Effects of size and atomic defects on the buckling of single-layer and double-layer graphene nanoplates using AFEM

This study investigates the effect of single atomic vacancy defects with different random distributions on the buckling behavior of single- and double-layer graphene nanoplates. A parametric analysis was conducted to assess the influence of nanoplate dimensions, aspect ratio, defect concentration, number of layers, and boundary conditions on the critical buckling load ($${P}_{cr}$$). To capture the discrete nature of graphene, the nanoplates were modeled using a space frame approach, where covalent bonds between carbon atoms were represented as beam elements and interlayer van der Waals forces were simulated using linear elastic springs. The atomic positions were generated using MATLAB and imported into ANSYS, where neighboring atoms were connected based on an energy-equivalent mapping between interatomic and elastic beam energies. Springs were added between atoms located within a defined cutoff distance to represent long-range interlayer interactions. A linear finite element buckling analysis was performed by solving an eigenvalue problem using beam and spring elements with linear elastic behavior. Model validation was achieved by comparing simulation results to data available in the literature. The results show that vacancy defects significantly reduce $${P}_{cr}$$—up to 40% at 10% defect concentration. Furthermore, three distinct distributions of defects were examined for each concentration to explore spatial effects on buckling resistance.