Pressure vessel problem for chiral elastic tubes

The study of chiral materials is important for the investigation of carbon nanotubes, auxetic materials and bones. The chiral effects cannot be described within classical elasticity. In this paper, the problem of the circular tube under internal and external pressure is solved in the context of the linear theory of chiral Cosserat elasticity. The work is motivated by the recent interest in the using Cosserat elastic solid as model for auxetic materials, bones and chiral carbon nanotubes. First, the generalized plane strain of an isotropic chiral elastic material is investigated. Then, the solution of the pressure vessel problem is established. The salient feature of the solution is that, in the absence of body and surface moments, a pressure acting on the surface of a chiral tube produces a microrotation of the material particles. It is shown that the radial displacement and the radial stress are modified from the values predicted by the theory of achiral materials.