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Continuum elastic modeling of graphene resonators

Starting from an atomistic approach we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated. We find that already for deflections of the order of 0.5Å a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes.