Chiral effects in uniformly loaded rods

Abstract

Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The chiral effects cannot be described within classical elasticity. In the context of the linear theory of Cosserat elastic solids, we investigate the deformation of a chiral rod subjected to tractions on the lateral surface, to body loads, and to resultant forces and moments on the ends. The work is motivated by the recent interest in the using of the Cosserat elastic solid as model for auxetic composites, carbon nanotubes and bones. The three-dimensional problem is reduced to the study of some generalized plane strain problems. New chiral effects are presented. In the case of cylinders of arbitrary cross-section, the flexure produced by a transversal force, in contrast with the case of achiral materials, is accompanied by extension and bending by terminal couples. The body loads and the tractions on the lateral surface produce extension, flexure, torsion, bending by terminal couples and a plane strain. It is shown that a uniform pressure acting on the lateral surface of a chiral circular cylinder does not produce bending effects.