  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 Bajaj et al. 2013, 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 and found in good agreement with
the available experimental data.
