Explicit limits for nonperiodic homogenization and reduction of dimension

The aim of this Note is to give explicit limit expressions, for diffusion equations involving a small parameter ε, describing both nonperiodic homogenization and reduction of dimension. We consider two kinds of reduction of dimension: the case of plates and the case of thin cylinders. In particular, we give the limit diffusion equation for stratified plates. This is completely explicit and requires no special assumption, except stratification. In the case of thin cylinders, the formulae are less explicit, but we also indicate some simple applications to fibered materials. To cite this article: B. Gustafsson, J. Mossino, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 977–982.