Keywords: carbon nanotubes, atomic simulation, continuum simulation, higher-order continuum, multiscale method.

In addition to a large amount of experimental work, computational and theoretical modelling play an important role in capturing and understanding the delicate behaviour of nanostructures. The development of efficient computational techniques is an ongoing and challenging process in research into nanoscience and nanotechnology, forming a new branch of computational mechanics: computational nanomechanics. Atomic-based methods, such as molecular dynamics, can trace the single atomic motion in nanostructures, but they are limited to very small size due to their huge computational cost. Continuum-based methods extend classical continuum mechanics theory to nanostructures. They can significantly reduce the degrees of freedom in problems, and the theoretical and numerical analysis of large-scale structures becomes possible. Continuum simulation can also display certain nanostructure properties that cannot be found with atomic-based methods. However, continuum-based methods are not complete substitutes for atomic-based methods because they cannot capture the microscale physical laws of nanostructures. Multiscale analysis is currently emerging as a feasible and efficient approach to large-size problems. Multiscale methods couple continuum simulation and atomic simulation, taking advantage of both types of approach. The basic idea of the multiscale method is to use atomic simulation for the localized region in which the discrete motion of atoms is important, and to use the continuum method for the remaining regions in which the deformation is homogeneous and smooth.

The authors' research focuses mainly on the mechanical properties of a special type of nanostructure: the carbon nanotubes (CNTs). In the research domain of computational nanomechanics for CNTs, the authors have carried out systematic studies in the following areas: (1) the application of molecular dynamics and the atomic finite element method in simulating the damage and buckling phenomena of single-walled CNTs (SWCNTs) and multi-walled CNTs (MWCNTs); (2) the application of the higher-order continuum theory in establishing a fine continuum model of CNTs; (3) the implementation of a mesh-free method in the continuum numerical modelling of CNTs; and (4) the multiscale simulation of CNTs by coupling the mesh-free method and atomic simulation. In this chapter, the authors will introduce these topics and discuss their efficiency through selected examples.

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