Consider a finite domain of a multiphase film, if we extract an infinitesimal volume and presume it to be the smallest repeating unit cell of the entire film, then an representative volume element (RVE) of the film is constructed. The most important assumption when constructing an RVE of a heterogeneous system is that the under applied far-field deformation, the RVE and far-field continuum must have equivalent quantities of fields of interest that are averaged over the volume of the RVE. The average stress field from the RVE corresponding to a loading deformation is treated as being homogeneous to reflect the macroscopic stress to be found in the entire film. In this talk, I will touch base on the theoretical foundation of the RVE elasticity homogenization of heterogeneous system. An iterative solution based on the Augmented Lagrangian algorithm via the use of Fast Fourier Transform will be presented as well.