Dynamic Continuum Models for Carbon Nanotubes

Abstract

An energy equivalence principle-based dynamic continuum modeling method is proposed to predict reliable effective structural properties for the SWCNTs. In the proposed dynamic continuum modeling method, a repeating cell unit isolated from a single-walled carbon nanotube (SWCNT) is represented as an equivalent continuum beam element by the use of both the molecular mechanics and the structural mechanics. The proposed dynamic continuum modeling method benefits us to accomplish the structural and dynamic analysis for the SWCNTs without assuming the wall thickness of SWCNTs. The effective structural rigidities predicted by using the proposed dynamic continuum modeling method are shown to be in excellent agreement with those predicted by using the Young’s moduli cited from existing references. It is also shown that the SWCNTs have negligible effective coupling rigidities, but quite high effective transverse shear rigidity. I. Introduction INCE the carbon nanotubes were first discovered by Iijima, 1 extensive researches on carbon nanotubes have generated enormous interest in the scientific and engineering research communities in recent years due to their remarkable physical and mechanical properties. Due to their exceptionally high strength (up to 150 GPa), high stiffness (order of 1 TPa), high ductility (up to 15% max strain), high flexibility to bending and buckling, robustness under high pressure, and large aspect ratio, carbon nanotubes have been attracted as the promising reinforcing constituents in light-weight and high strength composites, ropes to tether satellites, scanning probe tips, ultrahigh frequency nanoactuators and nanosensors, etc. 2,3 During last few years, the evaluation of the macroscopic physical and mechanical properties of individual carbon nanotubes has presented significant challenges to many researchers in nanomechanics due to their extremely smallness. The SWCNTs can be considered as the two-dimensional graphene sheets that have been rolled into the tubes and their atomic structures can be expressed in terms of the chiral (or rolled-up) vector components (n, m), where n and m are integers: for example, (n, 0) denotes the zigzag SWCNTs of which chiral angle is 0 o and (n, n) denotes the armchair SWCNTs of which chiral angle is 30 o . 4