Phonons in conventional and auxetic honeycomb lattices

The modes of vibrations of conventional and auxetic honeycomb structures are studied by means of models where lattices are represented by planar networks, in which rodlike particles are linked by strings. In these structures, the translational and rotational degrees of freedom are strongly coupled. The auxetic network is obtained by modifying a model proposed by Evans in 1991 [Nature (London) 353, 124 (1991)], and is used to explain the negative Poisson's ratio of auxetic materials. Auxetics are materials with a negative Poisson elastic parameter, meaning that they have a lateral extension, instead of shrinking, when they are stretched. The phonon dispersions obtained in the case of the auxetic model are compared with those of a conventional honeycomb network, where rigid rodlike particles are inserted. The behavior of the rotational dispersions can explain some experimental observations on the properties of sound propagation in the auxetic materials.