Computational modeling of the transverse-isotropic elastic properties of single-walled carbon nanotubes

Various experimental and theoretical investigations have been carried out to determine the elastic properties of nanotubes in the axial direction. Their behavior in transverse directions, however, has not been well studied. In this paper, a combination of molecular dynamics (MD) and continuum-based elasticity model is used to predict the transverse-isotropic elastic properties of single-walled carbon nanotubes (SWCNTs). From this modeling study, five independent elastic constants of an SWCNT in transverse directions are obtained by analyzing its deformations under four different loading conditions, namely, axial tension, torsion, uniform and non-uniform radial pressure. To find the elastic constants in the transverse directions, the strain energy due to radial pressure is calculated from the MD simulation. Then, a continuum-based model is implemented to find the relation between the strain energy and maximum pressure under these two loading conditions. Based on the energy equivalence between the MD simulation and the continuum-based model, the transverse-isotropic elastic constants of SWCNTs are computed. The effectiveness of this approach is demonstrated by comparing the results with previous experimental and computational works.