Buckling instability of circular double-layered graphene sheets

In this paper, we study the buckling properties of circular double-layered graphene sheets (DLGSs), using plate theory. The two graphene layers are modeled as two individual sheets whose interactions are determined by the Lennard-Jones potential of the carbon-carbon bond. An analytical solution of coupled governing equations is proposed for predicting the buckling properties of circular DLGSs. Using the present theoretical approach, the influences of boundary conditions, plate sizes, and buckling-mode shapes on the buckling behaviors are investigated in detail. The buckling stability is significantly affected by the buckling-mode shapes. As a result of van der Waals interactions, the buckling stress of circular DLGSs is much larger for the anti-phase mode than for the in-phase mode.