Size-dependent response of ultra-thin films with surface effects

A modified continuum model of elastic films with nano-scale thickness is proposed by incorporating surface elasticity into the conventional nonlinear Von Karman plate theory. By using Hamilton’s principle, the governing equations and boundary conditions of the ultra-thin film including surface effects are derived within the Kirchhoff’s assumption, where the effects of non-zero normal stress and large deflection are taken into account simultaneously. The present model is then applied to studying the bending, buckling and free vibration of simply supported micro/nano-scale thin films in-plane strains and explicit exact solutions can be obtained for these three cases. The size-dependent mechanical behavior of the thin film due to surface effects is well elucidated in the obtained solutions.