A mode-independent method to predict graphene buckling on non-developable surfaces

Graphene sheets are usually supported by substrates to achieve stable morphology in practical applications. However, substrates are always bumpy with non-developable surfaces rather than perfectly flat. In this study, the morphology of graphene on non-developable convex and concave surfaces is investigated both theoretically and numerically. It turns out that the graphene could fully conforms, wrinkles or spans over on the surfaces depending on the geometrical scale of the graphene and the convex/concave surfaces. Furthermore, using a mode-independent fast method, a unified buckling criterion is established for morphology prediction of graphene on different substrates and under arbitrary in-plane loads.