Hard-to-Soft Transition in Radial Buckling of Multi-Concentric Nanocylinders
Hard-to-Soft Transition in Radial Buckling of Multi-Concentric Nanocylinders
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DOI：
10.4236/wjm.2012.21006
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
Sung-Jin Park;Motohiro Sato;Tetsuro Ikeda;H. Shima
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文献类型：
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作者：
Sung-Jin Park;Motohiro Sato;Tetsuro Ikeda;H. Shima
我们调查的横截面屈曲的多同心管状纳米材料，这被称为多壁碳纳米管（MWNTs），使用基于薄壳理论的分析。MWNTs在静水压力下经历径向屈曲。其结果是，根据管间间距d以及组成管的数量N和最内管直径获得不同的屈曲模式。所有的屈曲模式分为两个变形阶段。在对应于椭圆变形的第一阶段中，径向刚度随着N的增加而迅速增加。相反，第二阶段产生沿圆周沿着的波浪形波纹结构，其径向刚度随着N的增加而下降。碳纳米管的核-壳结构直接导致了径向屈曲时的硬-软相变。特别注意的是，d的变化如何影响临界管数Nc，这将在N -壁纳米管中观察到的两个变形相分开，即，椭圆相N Nc.我们表明，一个较大的d往往会导致在一个较小的Nc，这是由于在硬到软的过渡过程中的径向屈曲的多壁碳纳米管的同心管之间的原子间力的主要作用。
We investigate the cross-sectional buckling of multi-concentric tubular nanomaterials, which are called multiwalled carbon nanotubes (MWNTs), using an analysis based on thin-shell theory. MWNTs under hydrostatic pressure experience radial buckling. As a result of this, different buckling modes are obtained depending on the inter-tube separation d as well as the number of constituent tubes N and the innermost tube diameter. All of the buckling modes are classified into two deformation phases. In the first phase, which corresponds to an elliptic deformation, the radial stiffness increases rapidly with increasing N. In contrast, the second phase yields wavy, corrugated structures along the circumference for which the radial stiffness declines with increasing N. The hard-to-soft phase transition in radial buckling is a direct consequence of the core-shell structure of MWNTs. Special attention is devoted to how the variation in d affects the critical tube number Nc, which separates the two deformation phases observed in N -walled nanotubes, i.e., the elliptic phase for N Nc. We demonstrate that a larger d tends to result in a smaller Nc, which is attributed to the primary role of the interatomic forces between concentric tubes in the hard-to-soft transition during the radial buckling of MWNTs.