Phonons in honeycomb and auxetic two-dimensional lattices

TL;DR

This paper investigates phonon modes in honeycomb and auxetic 2D lattices, revealing that auxetic structures exhibit a complete phonon bandgap and direction-dependent sound propagation, which explains their unique acoustic properties.

Contribution

It introduces a modified auxetic lattice model based on Evans et al.'s work, demonstrating the existence of a phonon bandgap and anisotropic phonon dispersion in auxetic materials.

Findings

Auxetic lattices have a complete phonon bandgap.

Goldstone mode velocity varies with propagation direction.

Auxetic structures absorb noise more efficiently.

Abstract

The modes of vibrations in honeycomb and auxetic structures are studied, with models in which the lattice is represented by a planar network where sites are connected by strings and rigid rods. The auxetic network is obtained modifying a model proposed by Evans et al. in 1991, and used to explain the negative Poisson's ratio of auxetic materials. This relevant property means that the materials have a lateral extension, instead to shrink, when they are stretched. For what concerns the acoustic properties of these structures, they absorb noise and vibrations more efficiently than non-auxetic equivalents. The acoustic and optical dispersions obtained in the case of the auxetic model are compared with the dispersions displayed by a conventional honeycomb network. It is possible to see that the phonon dispersions of the auxetic model possess a complete bandgap and that the Goldstone mode group velocity is strongly dependent on the direction of propagation. The presence of a complete bandgap can explain some experimental observations on the sound propagation properties of the auxetic materials.