Kulathunga D D T K, Ang K K, Reddy J N
Department of Civil Engineering, National University of Singapore, 117576, Singapore.
J Phys Condens Matter. 2009 Oct 28;21(43):435301. doi: 10.1088/0953-8984/21/43/435301. Epub 2009 Oct 5.
The accuracy of widely employed classical shell-theory-based formulae to calculate the buckling strain of single- and double-walled carbon nanotubes is assessed here. It is noted that some simplifications have been made in deriving these widely employed formulae. As a result critical buckling strains calculated from these formulae are independent of aspect ratio (length/diameter). However, molecular dynamics simulation results in the literature show an aspect ratio dependence of buckling strain. Therefore, analytical expressions are derived in this paper to calculate buckling strains of single- and double-walled carbon nanotubes based on classical shell theory without simplifications. Applicability of these expressions is further verified through molecular dynamics simulations based on the COMPASS force field. In addition, improvement in results achieved through a refinement of classical shell theory is assessed by calculating buckling strains based on first-order shell theory. Results show that simplified formulae introduce a significant error at higher aspect ratios and smaller diameters. The formulae derived here show reasonable agreement with the molecular dynamics results at all aspect ratios and diameters. First-order shell theory is found to produce a slight improvement in results for CNTs with smaller diameters and lower aspect ratios.
本文评估了广泛使用的基于经典壳理论的公式计算单壁和双壁碳纳米管屈曲应变的准确性。需要注意的是，在推导这些广泛使用的公式时做了一些简化。因此，由这些公式计算出的临界屈曲应变与长径比（长度/直径）无关。然而，文献中的分子动力学模拟结果表明屈曲应变与长径比有关。因此，本文推导了基于经典壳理论的单壁和双壁碳纳米管屈曲应变的解析表达式，且未做简化。通过基于COMPASS力场的分子动力学模拟进一步验证了这些表达式的适用性。此外，通过基于一阶壳理论计算屈曲应变，评估了经典壳理论细化所取得的结果改进。结果表明，简化公式在高长径比和小直径情况下会引入显著误差。本文推导的公式在所有长径比和直径情况下与分子动力学结果都显示出合理的一致性。发现一阶壳理论对于较小直径和较低长径比的碳纳米管在结果上有轻微改进。
