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.