Molecular Dynamics Simulation and Continuum Shell Model for Buckling Analysis of Carbon Nanotubes

Abstract

Carbon nanotubes (CNTs) have potential applications in various fields of science and engineering due to their extremely high elasticity, strength, and thermal and electrical conductivity. Owing to their hollow and slender nature, these tubes are susceptible to buckling under a compressive axial load. As CNTs can undergo large, reversible post-buckling deformation, one may utilize this postbuckling response of CNT to manufacture mechanical energy storage devices at the nano-scale, or use it as a nano-knife or nano-pump. It is therefore important to understand the buckling behavior of CNTs under a compressive axial load. Experimental investigations on CNT buckling are very expensive and difficult to perform. As such, researchers often rely on molecular dynamics (MD) simulations, or continuum mechanics modeling to study their mechanical behaviors. In order to develop a good continuum mechanics model for buckling analysis of CNTs, one needs to possess adequate experimental or MD simulation data for its calibration. For ''short'' CNTs with small aspect ratios (B10), researchers have reported different critical buckling loads/strains for the same CNTs based on MD simulations. Moreover, existing MD simulation data are not sufficiently comprehensive to allow rigorous benchmarking of continuum-based models. This chapter presents extensive sets of MD critical buckling loads/strains for armchair single-walled CNT (SWCNTs) and double-walled CNTs (DWCNTs), with various aspect ratios less than 10. These results serve to address the discrepancies found in the existing MD simulations, as well as to offer a comprehensive database for the critical buckling loads/strains for various armchair SWCNTs and DWCNTs. The Adaptive Intermolecular Reactive Bond Order (AIREBO) potential was adopted for MD simulations. Based on the MD results, the Young's modulus, Poisson's ratio and thickness for an equivalent continuum cylindrical shell model of CNTs are calibrated. The equivalent continuum shell model may be used to calculate the buckling loads of CNTs, in-lieu of MD simulations.

Molecular Dynamics Studies of Load Transfer in Nanocomposites Reinforced by Defective Carbon Nanotube

“…It is a mixture of globalized beam-like buckling for a long and slender CNT and localized shell-like buckling within the atomic layer of a short CNT. In agreement with the findings of Wang et al [54,87], we conclude that CNTs with aspect ratios more than 6 exhibit beam-shell buckling mode, such as a single beam while preserving its circular cross section with localized shell buckling within the atomic layer. From Fig.…”

“…Experimental researchers have observed graphs of CNTs in buckled state both as individual nanotubes [43][44][45] and when embedded in nanocomposites [46,47]. A large volume of theoretical work, based on both continuum-based shell and beam theories [48][49][50], and atomistic techniques such as MD [51][52][53][54], concentrates on buckling of nanotubes by themselves. However, an increasing number of researchers are interested in the compressive behavior of nanotubes when embedded in composites.…”

“…Our results are consistent with those reported by other researchers. For instance, Wang et al [54] used MD simulations to study a broad range of armchair SWCNTs based on AIREBO potential. Their results showed that the buckling strain is in the range of 0.0131 to 0.0734 and the buckling load varies from 18.6 nN to 86.8 nN.…”

Mechanical properties of CNT-reinforced Ni3Al composites: the role of chirality, temperature, and volume fraction

“…The yield stress transition at particular point would mostly be contributed by the transition point of yield stress of inserted CNT at certain radius. According to Wang's work [52], it is concluded that the critical buckling force drops with increasing aspect ratio (L/D, L stands for CNT length, D stands for CNT diameter) for single-wall CNTs. Therefore, in our work the steadily decreasing aspect ratio L/D with larger CNTs is bound to cause the tendency transition in yield stress.…”

Multiscale nanocomposites and laminates reinforced by carbon nanotubes and fibres

“…Values for CNT diameter and thickness aren't well defined in continuum models. As an example, while inter-planar spacing values of 0.34 nm between graphene sheets are commonly used for tube thickness, Wang et al (2014) found that by comparing the continuum shell model results with those obtained from MD simulations that the effective CNT thickness was 0.066nm. Furthermore, Odegard et al (2005) used a truss-based model and found the actual tube thickness to be 0.65nm.…”