Transversely isotropic elastic properties of single-walled carbon nanotubes

While it is known that the elastic properties of a single-walled carbon nanotube (SWNT) are transversely isotropic, the closed-form solutions for all five independent elastic moduli have not been solved completely. In this paper, an energy approach in the framework of molecular mechanics is used to evaluate the local and global deformations of a SWNT in a unified manner. This is carried out under four loading conditions: axial tension, torsional moment, in-plane biaxial tension, and in-plane pure shear, respectively, from which the closed-form expressions for the longitudinal Young's modulus, major Poisson's ratio, longitudinal shear, plane strain bulk, and in-plane shear moduli are obtained. It is shown that as the tube diameter increases, the major Poisson's ratio approaches a constant, the longitudinal Young's and shear moduli and the plane strain bulk modulus are inversely proportional to the tube diameter, and the in-plane shear modulus is inversely proportional to the third power of the tube diameter. The dependence of the elastic moduli of a SWNT on the tube diameter and helicity is displayed and discussed.