Electrothermics

5.6. Homogenization techniques

Calculating the temperature distribution in a composite material requires solving simultaneous thermal and electromagnetic equations. Homogenization techniques must be applied to both these equations to determine the equivalent physical properties of the material.

There exist a large number of homogenization techniques. Three of them are discussed in this chapter.

The first method, based on an iterative method, uses the technique of the inverse problem. This method consists of seeking the equivalent properties that would give the results closest to the true results. This method is applicable to all periodic or aperiodic structures. In the latter case, it requires a global solution to the full system, which decreases its efficiency. Nevertheless, it becomes interesting when the composite material to study includes repetitive subsystems [TRI 98a].

The second method, based on the spatial filtering of quick fields, replaces the solution to the global problem by the solution at the level of an elementary cell. This method, called dynamic homogenization, is applicable to structures with periodic motifs with identical elementary cells. This is the case for composites with woven structures, for example, or UD structures (if the fibers are perfectly parallel and regularly placed) [TRI 00a, ELF 96a, ELF 96b, ELF 96c].

The third method, based on the law of large numbers, replaces the solution to the global problem by a solution at the level of a representative ...