手性单壁碳纳米管的壳理论
A Shell Theory for Chiral Single-Wall Carbon Nanotubes
摘要：
在本文中，我们提出了一个表征的机械响应的线性弹性壳，我们关联到一个单壁碳纳米管的任意手性。在Bajaj等人2013年的文章中，我们给出了锯齿形和扶手椅形纳米管的特征;特别是，我们表明，我们假设的相关壳的正交各向异性响应在石墨烯极限下变得各向同性，也就是说，当壳半径越来越大时。在这里，我们给出了一个明确的配方，以构建与任何手性的纳米管相关的壳的响应相关的锯齿形或扶手椅形纳米管的一般各向异性的响应。在扭转问题的情况下，证明了各向异性夹带的机械效应的预期耦合，其中伴随扭转的轴向延伸被解析地确定，并发现与现有的实验数据吻合良好。
英文摘要：
In this paper, we propose a characterization of the mechanical response of the linearly elastic shell we associate to a single-wall carbon nanotube of arbitrary chirality. In Bajaj et al. 2013, we gave such a characterization in the case of zigzag and armchair nanotubes; in particular, we showed that the orthotropic response we postulated for the associated shells is to become isotropic in the graphene-limit, that is, when the shell radius grows bigger and bigger. Here we give an explicit recipe to construct the generally anisotropic response of the shell associated to a nanotube of any chirality in terms of the response of the shell associated to a related zigzag or armchair nanotube. The expected coupling of mechanical effects that anisotropy entrains is demonstrated in the case of a torsion problem, where the axial extension accompanying twist is determined analytically and found in good agreement with the available experimental data.
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