here we show solely from the thermomechanical properties of self-synthesized beeswax how the honeybees permanently transform the fresh circular cells to rounded hexagons by creating a temperature gradient in the vicinity of the triple junctions of circular cell walls. By assuming conventional Fourier's law of heat conduction and mechanical properties of beeswax, we show via computer simulations that with increasing temperature gradient, the stress on the adjacent circular cell walls increases due to enhanced fusion, leading to the deformation from the original positions of the circular cell walls. The calculated von Mises stresses are found to be significantly larger than the yield stress, indicating the permanent deformation of the circular cell walls to rounded hexagonal shape. This suggests that it is the thermomechanical properties of the building material for which the comb cells take rounded hexagonal shapes.

Evaluating and Comparing the Natural Cell Structure and Dimensions of Honey Bee Comb Cells of Chinese Bee, Apis cerana cerana (Hymenoptera: Apidae) and Italian Bee, Apis mellifera ligustica (Hymenoptera: Apidae)

“…In this regard, there is a view that bees build beeswax secreted by their wax glands into an array of closed-packed cylinders, which are in contact with each other, and under the heat generated by bees, the beeswax reaches a liquid equilibrium state. The adjacent cylindrical cells are connected in the triple junction to each other, and the circular cells rapidly transform into hexagonal structures ( Pirk et al 2004 , Karihaloo et al 2013 , Oldroyd and Pratt 2015 , Talukdar and Dutta 2019 ). According to Pirk et al (2004) and Karihaloo et al (2013) , thermoplasticity and surface tension of beeswax play a key role in this process.…”

“…Recently, there has been growing interest and debate on understanding the structure, size, organization and form of the honey bee comb cells ( Hepburn et al 2014 , Saucy 2014 , Nazzi 2016 , Svečnjak et al 2019 ). Many research studies have been conducted to understand the structure, size, and mechanisms of formation, revealing a lot of data on the rules of honey bee comb cell construction( Pirk et al 2004 , Bauer and Bienefeld 2013 , Karihaloo et al 2013 , Hepburn et al 2014 , Oldroyd and Pratt 2015 , Nazzi 2016 , Oeder and Schwabe 2017 , Jeong et al 2018 , Narumi et al 2018 , Jeong et al 2019 , Talukdar and Dutta 2019 ).…”

Natural Hexagons

“…Have bees acquired some sophisticated geometrical tools over their evolutionary history? It is only recently that some researchers have been able to decipher a vital clue regarding this long-standing revered mystery [10][11][12]. These studies reveal that the hexagonal cells appear spontaneously from the fresh circular cells solely due to the thermomechanical properties of the construction material.…”

“…The simplest possible way to achieve this has been described in [12] where, with the help of computer experiment, it is revealed that without heating the beeswax to the entire melting range, bees can progressively stretch the adjoining walls, increase the contact area between them, straighten them up, and transform the isodiametric cells…”

A New Type of Hierarchical Honeycomb in-Plane Impact Study

“…Honeycomb materials have good mechanical properties and excellent thermal conductivity, therefore, they are widely used in aerospace, construction, transportation, and other fields [1][2][3][4][5]. Additionally, there are many multicellular cell structures in nature, such as wood, bone, and the outer skin of plant cells that are light weight and have good mechanical properties, and therefore they have been the focus of many bionic studies [6][7][8][9].…”