Abstract

In two dimensions there are optimal bounds for the effective conductivity of arbitrary mixtures of two heat conducting materials: one isotropic and the other anisotropic; used in fixed volume fractions and allowing for rotations. Some of those bounds involve a rank-two lamination, but others involve a microstructure of coated disks. We create a region of laminates of rank at most three, which gives a very good approximation of the optimal bound if the starting material has a moderate degree of anisotropy. We also study the stability under homogenization of this region, meaning that whenever one homogenizes a mixture of two materials belonging to it, the effective diffusion tensor also belongs to this region. This is done to show that the region we create cannot be easily enlarged. © 2003 Elsevier Ltd. All rights reserved.