FLOWER PATTERNS APPEARING ON A HONEYCOMB STRUCTURE AND THEIR BIFURCATION MECHANISM

Abstract

Illuminative deformation patterns of a honeycomb structure are presented. A representative volume element of a honeycomb structure consisting of 2 × 2 hexagonal cells is modeled to be a [Formula: see text]-equivariant system. The bifurcation mechanism and an exhaustive list of possible bifurcated patterns are obtained by group-theoretic bifurcation theory. A flower mode of the honeycomb is shown to have the same symmetry as the so-called anti-hexagon in the Rayleigh–Bénard convection. A numerical bifurcation analysis is conducted on an elastic in-plane honeycomb structure consisting of 2×2 cells to produce beautiful wallpapers of bifurcating deformation patterns and, in turn, to highlight the achievement of the paper. New deformation patterns of a honeycomb structure have been found and classified in a systematic manner. Knowledge of the symmetries of the bifurcating solutions has turned out to be vital in the successful numerical tracing of the bifurcated paths. This paper paves the way for the introduction of the results hitherto obtained for flow patterns in fluid dynamics into the study of patterns on materials.