Characterization of mechanical properties of graphene nanoplates with vacancy defects using AFEM

The present work has studied the impact of atomic vacancy defects with different distributions on the elastic properties of various sizes of single-layer and double-layer graphene nanoplates. To maintain the discrete nature of nanoplates, they were equivalentized with space frame structures, and then the atomic finite element method (AFEM) was used to predict the mechanical properties and behavior. To verify the methodology, numerical results in the field of elastic properties were validated with the results reported in the open literature. The simulation results showed that the elastic properties in small-size nanoplates depend on the direction, but this dependence decreases with increasing the size and approaches isotropy gradually. Furthermore, it was observed that defects occurring at the atomic scale greatly affect the elastic properties. It was found that the type of defects distribution affects the effective properties of graphene; however, according to the numerical results, this dependence weakens as the nanoplate size increases. Overall, the presence of atomic vacancies leads to a reduction in the elastic stiffness coefficients and an increase in the Poisson's ratios; though, as the nanoplate size increases, the impact of the defects decreases. On the other hand, it was found that the impact of defects in double-layer nanoplates is less than that in single-layer ones. For instance, Young's modulus and shear modulus for a 10% distribution of defects, regardless of the nanoplate size, are reduced by about 60% and 63% for a single-layer and about 50% and 53% for a double-layer, respectively.