Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach

The development of a finite element formulation that is appropriate for the computation of Young’s and Shear modulus of single walled carbon nanotubes (SWCNTs) is the purpose of this paper. The method utilizes the atomistic microstructure of the nanotubes. According to the three-dimensional atomic nanostructure of SWCNTs, nodes are defined at the atom locations. Appropriate spring-type elements interconnect these nodes to simulate properly interatomic interactions. This approach is implemented via the use of three-dimensional spring-like elements each node of which obeys to three translations and three rotations. In this way, molecular mechanics theory can be applied directly while the atomic bonds are modeled by using exclusively physical variables such as bond stretching, bond angle bending and torsional rotation resistance force constants. With the proposed method, the Young’s and shear modulus of numerous SWCNTs were determined. The effect of the nanotube radius and thickness on the mechanical behavior of SWCNTs was tested and demonstrated. The numerical results show good agreement with other corresponding values which are available in the literature.