A note on the homogenization of incommensurate thin films

Abstract

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.