Formulation of 2D graphene deformation based on chiral-tube base vectors

Abstract

The intrinsic feature of graphene honeycomb lattice is defined by its chiral index (n,m), which can be taken into account when using molecular dynamics. However, how to introduce the index into the continuum model of graphene is still an open problem. The present manuscript adopts the continuum shell model with single director to describe the mechanical behaviors of graphene. In order to consider the intrinsic features of the graphene honeycomb lattice—chiral index (n,m), the chiral-tube vectors of graphene in real space have been used for construction of reference unit base vectors of the shellmodel; therefore, the formulations will contain the chiral index automatically, or in an explicit form in physical components. The results are quite useful for future studies of graphene mechanics.