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

TL;DR

This paper investigates the buckling transition of 2D elastic honeycombs under compression, combining numerical simulations with Landau theory to analyze pattern formation and symmetry properties.

Contribution

It introduces a comprehensive analysis of buckling patterns in elastic honeycombs using numerical methods and Landau theory, revealing symmetry-preserving and chiral configurations.

Findings

Buckling pattern preserves sixfold symmetry but is chiral.

Non-isotropic compression leads to elemental distortion patterns.

Numerical results align well with Landau theory predictions.

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.