Mechanics of carbon nanotubes: A continuum theory incorporating interatomic potentials

Carbon nanotubes are considered ideal for novel technological applications because of their superior mechanical, electrical, chemical and biological properties. Experiments and atomistic studies have shown that they are of very high stiffness and strength, and are capable of sustaining unusually large elastic deformations. These properties, together with that carbon nanotubes are of low density, make them intriguing candidates for nanoscale mechanical systems such as nanocomposites and nanostructures.; The mechanical properties of carbon nanotubes have been studied with atomistic simulation techniques and continuum analogue approaches. However, atomisitic simulations are severely limited by their constraints on time and length scales, while continuum analogues are ad hoc and are unable to capture the physical mechanism. Recently, there are attempts to model carbon nanotubes by incorporating atomic information in a continuum theory. It is found that, under certain conditions, they are applicable for nanoscale structures.; A nanoscale continuum theory is proposed in this thesis for the constitutive behavior of carbon nanotubes. The atomic interactions are described by an empirical interatomic potential, and are linked to the macroscopic deformation of the carbon nanotube through a systematic approach. Hence the constitutive behavior of carbon nanotubes is described as the collective behavior of the carbon atoms, and no additional parameter is introduced during the process.; The elastic modulus predicted by the proposed continuum theory is in good agreement with experimental and atomistic findings. It is also found that the critical strain at which instability occurs when a carbon nanotube is subject to tension is agreeable to that predicted by atomistic models.