On Some Mechanics Problems In One Dimensional Nanostructures

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...