Bending of multilayer nanomembranes

Governing equations are developed for bending of an elastic circular membrane under in-plane tension (prestress) and out-of-plane uniform pressure or concentrated force. These relations are applied to fitting observations on nanomembranes made of CVD-grown and mechanically exfoliated graphene, graphene oxides with various concentrations of defects, molybdenum disulfide, bismuth selenite, and tungsten diselenide. Good agreement is demonstrated between the experimental data and results of simulation. It is shown that the elastic modulus per layer of a multilayer membrane is independent of the number of layers n, whereas the prestress grows exponentially with n. Simple equations are suggested to describe the effect of defects in the crystalline structure of a nanomembrane on its mechanical properties. These equations and validated by comparison of the model predictions with observations of graphene oxide.