Nonlinear Responses of Nanoscale FGM Films Including the Effects of Surface Energies

A nonclassical thin plate theory is developed for the nonlinear elastic behavior of functionally graded films of nanoscaled thickness. The film bulk is modeled using the classical continuum theory of elasticity associated with the Kirchhoff hypothesis and the nonlinear strain of von Karman type. The elastic deformation of surface layers is modeled by the theory of surface elasticity proposed by Gurtin and Murdoch. The governing differential equations and boundary conditions including surface effects are derived based on the principle of minimal potential energy. A functionally graded material strip made of aluminum and silicon, whose effective bulk material properties are predicted using the Mori-Tanaka model with a power-law volume fraction profile, is considered as an illustrative example of application of the present model. It is shown that the size-dependent nonlinear responses vary with the aspect ratio and the volume fraction profile of the constituent material phases.