ABSTRACT
Situations frequently occur where continuous media contain heterogeneities which are very fine compared with their macroscopic dimensions; this can be seen in many areas of physics, for instance composite materials, suspensions or porous media, in electromagnetism transformer laminae or cermet (ceramic-metal mixtures used for converting solar energy). The entire mechanics of continuous media is also an example, the materials being composed of atoms or molecules. But generally the mechanics specialist is not preoccupied with this microscopic structure, the sizes of atoms not being directly observable; it may be otherwise in soil mechanics where, for sand, the grain size makes the medium microstructure perfectly accessible but remaining very fine in relation to the dimensions of the sample being studied. These media display two different structures according to the scale of observation; they may be considered as homogeneous media at macroscopic scale or as heterogeneous media at microscopic scale. Experimental data are generally obtained at a macroscopic level, since the specimens have large dimensions compared with the size of heterogeneities; at the other extreme, the material characteristics are often understood at microscopic scale, and it is often interesting to be able to deduce the macroscopic properties of the material from its microscopic description. It is therefore natural that methods of homogenization have been developed, their purpose being to find a homogeneous material ‘equivalent’ to the finely heterogeneous material.
