HETEROGENEOUS MEDIUM - IS AN EQUIVALENT MACROSCOPIC DESCRIPTION POSSIBLE

The aim of this paper is to answer the question: considering a finely heterogeneous medium submitted to some excitation, does an equivalent macroscopic description exist? An equivalent macroscopic description means here an intrinsic description, independent of the macroscopic boundary conditions. It is well known that the condition residues in a good separation of scales. This separation concerns both the structure of the medium and the excitation itself. The homogenization process using double scale asymptotic developments appears then to be the appropriate method giving the right answer to the question. This is emphasized in two simple examples.