Introduction to Homogenization

The aim of this talk is to describe the mathematical theory of homogenization and describe Tartar’s method. This theory has been introduced in order to describe the behavior of composite materials used by the material scientists by a homogenized material. In general, the effective behavior is not the averaged behavior. Theory of homogenization has a reaching applications in many areas (including composite materials) like porous media, analysis of their structures, to name a few. We do not describe these applications in this short presentation but we see how Tartar’s Method uses two scales for the characterization of the material, the microscopic one, describing the heterogeneities, and the macroscopic one, describing the global behavior of the composite. The aim of ’homogenization’ is precisely to give the macroscopic properties of the composite by taking into account the properties of the microscopic structure. For the good understanding of this area one must have a sound knowledge of Distribution Theory, Functional Analysis, Measure Theory and of course Differential Equations.