Phonons dispersions in auxetic lattices

Abstract

The modes of vibrations in auxetic structures are studied, with models where the two-dimensional lattice is represented by a planar mesh with rod-like particles connected by strings. An auxetic membrane can be obtained modifying a honeycomb one, according to a model proposed by Evans et al. in 1991 and used to explain a negative elastic Poisson's ratio. This property means that auxetic materials have a lateral extension, instead to shrink, when they are stretched. The models here proposed with rod-like particles inserted in the structure have interesting behaviour of acoustic and rotational branches of phonon dispersions. Complete bandgaps of vibrations can be obtained for a proper choice of lattice coupling parameters and distribution of masses in the unit cell of the lattice. © 2007 IOP Publishing Ltd.