The Method of Homogenization

Abstract

It is common in engineering and scientific problems to have to deal with materials formed from multiple constituents. Examples include laminated plates, fiber reinforced composites, fluid-filled porous solids, and bubbly fluids. Solving a mathematical problem that includes such variations in the structure can be very difficult. It is therefore natural to try to find simpler equations that effectively smooth out whatever substructure variations there may be. An example of this situation occurs when describing the motion of a fluid or solid. One usually does not consider them as composites of discrete interacting molecules. Instead, one uses a continuum approximation that assumes the material to be continuously distributed. Using this approximation, material parameters, such as the mass density, are assumed to represent an average.