Analysis of Single-Walled Carbon Nanotubes Using a Chemical Bond Element Model

Abstract

A three dimensional nano-scale finite element model (FEM), called the chemical bond element model, is proposed for the simulation of mechanical properties of single-walled carbon nanotubes (SWCNTs) based upon molecular mechanics method. Chemical bonds between carbon atoms are modeled by chemical bond elements. The constants of a sub-stiffness matrix are determined by using a linkage between molecular mechanics and continuum mechanics. In order to evaluate the correctness and performance of the proposed model, simulation was done to determine the influence of nanotube wall thickness, radius and length on the elastic modulus (Young's modulus and shear modulus) of SWCNTs. The simulation results show that the choice of wall thickness significantly affects the Young's modulus and shear modulus. The force field constants is also very important, because the elastic modulus is sensitive to force field constants and the elastic properties of SWCNT are related to the radii of the tubes. The contribution of length to elastic modulus is insignificant and can be ignored. In comparison with the Young's modulus and shear modulus reported in the literature, the presented results agree very well with the corresponding theoretical results and many experimental measurements. Furthermore, if the force constants are properly chosen, the present method could be conveniently used to predict the mechanical behavior of other single-walled nanotubes such as boron nitride nanotubes. The results demonstrate the value of the proposed model as a valuable tool in the study of mechanical behaviors of carbon nanotubes and in the analysis of nanotube-based equipments.