An energy-equivalent model on studying the mechanical properties of single-walled carbon nanotubes

In this paper, an energy-equivalent model is put forward for studying the mechanical properties of single-walled carbon nanotubes (SWCNTs). The equivalent Youngʹs modulus and shear modulus for both armchair and zigzag SWCNTs are derived by combining the methods of molecular mechanics and continuum mechanics. On the one hand, based on the principle of molecular mechanics, the total system potential energy associated with both stretching and angular variations is obtained. On the other hand, considering SWCNT as a thin cylinder subjected to an axial or torsion loading, the strain energy can be obtained based on continuum mechanics. Equating the total system potential energy to the strain energy, one derives the equivalent Youngʹs modulus, shear modulus and Poissonʹs ratio. Finally, computations of the mechanical properties reveal that the elastic constants exhibit a strong dependence on the diameter of nanotubes. Youngʹs modulus and shear modulus for both armchair and zigzag nanotubes increase with increasing tube diameter, but the variation trend of Poissonʹs ratios is reverse. The present results agree well with existing results and approach to those of carbon graphite when the diameter is large. Therefore, the method presented here is valid for both carbon nano-tubes and carbon graphite.