On finite element modeling of single- and multi-walled carbon nanotubes.

In this study, Single-Walled and Multi-Walled Carbon Nanotubes in their perfect forms were investigated by the Finite Element Method. Details on the modeling of the structure are provided in this paper, including the appropriate elements, the element properties that should be defined based on the atomic structure of Carbon Nanotubes and the corresponding chemical bonds. Non-covalent van der Waals interactions between two neighbor atoms as well as the required approximations for the modeling of the structures with this kind of interaction are also presented. Specific attention was dedicated to the necessity of using some time- and energy-consuming steps in the simulation process. First, the effect of simulating only a single ring of the whole structure is studied to find out if it would represent the same mechanical behavior as the long structure. Results show that by applying an appropriate set of boundary conditions, the stiffness of the shortened structure is practically equal to the long perfect structure. Furthermore, Multi-Walled Carbon Nanotube structures with and without defining the van der Waals force are studied. Based on the observations, applying the van der Waals force does not significantly influence the obtained Young's modulus of the structure in the case of a uniaxial tensile test.