Perturbation analysis of a wavy film in a multi-layered structure

A free surface in a multi-layer can experience an undulation due to surface diffusion during fabrication or etching process. In order to analyze the undulation, the elasticity solution for the undulating film is needed. Considering the undulation as a perturbation of a flat surface, a boundary value problem for 2D elasticity is formulated. The solution procedure is straightforward, but very lengthy especially for a multi-layer.

The solution for plane strain condition can be easily converted into the solution for equi-biaxial stress condition. So our solution may be useful for those who deal with equi-biaxial stress condition.

Please find the attached files. These are two Maple worksheets.(After downloading the files, please change the file extension from doc to mws). The first Maple worksheet(perturbation_2layer_post.mws) is for a wavy film on a substrate with a finite thickness, and shows an explicit formula for strain energy change due to undulation. The other Maple worksheet(perturbation_N_layer_post.mws) is for a wavy film in a multi-layered structure with an arbitrary number of layers.

My Maple is version 10, but I guess that the files can be executable in a lower version Maple. Any comments are welcomed.