Finite Element Modeling of van der Waals Interaction for Elastic Stability of Multi-Walled Carbon Nanotubes

Abstract

The purpose of this study is to assess the effect of van der Waals interactions within multi-walled carbon nanotubes with the three dimensional finite element models. The elastic buckling behaviors of nanotubes are treated under axial compressive force acting on open both ends of nanotubes and considered with various boundary conditions. The analysis is based on the assumptions that the covalent bond of each wall is represented by an elastic beam element while the van der Waals force of adjacent walls are represented by a nonlinear truss element following the Lennard-Jones “6-12” theory. The models of double-walled carbon nanotubes are used to explain the characteristic of multi-walled carbon nanotubes and then results compared with the column theory. The results show that the critical load of nanotubes depends on atomic arrangement, tube length, and number of walls, while the van der Waals force has a small effect on the buckling load for multi-walled carbon nanotubes.