A multiscale computational framework for the modeling of carbon nanotubes

A multiscale computational framework is presented for developing a coupled self-consistent system of equations involving molecular mechanics at the small scale and quasi-continuum mechanics at the very large scale. The finite element method developed on the multiscale variational framework furnishes a two level statement of the problem. It provides the multiple-scale analysis capability by concurrently feeding the information at the molecular scale, formulated in terms of the nano-scale material moduli, into the quasi-continuum equations. Interatomic interactions are incorporated into the model through a set of analytical equations with internal variables that are a function of the local state of deformation [1]. Multi-body potentials of the Tersoff-Brenner type are employed to model point defects that affect atomic structure locally, and therefore generate localized displacements with localized force fields. The nano-scale material moduli are integrated into a modified form of the Geometrically Exact Shell Model [2] to model nanotubes. Representative numerical examples are shown to validate the model and demonstrate its range of applicability.