Modeling of anisotropic elastic properties of multi-walled zigzag carbon nanotubes

Abstract

Non-linear three dimensional finite element model of double wall carbon nanotube has been developed to evaluate its anisotropic elastic properties. Carbon nanotube was modeled as a frame-like structure and its elastic properties have been considered in the sense of the average over volume (effective) response on the axial and radial loadings. The principal bonds between two adjacent atoms were simulated using equivalent pseudo-rectangular beam elements which exhibit different flexural rigidity along the two principal centroid axes of the cross-section. The simulation of the interlayer van der Waals force with intrinsic nonlinearity and complicated applying region has been performed. Resulting Young's moduli of double walled carbon nanotube of diameter of 0.7–2 nm was found to vary from 0.2 to 0.5 TPa in axial direction and from 1.4 to 43.3 GPa in radial direction. The radial Young's modulus exponentially decays with the tube diameter.