Effective-medium approximation for composite media: Realizable single-scale dispersions

It is known that the popular effective medium approximation (EMA) for the e ffective conductivity sigma (e) of a composite is exactly realizable by cer tain multiscale hierarchical microstructures. We have found a class of peri odic, single-scale dispersions that achieve the EMA function at a given pha se conductivity ratio for a two-phase, two-dimensional composite over all v olume fractions. Moreover, to an excellent approximation (but not exactly), the same structures realize the EMA for almost the entire range of phase c onductivities and volume fractions. The inclusion shapes are given analytic ally by the generalized hypocycloid, which in general has a nonsmooth inter face. To find these structures, we utilized target optimization techniques and a theorem concerning the spectral function. (C) 2001 American Institute of Physics.