Deformation analysis of single-wall carbon nanotubes: a shell theory based on the interatomic potential

The aim of the current study is to present a finite deformation shell theory incorporating interatomic potentials for single-wall carbon nanotubes (CNTs). For this purpose, a linkage between the strain energy density induced in the continuum and the interatomic potential is established by the employment of the modified Cauchy-Born rule. This theory, which considers the nonlinear, multi-body atomistic coupling and the CNT chirality, incorporates the important effects of bending moment and curvature for a curved surface. The theory is applied to extract the constitutive relations, which bypass the use of nanotube thickness and Young’s modulus, among stress, moment, strain, curvature and the interatomic potential. It is found that the chirality affects the mechanical behavior of the nanotube in tension and bending and this effect is less profound for the CNTs with higher radius at vanishing strain and curvature.