A shell theory for chiral single-wall carbon nanotubes

In this paper, we propose a characterization of the mechanical response of the linearly elastic shell we associate to a single-wall carbon nanotube of arbitrary chirality. In Favata and Podio-Guidugli (2012), we gave such a characterization in the case of zigzag and armchair nanotubes; in particular, we showed that the orthotropic response we postulated for the associated shells is to become isotropic in the graphene-limit, that is, when the shell radius grows bigger and bigger. Here we give an explicit recipe to construct the generally anisotropic response of the shell associated to a nanotube of any chirality in terms of the response of the shell associated to a related zigzag or armchair nanotube. The expected coupling of mechanical effects that anisotropy entrains is demonstrated in the case of a torsion problem, where the axial extension accompanying twist is determined analytically.