Non-classical generalized deformable theory for functionally graded ultra-thin films

A generalized refined theory including surface effects is developed for functionally graded (FGM) ultra-thin films. The classical generalized shear deformable theory is adopted to model the film bulk, while the bulk stresses on the surfaces are required to balance the surface stresses, which are determined according to the linear theory of surface elasticity [1-2]. As a result, a non-classical generalized deformable theory is developed. A simply supported thin film in cylindrical bending is considered as an example to illustrate the application of the present theory. It is established that the shape function and the deflection exhibit significant size-dependence as the film thickness falls below micro-scales (Fig. 1). By comparing to the Kirchhoff plate theory including surface effects [3], the necessity of the present theory for FGM thin films is solidly validated.