Elastic buckling of single-layered graphene sheet

The elastic buckling behavior of defect-free single-layered graphene sheet (SLGS) is investigated using an atomistic modeling approach. In this regard, the molecular structural mechanics that is comprised of equivalent structural beams is employed. The elastic buckling forces of the cantilever and bridge zigzag and armchair SLGSs with different side lengths and aspect ratios are calculated. It is discerned that the elastic buckling force per unit width of the SLGS changes nonlinearly with respect to the side length while it is insensitive to the aspect ratio. In addition, the elastic buckling force of the zigzag sheet is larger than that of the armchair sheet with equivalent geometrical parameters. The atomistic simulation results are also used to develop predictive equations via a statistical nonlinear regression model. The proposed equations can estimate the elastic buckling force of the SLGS within 5 percent difference with the molecular structural mechanics method.