Abstract

Cuts with Negative Poisson'S Ratio in Crystals

S.P.Tokmakova (N.N.Andreev Acoustics Institute, Moscow, Russia)

e-mail: stokm@yandex.ru; sveta@akin.ru

Anisotropic materials have properties that depend on direction. For example in crystals it is possible for Poisson's ratio to be negative in one direction and highly positive in another direction. In the paper a set of cubic, hexagonal and monoclinic crystals was investigated. The stereographic projections of Poisson's ratio and Gruneisen parameters were computed for each crystal. From these stereographic projections the Poisson's ratio for any directions of stretch and lateral strain in crystal was calculated. By analysis of the above results the crystals with negative values of Poisson's ratio were revealed. For these crystals the angular dependence of stretched orientations corresponding to negative Poisson's ratio was determined. From the second and third-order elastic constants the stereographic projections of the Gruneisen parameters for the longitudinal and shear acoustic modes were computed. (The nonlinear elastic behavior of a crystal (the anharmonicity of lattice vibrations) under stress is usually expressed in terms of the acoustic Gruneisen parameter.) Some simple models and structures with negative Poisson's ratio are considered and some possible applications of materials with negative Poisson's ratio basing on their unusual acoustic properties are discussed. Elastic moduli of crystals from the manual of Landolt-Bornstein (1992) were applied in calculations.

Section : 2