Wang C Y, Ru C Q, Mioduchowski A
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada.
J Nanosci Nanotechnol. 2003 Feb-Apr;3(1-2):199-208. doi: 10.1166/jnn.2003.185.
This paper studies elastic buckling of individual multiwall carbon nanotubes under radial pressure. The analysis is based on a multiple-elastic-shell model in which each of the concentric tubes of a multiwall carbon nanotube is described as an individual elastic shell. According to their radius-to-thickness ratios, the multiwall carbon nanotubes discussed here are classified into three types: thin, thick, and (almost) solid. The critical pressure for elastic buckling is calculated for examples of all three types. It is found that a thin N-wall nanotube (defined by a radius-to-thickness ratio larger than 4) is approximately equivalent to a single-layer elastic shell whose effective bending stiffness and thickness are N times the effective bending stiffness and thickness of single-wall carbon nanotubes. Based on this result, an approximate method is suggested for replacing the problematic multiwall nanotube of many layers with a multilayer elastic shell of fewer layers. In particular, the critical pressure predicted by the present model is in good agreement with known experimental results.
本文研究了单个多壁碳纳米管在径向压力下的弹性屈曲。分析基于多弹性壳模型，其中多壁碳纳米管的每个同心管都被描述为一个单独的弹性壳。根据半径与厚度之比，这里讨论的多壁碳纳米管分为三种类型：薄型、厚型和（几乎）实心型。计算了所有三种类型示例的弹性屈曲临界压力。结果发现，薄的N壁纳米管（由半径与厚度之比大于4定义）近似等同于单层弹性壳，其有效弯曲刚度和厚度是单壁碳纳米管有效弯曲刚度和厚度的N倍。基于这一结果，提出了一种近似方法，用层数较少的多层弹性壳替代有问题的多层多壁纳米管。特别是，本模型预测的临界压力与已知实验结果吻合良好。
