Based on a new molecular structural mechanics model, the effective in-plane mechanical properties of monolayer graphene sheet is analytically analyzed in this paper. The energy equivalence between the basic cell of the atomic structure of graphene and the corresponding basic cell, defined in the homogenization of periodic cellular media, of its equivalent periodic framed structure is used to determine the mechanical properties of the equivalent structural members representing the C-C bonds of graphene. The resulting relationship between the mechanical parameters of the equivalent structural members and the force constants defined in molecular mechanics are different from those used in other molecular structural mechanics models. And these mechanical parameters yield more accurate effective mechanical properties of graphene, especially the Poisson ratio, than the existing molecular structural mechanics models.

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.