【作者】 李海军；

【导师】 郭万林；

【作者基本信息】 南京航空航天大学 ， 固体力学， 2006， 博士

【摘要】 碳纳米管具有非常优异的力学、热学、电学和光学性能,应用前景广阔。自从碳纳米管被发现以来,对其力学性能的理论预测一直是一个热门研究领域。本文基于原子势建立了碳纳米管的有限元模型,基于该模型开展了碳纳米管的若干关键力学问题研究,主要包括以下内容:(1)碳纳米管有限元模型构建。提出一种新的能够完备地替代谐和势描述C-C共价键的等效梁单元,该单元能够区分C-C键的σ-σ键角和σ-π键角的不同弯曲刚度。通过分析石墨层的本构关系确定了等效梁单元的参数。基于该等效梁单元建立了单壁碳纳米管的有限元模型,并用非线性弹簧等效Lennard-Jones势描述多壁碳纳米管层间范德华作用从而建立了多壁碳纳米管的有限元模型。本文模型能够直接在标准商业有限元软件中实现,从而可以利用商业有限元软件的强大功能开展碳纳米管力学问题的模拟。(2)碳纳米管弹性模量计算。将单壁碳纳米管看作横观各向同性材料,系统地计算了其独立的5个弹性模量随直径和手性的变化。发现其直径越小,弹性模量对直径和手性的依赖性越强,且各向异性越明显;随着直径的增大,弹性模量的各向异性逐渐消失,当直径足够大时候,碳纳米管退化成各向同性材料,弹性模量趋于石墨层的模量。这些结果拓展了前人的文献报道,提供了一个对单壁碳纳米管各向异性性质的完整理解。(3)碳纳米管屈曲行为模拟。应用特征值屈曲计算方法系统地分析了单壁和多壁碳纳米管临界压缩屈曲模态和临界压缩屈曲应变随其长径比的变化,发现相同长度的单壁碳纳米管承受临界压缩屈曲应变的能力有一个最优直径,处在该直径的单壁碳纳米管承受压缩屈曲应变的能力最强。还用一种附加阻尼的方法对单壁碳纳米管的弯曲屈曲行为进行了初步探讨,结果为相关分子动力学计算所验证。(4)碳纳米管振动模态分析。应用特征值振动方法计算了单壁和多壁碳纳米管的各种振动模态,着重分析了多壁碳纳米管的“刚性”同轴振动模态(仅由范德华力决定的模态)。本文计算范围内碳纳米管的振动频率均在GHz以上,表明碳纳米管有望成为设计高频纳米器件的理想材料。(5)碳纳米管拉曼活性模态计算。用特征值振动方法计算了单壁碳纳米管的拉曼模态,计算表明低阶拉曼模态与相关实验和理论报道相当吻合,尤其径向呼吸模态与前人第一原理计算结果高度一致,说明本文模型在拉曼模态计算方面具有一定的适用性。本文还对多壁碳纳米管的径向呼吸模态进行了详细预测,结果表明多壁碳纳米管存在与其层数相同阶数的径向呼吸模态,且其振动频率分别高于各层单壁碳纳米管径向呼吸模态的频率。(6) Casimir力和静电力驱动下的GHz振动探讨。从多壁碳纳米管得到启发,抽象出双层同轴圆柱管模型,探讨了该模型在Casimir力和静电力作用下的振动特性,结果显示在纳米尺度该模型振动频率即可达到GHz以上,表明在纳米尺度GHz高频振动的普遍存在性。更多还原

【Abstract】 Carbon nanotubes (CNTs) have very amazing mechanical, electronic, thermal and optical properties, which enable them many potential applications. Since the discovery of CNTs, great attention has been paid to the prediction of their mechanical behaviors. In this dissertation, a finite element model of CNTs is proposed basing on their atomic potentials, and several key mechanical problems of CNTs are studied by the model. The major contents are following:(1) Finite element modeling of CNTs. In order to capture the distinguishing in-planeσ-σand out-of-planeσ-πbond angle bending rigidities of C-C bonds in CNTs, we propose a novel equivalent beam element, which can perfectly replace the harmonic potentials to describe the bond stretching, bond angle variance, inversion angle variance and torsion of the C-C bonds. The parameters of the equivalent beam element are extracted from the constitutive relations of a graphite sheet under different load conditions. Using the equivalent beam elements, the frame structure finite element model of single-walled carbon nanotubes (SWNTs) is developed. Then nonlinear spring elements are used to replace the Lennard–Jones potentials to represent the interlayer van der Waals interactions of multi-walled carbon nanotubes (MWNTs) and the corresponding finite element model of MWNTs is constructed. The present model can be incorporated into any standard commercial finite element software. Since the commercial finite element softwares are comprehensively developed and have very powerful calculation abilities, many mechanical problems of CNTs can be solved by the models in prospect.(2) Calculations of the elastics moduli of SWNTs. The five independent elastic moduli of SWNTs with arbitrary chirality and diameter are evaluated systematically. It is found that the elastic properties of SWNTs are transversely isotropic when the tube diameter is small. The smaller the tube diameter, the stronger the dependence of the elastic properties on the tube size and chirality, while when the tube diameter is large enough, the SWNTs degenerate from transversely isotropic to isotropic and the elastic moduli tend to that of a graphite sheet. This work extends the previously reported results and provides a full understanding of the anisotropic elastic properties of SWNTs(3) Simulation of the elastic buckling of CNTs. The compression buckling behavior of CNTs is predicted by using the eigenvalue buckling analysis. It is found that the critical buckling modes and the critical buckling strains are varied with the aspect of the CNTs. The results also indicate that there exists an optimum diameter for SWNTs with the same lengths at which the critical compression buckling strain reaches its maximum value. The bending buckling of SWNTs is also been studied elementarily through the automatic addition of artificial damping to the model. The results show good agreement with previous molecular dynamics calculations.(4) Analysis of the vibration modes of CNTs. By using the eigenvalue extraction method, the vibration modes of SWNTs and MWNTs are studied, and the rigid coaxial vibration modes, which are mainly determined by the interlayer van der Waals interations, are especially concerned. It is shown that in our calculation range, all the vibration frequencies of CNTs are above the order of GHz, indicating that CNTs may be an ideal material for high frequency nano devices.(5) Calculation of the Raman-active modes of CNTs. The Raman modes of SWNTs are extracted by the eigenvalue extraction method. It is shown that the present calculated frequencies of the low-order Raman modes agree well with the related experimental and theoretical results, especially that of the radial breathing modes (RBMs) are greatly consistent with existing ab initio results. This indicates that the present method is applicable for the calculation of Raman-active modes of CNTs, especially for the calculation of RBMs. So we conduct detailed prediction of the RBMs of MWNTs. Results show that RBM number of a MWNT equals to its layer number, and the frequency of each RBM is higher than the RBM frequency of the corresponding SWNT of each MWNT layer.(6) Investigation on the GHz oscillation driven by Casimir or electrostatic force. A mechanical oscillator model of double-walled coaxial cylindrical tubes, which is analogous to double-walled carbon nanotubes, is proposed and the oscillation behavior of the model driven by Casimir or electrostatic force is studied by energy approach It is shown that when the model is at nano-scale, its oscillation frequency can reach or even exceed the order of GHz, indicating that GHz high frequency oscillation may be quite common phenomenon at nano-scale.更多还原