OPTIMUM COMPOSITE-MATERIAL DESIGN

The microstructure identification problem is treated : given certain phases in given volume fractions, how to mir them in a periodic cell so that the effective material constants of the periodic composite lie the closest possible to ce,tain prescribed values ? The problem is studied for the linear conduction equation. It is stated in terms of optimal control theory; the admissible microgeometries are single inclusion ones. Existence of solution is proved under suitable hypotheses, as well as the convergence of numerical approximations. Numerical examples are presented. In the conduction case, the full characterization of the G(0)-closure set (the set of all effective conductivities that result from taking the given phases in the given volume fraction mixed in any feasible microgeometry) is known. One carried out numerical experiments how well can its boundaries be attained using the subclass of single inclusion microgeometries. Results of these experiments are shown as well.