Existence criteria and validity of plate models for graphene-like materials

Graphene-like (GL) materials have enriched the application prospects of two-dimensional materials by virtue of their various structures and properties. However, the following theoretical issues remain unsolved: how can stable GL materials exist and is plate idealization valid for any GL materials? Here we answer these questions based on an atomistic potential-based approach. The existence criteria for GL materials with three common structures, including planar honeycomb (PH), buckled honeycomb (BH), and honeycomb MX2 (2H-MX2) structures, were established. Moreover, the validity of classic linear-elastic plate models for these materials was examined. A validity factor, which represents the validity of using thin plate models to investigate the overall mechanical response of GL sheets, was defined. We determined that 2H-MX2 sheets can approximately be modeled as thin plates for arbitrary loadings, unlike PH and BH sheets.