Discrete-Continuous and Continuous-Moment Models of Graphene under In-Plane Deformation

Abstract

A model of in-plane graphene deformation is developed by considering a linear chain of atoms with regard to the independent moment interaction and noncentral force interaction between atoms. A discrete and continuous beam models of the linear chain of atoms are constructed. Assuming that each graphene atom interacts only with its nearest neighbors, the atomic system is replaced by a beam system using the obtained continuous beam model of the linear atomic chain. A discrete-continuous and continuous models of graphene are derived. The first one is a special molecular dynamics model, and the second is a plane stress model of the moment theory of elasticity with independent displacement and rotation fields. The elastic constants of the second model are determined through the atomic structure parameters of graphene. It is shown that the problems of in-plane graphene deformation can be solved using both the discrete-continuous model (beam system model) and the continuous model as the plane stress model of the moment theory of elasticity with independent displacement and rotation fields with known elastic constants.