Investigation Of The Thermal-mechanical Properties Of CNTs Based On Higher Order Cauchy-Born Rule And The Mechanical Properties Of Nanotubes With Topological Defects

With the fast development of nanotechnology, nano-mechanics has become a hot research topic in the field of computational mechanics and material science. Among a lot of nano-materials, carbon nanotubes (CNTs) are believed to be a promising building block for the construction of nano-device because of its exceptional mechanical and electronic properties. A lot of progresses have been made in developing the theoretical and computational methods for the analysis of the mechanical properties of CNTs. It should be pointed out, however, that most of these works are concentrated on the perfect CNTs and assuming that the temperature is absolute zero. Few works has been done to study the mechanical properties of CNTs taking temperature effects and topological effects into consideration.Based on the above background, in the present thesis, the mechanical properties of CNTs are firstly investigated under finite temperature condition. A higher order Cauchy-Born rule is used to describe the kinematic of the finite deformation of CNTs. By using Helmholtz free energy as thermodynamic potential with local harmonic approximation, the equilibrium lattice constants for CNTs under finite temperature are obtained by energy relaxation. Then the heat capacity and thermal expansion coefficient of CNTs are investigated. We find that the results obtained by our methods are in good agreement with those obtained by experimental and atomistic simulation methods. We also study the dependence of the Young's modulus of CNTs on temperature. The results also agree well with that obtained by molecular dynamic simulations.Because the existence of topological defects in CNTs may change the physical and mechanical properties of CNTs significantly, therefore the study of the topological defects in CNTs has attracted more and more attentions recently. In the second part of this thesis, we present a comparative study of the pure carbon and compound BC3 nanotubes containing different kinds of topological defects (7-, 8- and 9-membered rings) under uniaxial tensions in the framework of all-electron density functional theory (DFT). We find that the formation energies of the topological defects for pure carbon nanotubes are significantly higher than those for compound BC3 nanotubes. For both pure and compound nanotubes, sidewall defects by 7-and 8-membered rings become energetically preferred to form when the uniaxial strain...