【作者】 王立峰；

【导师】 胡海岩； 郭万林；

【作者基本信息】 南京航空航天大学 ， 一般力学与力学基础， 2005， 博士

【摘要】 随着纳米科技的发展,纳米结构的力学问题日益受到关注。与宏观结构不同,纳米尺度结构需要考虑量子效应,表面效应,多场耦合效应,原子间存在长程 Van der Waals 力,且结构是离散的,宏观连续介质力学方法在纳米尺度的适用性需要经过验证。 本文以碳纳米管及铜纳米线等一维纳米结构为研究对象,采用连续介质力学分析与分子动力学计算相结合的方法,对单壁及多壁碳纳米管的屈曲、碳纳米管与刚性壁的碰撞、碳纳米管中纵波与弯曲波的传播、铜纳米线的表面效应引起的尺寸效应、铜纳米线的动力屈曲和纳尺度的温度问题等进行了研究。论文共计八章,其主要研究内容及学术贡献如下: (1) 研究了碳纳米管的屈曲及后屈曲。先用基于 Tersoff-Brenner 势的分子动力学方法研究单壁碳纳米管在轴向载荷下的非线性后屈曲行为,发现碳纳米管在后屈曲阶段近似为等力弹簧,其屈曲过程是能量吸收的过程,碳纳米管可作为很好的吸能元件。连续介质力学可以较好地给出碳纳米管的屈曲点,但只能给出近似的后屈曲行为。然后用分子动力学方法模拟了多壁碳纳米管在压缩、弯曲变形下力与变形的关系。通过与组成多壁碳纳米管的各单壁碳纳米管的比较分析,揭示了多壁碳纳米管层间 Van der Waals 力对碳纳米管力学性质的影响。采用 6-12 形式的Lennard-Jones 势描述碳纳米管壁间 Van der Waals 力。计算结果表明,多壁碳纳米管的比强度明显高于单壁碳纳米管。Van der Waals 力对杨氏模量影响不大,但对碳纳米管屈曲行为的影响却相当显著。 (2) 用分子动力学方法模拟碳纳米管与刚性壁的正碰撞过程,并与弹性动力学方法的分析结果进行对比。在分子动力学模拟中,采用 Tersoff-Brenner 势描述碳纳米管的原子间相互作用,用 6-12 形式的 Lennard-Jones 势描述碳纳米管与刚性壁间相互作用。结果表明,两种方法所得到的应力波传播速度吻合较好,应力波的传播过程是原子的动能和原子间势能的转化过程。与弹性动力学分析结果不同的是,在发生屈曲以前,碳纳米管与刚性壁的接触时间不仅与碳纳米管的长度近似成线性关系,还与管径及碰撞初速度有关。碰撞过程中,碳纳米管端部应力并非定值,但其平均值与弹性动力学计算结果相差不大。 (3) 用连续介质力学方法及基于 Tersoff-Brenner 势的分子动力学方法对比研究了碳纳米管中纵波的传播及频散问题。主要考虑了微结构对碳纳米管中纵波频散的影响。首先用分子动力学模拟了不同周期的纵波在碳纳米管中的传播。然后基于各种弹更多还原

【Abstract】 Recent years have witnessed an increasing interest in the mechanics of nano-structures with rapid development of nano-technology. Different from the continuum mechanics, the study on the mechanical property of nano-structures may have to take the effects of surface energy, temperature, van der Waals force among atoms, as well as other interacted fields, into account. It is necessary, hence, to validate the continuum mechanics before it is applied to any nano-structures. The objective of this dissertation is to check the validity of the continuum mechanics, especially the continuum dynamics, for the nano-structures of one dimension, such as the carbon nanotubes and copper nanowires, with help of molecular dynamics simulations. The studies presented in the dissertation include the buckling of both single-walled and multi-walled carbon nanotubes, the impact of carbon nanotubes with a rigid wall, the dispersion of both longitudinal and flexural waves in carbon nanotubes, the size effect on the effective Young’s modulus of copper nanowires, the dynamic buckling of copper nanowires and the effect of temperature in nano-scale problems. The dissertation begins with a brief survey on the mechanics problems in nano science and technology in Chapter 1. There follows the main body of the dissertation, from Chapters 2 to 7. It terminates with a few concluding remarks in Chapter 8. The results and the main contributions of the dissertation are as following. Chapter 2 reveals the buckling behavior of carbon nanotubes through the use of molecular dynamics simulation based on the Tersoff-Brenner potential. The chapter first presents the buckling and the postbuckling of single-walled carbon nanotubes subjected to a cyclic axial compressive load and gives the bifurcation behavior in buckling process simulated with very fine time steps. In the whole cycle of nonlinear deformation, the carbon nanotubes exhibit the profound hysteretic behavior and the energy absorption ability. The molecular dynamics simulation indicates that the carbon nanotube behaves approximately as an ideal plastic spring when the cyclic strain is applied within the same postbuckling mode. In comparison, the theory of continuum mechanics gives a good prediction for the critical buckling strength, but only provides a rough estimation for the post-buckling behaviors. Then, the chapter presents the molecular dynamics simulations for both single-walled and multi-walled carbon nanotubes subjected to different external loads to examine the influence of the van der Waals force on the property of multi-wall carbon nanotubes. In this part, the van der Waals force between the walls is approximated through the use of the ‘6-12’ Lennard-Jones potential. Although the van der Waals force has no remarkable effect on the Young’s modulus, its influence on the strength and buckling behavior of carbon nanotubes is significant. Chapter 3 focuses on the impact of carbon nanotubes with a rigid wall with help of molecular dynamics simulations, where the interatomic interactions are described by a Tersoff-Brenner potential and the interactions between the atoms of carbon nanotubes and the rigid wall are approximated by the ‘6-12’ Lennard-Jones potential. The simulations show that the velocity of stress waves predicted by molecular dynamics falls into the same range by the theory of elasticity. Different from an elastic rod, the impact duration of a nanotube is not only proportional to the length of nanotube, but also depends on the initial impact velocity and the diameter of nanotube. Furthermore, the stress at the end of nanotube is not a constant during impact. However, its mean value is close to the result given by theory of elasticity. Chapter 4 presents the study on the longitudinal wave propagation and dispersion in single-walled carbon nanotubes through the use of the continuum mechanics and the molecular dynamics simulation based on the Terroff-Brenner potential. The study focuses on the effects of non-local elasticity characterizing the microstructure on the wave disp更多还原