Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.