Mathematical model of the elastic properties of transversely isotropic single-walled carbon nanotube

This paper is devoted to development of a mathematical model describing the elastic properties of transversely isotropic single-walled carbon nanotube (SWCNT). Relations that link elastic properties of single-layer graphene and element of compliance coefficients matrix are obtained by using the methods of generalized continuum mechanics. Also, the geometry parameters of SWCNT influence on its elastic characteristics is established. The example of the developed model applying to calculation the elastic properties of the SWCNTs with «Zigzag» and «Armchair» configurations are presented. The obtained mathematical model allows us to predict the elastic behavior of SWCNT, which one is very important in the design of perspective composite materials based on it.