Development of empirical relations for the transversely isotropic properties of zigzag, armchair and chiral single-walled carbon nanotubes

Finite element analysis has been performed to evaluate transversely isotropic properties of the single walled carbon nanotubes (SWCNTs).Finite element models of SWCNTs are generated by specifying the C-C bond rigidities (which are arrived by equating the energies from molecular mechanics and continuum mechanics). The five independent transversely isotropic properties for different chiralities are evaluated using the stress fields of thick-walled cylinders and the elastic deformations of SWCNTs subjected to pure extension, internal pressure and pure torsion loads. The adequacy of the elastic properties is demonstrated through modelling of an equivalent overall orthotropic hollow thick-walled cylinder under different loading conditions. Empirical relations are provided for the five independent elastic constants useful for armchair, zigzag and chiral zigzag SWCNTs