Abstract At the nanolevel, a classical continuum approach seems to be inapplicable to evaluate the mechanical behaviors of materials. With the introduction of scale parameter, the scale effect can be reasonably described by the modified continuum theory. For boron nitride nanotubes (BNNTs), the scale effect can be reflected by the curvature and the dangling bonds at both ends, mainly the former for a slender tube. This study aims to achieve a good capability of classical Euler–Bernoulli theory to directly predict the bending behaviors of single-walled BNNTs without introducing scale parameters. Elastic properties of BNNTs involving the scale effect have been first conducted by using an atomistic-continuum multiscale approach, which is directly constructed based on the atomic force field. The well-determined hexagonal boron nitride sheet is inherited in the present study of single-walled BNNTs which can be viewed as rolling up a boron nitride sheet into a seamless hollow cylinder. Euler–Bernoulli theory solution of bending deflection on the basis of the present thickness is found to be much closer to the atomistic-continuum simulation results than the commonly used interlayer space. Case studies with different tubular lengths, radii and constraints are investigated, and from which the yielded scattered scale parameters in modified continuum theories are discussed.

中文翻译：

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基于经典 Euler-Bernoulli 梁理论的单壁 BNNT 弯曲挠度的精确解

摘要 在纳米级，经典的连续介质方法似乎不适用于评估材料的力学行为。随着尺度参数的引入，尺度效应可以用修正的连续统理论来合理地描述。对于氮化硼纳米管（BNNTs），其尺度效应可以通过曲率和两端的悬空键来体现，主要是前者用于细长管。本研究旨在实现经典欧拉-伯努利理论的良好能力，在不引入尺度参数的情况下直接预测单壁 BNNT 的弯曲行为。涉及尺度效应的 BNNT 的弹性特性首先通过使用原子连续多尺度方法进行，该方法直接基于原子力场构建。在目前对单壁 BNNT 的研究中继承了明确的六方氮化硼片，可以将其视为将氮化硼片卷成无缝中空圆柱体。发现基于当前厚度的弯曲偏转的 Euler-Bernoulli 理论解比常用的层间空间更接近原子连续模拟结果。研究了具有不同管长度、半径和约束的案例研究，并从中讨论了修正连续介质理论中产生的散射尺度参数。发现基于当前厚度的弯曲偏转的 Euler-Bernoulli 理论解比常用的层间空间更接近原子连续模拟结果。研究了具有不同管长度、半径和约束的案例研究，并从中讨论了修正连续介质理论中产生的散射尺度参数。发现基于当前厚度的弯曲偏转的 Euler-Bernoulli 理论解比常用的层间空间更接近原子连续模拟结果。研究了具有不同管长度、半径和约束的案例研究，并从中讨论了修正连续介质理论中产生的散射尺度参数。