On the coupling of axial and shear deformations of single-walled carbon nanotubes and graphene: a numerical study

This paper presents a numerical investigation for the evaluation of elastic coupling of extension and twist in single-walled carbon nanotubes. The carbon nanotubes are modelled according to their atomistic structure. The harmonic approximation is utilized for describing the interaction potential energies. The force field is simulated via suitable straight and torsional springs that express the interatomic interactions and interconnect nodes placed on the atomic positions. By using appropriate boundary conditions, the nanotubes are loaded axially and the resulted twist is numerically predicted using finite element procedures. The numerical outcomes reveal that the stretching deformation of single-walled carbon nanotubes leads to their torsion only for the chiral case. A complete parametric study with respect to geometric characteristics of nanotubes shows that the coupling is strongly dependent on the diameter, chiral angle, and nanotube length. To explain these observations, the inherent graphene sheet geometries used for the generation of single-walled carbon nanotubes are also studied under extension. The results prove similar coupling phenomena occur between extension and in-plane shear. Comparisons with results provided in the open literature are also performed, where possible.