Finite element modeling of single-walled carbon nanotubes

Abstract

A three-dimensional finite element (FE) model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) is proposed. The model development is based on the assumption that carbon nanotubes, when subjected to loading, behave like space-frame structures. The bonds between carbon atoms are considered as connecting load-carrying members, while the carbon atoms as joints of the members. To create the FE models, nodes are placed at the locations of carbon atoms and the bonds between them are modeled using three-dimensional elastic beam elements. The elastic moduli of beam elements are determined by using a linkage between molecular and continuum mechanics. In order to evaluate the FE model and demonstrate its performance, the influence of tube wall thickness, diameter and chirality on the elastic moduli (Young's modulus and shear modulus) of SWCNTs is investigated. The investigation includes armchair, zigzag and chiral SWCNTs. It is found that the choice of wall thickness significantly affects the calculation of Young's modulus. For the values of wall thickness used in the literature, the obtained values of Young's modulus agree very well with the corresponding theoretical results and many experimental measurements. Dependence of elastic moduli to diameter and chirality of the nanotubes is also obtained. With increased tube diameter, the elastic moduli of the SWCNTs increase. The Young's modulus of chiral SWCNTs is found to be larger than that of armchair and zigzag SWCNTs. The presented results demonstrate that the proposed FE model may provide a valuable tool for studying the mechanical behavior of carbon nanotubes and their integration in nano-composites.