【作者】 张晓宇；

【导师】 黄再兴；

【作者基本信息】 南京航空航天大学 ， 工程力学， 2005， 硕士

【摘要】 研究碳纳米管力学性质常用的理论方法有分子动力学、紧缚算法及从头算法等等,但这些方法都很难进行大尺模拟计算,而连续介质理论和有限元方法被证实是很有前景的跨尺度计算工具。本文运用连续介质力学和有限元方法,研究了碳纳米管的稳定性、弹性性质及接触问题,探讨了宏观力学在纳米尺度的适用性。首先,分别基于圆柱模型和圆柱壳模型,在碳纳米管的边界条件中引入表面能因子,推导了碳纳米管最小半径的判别式,得到的最小半径与实验及量子力学计算结果相近。第二,基于薄膜模型和指数 Cauchy-Born 法则,用准连续介质力学方法推导了单壁碳纳米管的连续介质本构方程,并计算了单壁碳纳米管的杨氏模量和泊松比;然后根据推导的本构方程,研究了碳纳米管结构对其弹性性质的影响。最后,基于薄壳模型和前面得到的碳纳米管弹性常数,用有限元软件 ABAQUS 模拟了单壁碳纳米管的接触问题,其中碳管间的 van der Waals 力由用户子程序 UINTER 定义。更多还原

【Abstract】 Most theoretical investigations on the mechanical properties of carbon nanotubes (CNT) are based on atomic theories, which are not suitable for the large-scale simulation. On the contrary, continuum mechanics and finite element (FE) method have been proved to be promising tools to deal with the multi-scale computations. In this paper, the configuration stability, the elastic properties and the contact problems of CNT are studied by the continuum mechanics and FE. The applicability of macro-scale mechanics in nano-scale is also discussed. Firstly, the criteria determining the minimum radii of CNT are deduced by introducing the surface energy factor into the boundary conditions of CNT. The minimum radii deduced based on cylindrical column model and cylindrical shell model are similar to those obtained by the experiments and the modeling via quantum mechanics. Secondly, based on the membrane model and exponential Cauchy-Born rule, the constitutive equations of single wall carbon nanotube (SWCNT) are deduced by qusi-continuum method. Young’s modulii and Poisson’s ratio obtained are within the range of the results from the experiments and other theoretical researches. Also, the influences of the structure on the elastic properties of SWCNT are studied. Finally, FE software ABAQUS is used to model the contact of SWCNTs. The elastic constants are obtained from the deduction before and van der Waals interaction is defined by user subroutine UINTER.更多还原