The buckling transition of 2D elastic honeycombs: Numerical simulation and Landau theory

Abstract

I study the buckling transition under compression of a two-dimensional, hexagonal, regular elastic honeycomb. Under isotropic compression, the system buckles to a configuration consisting of a unit cell containing four of the original hexagons. This buckling pattern preserves the sixfold rotational symmetry of the original lattice but is chiral, and can be described as a combination of three different elemental distortions in directions rotated 2pi/3 from each other. Non-isotropic compression may induce patterns consisting in a single elemental distortion or a superposition of two of them. The numerical results compare very well with the outcome of a Landau theory of second order phase transitions.