Nano-indentation of circular graphene flakes

Nano-indentation of circular graphene flakes are studied by using Molecular Dynamics simulation. We show that the theory of continuum elasticity based on nonlinear F\"{o}pple-Hencky equations is applicable on a circular suspended graphene flake. Our simulation results are plenty compatible to those results calculated by the nonlinear elasticity theory. We find the force-displacement curves in good agreement with the recent experimental measurements and conclude they are temperature independent. In addition, we find the vibration frequency for such a system and monitor that it behaves as a sinusoidal manner at small circular graphene size.