Stereographic projections of Poisson's ratio in auxetic crystals

Abstract

AbstractAuxetic behavior (negative values of Poisson's ratio) in some cubic metals for a stretch along a cube‐face diagonal was investigated in detail by R. H. Baughman et al., F. Milstein, K. Huang, M. Jain, M. P. Verma. Directions with extreme values of Poisson's ratio in crystals for a stretch along a cube‐face diagonal and corresponding lateral strain along the orthogonal cube‐face diagonal and cube‐axis were considered by the authors. In this paper the stereographic projections of Poisson's ratio for a set of natural crystals with cubic, hexagonal and monoclinic symmetry were computed. From these stereographic projections the Poisson's ratio for any possible directions of stretch and lateral strain in the crystal were calculated and orientations of stretch and lateral strain with extreme values of Poisson's ratio were obtained. Crystals with auxetic behavior were revealed. Orientations of stretch directions and lateral strain directions with negative values of Poisson's ratio were determined. By analysis of the above results cuts with optimal negative values of Poisson's ratio were revealed in zinc, molybdenum sulfide, carbon, graphite, polypropylene, monoclinic natural minerals labradorite and augite, a complex silicate and in a set of cubic alloys. The exotic behavior of change of cross‐section of a cylindrical rod during stretching along the rod axis was revealed in the naturally‐occurring mineral SiO2 cristobalite – an example of a molecular auxetic. The elastic constants of crystals from the manual of Landolt–Börnstein were used in the calculations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)