The intrinsic stiffness of single-wall carbon nanotubes

Single-wall carbon nanotubes have been frequently modeled as linear elastic thin shells. We have compared the atomistic-based shell theory for single-wall carbon nanotubes which was established directly from the interatomic potential to the classical linear elastic shell theory. It is shown that the constitutive relation is linear (within 2% error) only for strain up to 1%. The constitutive relation is approximately isotropic prior to deformation, but the degree of anisotropy increases rapidly as the deformation increases. The coupling between the stress and curvature, and between the bending moment and strain, which is neglected in the classical shell theory, is important for the constitutive behavior of single-wall carbon nanotubes.