Prediction of the biaxial buckling and vibration behavior of graphene via a nonlocal atomistic-based plate theory

The present article is concerned with the applicability of an elastic plate theory incorporating the interatomic potentials for biaxial buckling and vibration analysis of single-layer graphene sheets (SLGSs) and accounting for the small scale effects. For this purpose, the relations based on the interatomic potential and Eringen’s nonlocal equation are incorporated into the classical plate theory. The former relations are obtained through constructing a linkage between the strain energy induced in the continuum and the potential energy stored in the atomic bonds using the Cauchy–Born rule. The nonlocal governing equations of motion for buckling and vibration of the SLGSs with simply-supported boundary conditions are exactly solved and explicit formulae for the frequencies and critical buckling load are derived. The results generated from the present model are compared with those of molecular dynamic (MD) simulations and the other previously reported ones and a good agreement is achieved. The model developed herein is independent of Young’s modulus which is of an ambiguous definition in the literature. It is found that the small scale effect on buckling and vibrational response of the SLGSs is profound and it becomes more prominent when the side length is low.