# The Method of Homogenization

• Mark H. Holmes
Chapter
Part of the Texts in Applied Mathematics book series (TAM, volume 20)

## Abstract

It is common in engineering and scientific problems to have to deal with materials that are formed from multiple constituents. Some examples are shown in Fig. 5.1 and include laminated wood, a fluid-filled porous solid, an emulsion, and a fiber-reinforced composite. 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.

## Keywords

Homogenize Equation Period Cell Homogenization Procedure Cell Problem Multidimensional Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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