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Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes

机译：评估单壁碳纳米管屈曲应变的连续力学模型的评估

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This paper presents an assessment of continuum mechanics (beam and cylindrical shell) models in the prediction of critical buckling strains of axially loaded single-walled carbon nanotubes (SWCNTs). Molecular dynamics (MD) simulation results for SWCNTs with various aspect (length-to-diameter) ratios and diameters will be used as the reference solutions for this assessment exercise. From MD simulations, two distinct buckling modes are observed, i.e. the shell-type buckling mode, when the aspect ratios are small, and the beam-type mode, when the aspect ratios are large. For moderate aspect ratios, the SWCNTs buckle in a mixed beam-shell mode. Therefore one chooses either the beam or the shell model depending on the aspect ratio of the carbon nanotubes (CNTs). It will be shown herein that for SWCNTs with long aspect ratios, the local Euler beam results are comparable to MD simulation results carried out at room temperature. However, when the SWCNTs have moderate aspect ratios, it is necessary to use the more refined nonlocal beam theory or the Timoshenko beam model for a better prediction of the critical strain. For short SWCNTs with large diameters, the nonlocal shell model with the appropriate small length scale parameter can provide critical strains that are in good agreement with MD results. However, for short SWCNTs with small diameters, more work has to be done to refine the nonlocal cylindrical shell model for better prediction of critical strains.
机译：本文介绍了在预测轴向加载的单壁碳纳米管（SWCNT）的临界屈曲应变时连续力学模型（梁和圆柱壳）的评估。具有不同长宽比和直径的SWCNT的分子动力学（MD）模拟结果将用作此评估活动的参考解决方案。从MD模拟中，观察到两种不同的屈曲模式，即当长宽比小时，壳型屈曲模式，当长宽比大时，光束型屈曲模。对于中等长宽比，SWCNT以混合的梁壳模式弯曲。因此，人们可以根据碳纳米管（CNT）的长宽比选择束模型或壳模型。本文将显示，对于长径比大的SWCNT，局部欧拉束结果可与在室温下进行的MD模拟结果相媲美。但是，当SWCNT具有中等长宽比时，有必要使用更精确的非局部梁理论或Timoshenko梁模型来更好地预测临界应变。对于大直径的短SWCNT，具有适当小长度比例参数的非局部壳模型可以提供与MD结果非常吻合的临界应变。但是，对于直径较小的短SWCNT，必须做更多的工作来完善非局部圆柱壳模型，以便更好地预测临界应变。

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