Equivalent Mechanical Properties of Graphene Predicted by an Improved Molecular Structural Mechanics Model

Abstract

Based on molecular mechanics and the stick-spiral model, this paper first presents the analytical analysis of the effective in-plane mechanical properties of both zigzag and armchair monolayer graphene sheets. We find that the equivalent in-plane elastic constants of monolayer graphene sheets are the same in the two principal directions of graphene. The effective in-plane mechanical properties of graphene are then evaluated numerically using an improved molecular structural mechanics (MSM) model, in which the flexible connections are used to characterize the bond angle variations of graphene. Furthermore, the effective bending rigidity of the beam representing a C-C bond in this improved MSM model is determined from the energy equivalence over the basic cell of graphene and the force constants given by molecular mechanics. A rigidly connected frame model with the bending stiffness of the equivalent beams for C-C bonds different from the existing structural mechanics model is also used to evaluate the mechanical properties of graphene. The flexibly connected frame model gives very good results of Youngs modulus and Poisson ratio of monolayer graphene sheet. The new rigidly connected frame model presented here also gives improved results than the existing rigidly connected frame model of graphene.