Development of efficient size-dependent plate models for axial buckling of single-layered graphene nanosheets using molecular dynamics simulation

In the current paper, axial buckling characteristics of nanoscaled single-layered graphene sheets (SLGSs) are investigated on the basis of Eringen's nonlocal elasticity continuum and different plate theories namely as classical plate theory and first-order shear deformation theory. Through implementing of the nonlocal equations into the different types of plate theory, nonlocal plate models are developed to consider the small-scale effects in the axial buckling analysis of SLGSs. Generalized differential quadrature method is utilized to discretize the governing differential equations of the nonlocal elastic plate models along simply-supported and clamped boundary conditions. Afterward, molecular dynamics (MD) simulations are performed for a series of SLGS with various values of side-length and chiralities, the results of which are matched with those of nonlocal plate models to extract the appropriate values of nonlocal parameter. It is found that among the type of boundary conditions, chirality, and nonlocal plate theory, boundary conditions have the most significant influence on the recommended values of nonlocal parameter to predict the axial buckling behavior of SLGSs.