A note on the homogenization of incommensurate thin films

Dimension-reduction homogenization results for thin films have been obtained under hypotheses of periodicity or almost periodicity of the energies in the directions of the mid-plane of the film. In this note, we consider thin films, obtained as sections of a periodic medium with a mid-plane that may be incommensurate, that is, not containing periods other than 0. A geometric almost periodicity argument similar to the cut-and-project argument used for quasicrystals allows to prove a general homogenization result.