Mechanics and morphology of single-walled carbon nanotubes: from graphene to the elastica

Abstract

The elastica is referred to the shape of the curve into which the centreline of a flexible lamina is bent. Hence, single-walled carbon nanotubes (SWCNTs) are treated as the elastica obtained from bending of graphene. The corresponding large deformation accompanies both the material and geometrical non-linearities. The morphology of the free-standing SWCNTs such as the natural angle of twist, bond lengths, tube radius and wall thickness are determined. Moreover, it is shown that the induced self-equilibriated strain field has a remarkable impact on the mechanical behaviour of the nanotube. Utilization of an appropriate non-linear continuum constitutive relation for graphene leads to exact formulation of the governing equations of SWCNTs. Subsequently, through perturbation analysis, the asymptotic solutions of the initial elastic fields for the SWCNTs are presented. By performing ab initio calculations, the components of the fourth and sixth-order elastic moduli tensors in the constitutive model of graphene needed in this study are computed.