Abstract
The atomistic-continuum mechanics (ACM) and finite element method (FEM) were applied to construct an equivalent-continuum model to investigate the mechanical properties of carbon nanotube (CNT). In addition, the interatomic potential function between carbon atoms were described by two kinds of potential function, one was the Cornell’s potential function which was a linear function and the other was the Brenner’s Reactive Empirical Bond Order Potential (REBO) which was a non-linear one. Several models using continuum mechanics had been published including the equivalent-beam and the equivalent-truss models. By using the later model with linear interatomic force constant, the results of the linear analysis could be validated with the experiments. As a result, the authenticity of applying continuum mechanics and finite element method into the analysis of atomic-level material has been verified. Moreover, the modal analysis of carbon nanotubes by using finite element method was also validated. In classical continuum mechanics, the Young’s modulus could be directly measured by tensile test, or be calculated from the results of the corresponding vibration test. Applying the above concept to the prediction of Young’s modulus of carbon nanotubes theoretically could result in the same corresponding relation. In this research, both linear interatomic force constant and non-linear potential function REBO were chosen as the material properties of the atomistic-continuum transformation element. The discussion about the rationality of the equivalent-continuum model was proceeded by referring to the available experiments. Moreover, by selecting the appropriate potential function, the stress-strain relation could be carried out. At last, the modal analyses of the equivalent atomistic-continuum SWCNT model were proceeded and the corresponding continuum models were constructed. By analyzing the relation between the above two models, the reasonable wall-thickness of SWCNT could be acquired. The results showed that the Young’s modulus wouldn’t change obviously with the variation of tube radius and length, and the average number is about 1,050GPa which agreed with the most experimental and analytical results. In the modal analyses, the resonant frequency of SWCNT with the same mode shape was proportional to the tube radius, and was disproportional to the tube length. Finally, by comparing the analytical solution of the tube structure with the simulation results of equivalent-continuum shell model, the reasonable wall-thickness of SWCNT was acquired as 0.34nm which was chosen in the most publications.