Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes

Abstract

The research in the paper proposes the effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes (CNTs) through the analysis of a representative volume element (RVE) of the graphene layer via continuous elastic models. The bonds in the RVE are modeled with corresponding stretching and rotating springs. The in-plane stiffness of CNT in the equivalent elastic plate model is first obtained by equating the energy stored in the RVE and the strain energy induced in the continuous plate model under a uniaxial stretching subjected to CNT. The corresponding bending rigidity of CNT is derived by considering the inversion contributing to the bending resistance of the graphene sheet from a large deflection analysis in the elastic plate model of CNT. The results show that the in-plane stiffness of zigzag nanotube is more sensitive to the size of the tube than that of armchair nanotube. Besides, the in-plane stiffness of armchair nanotube is almost twice as big as that of zigzag nanotube at small size. Furthermore, the results also show that the effect of axial deformation on the derivation of bending rigidity is more obvious in armchair nanotube than that in zigzag nanotube at bigger curvature of bending. In addition, the explanation on the result that the bending rigidity of zigzag nanotubes is bigger than that of armchair tubes is provided from a mechanics analysis. In the end, the effect of radius on the bending rigidity is discussed in the research. It is hoped that the research in this paper may provide a benchmark on the derivation of mechanical properties of CNT from continuum models.