Extremal structures of multiphase heat conducting composites

this paper we construct microstructures of multiphase composites with unusual properties : their heat conductivity in one direction is equal to the harmonic or arithmetic mean of the phases’ heat conductivities and the conductivity in an orthogonal direction does not equal either arithmetic or harmonic mean. Two-dimensional three-phase structures are studied, but the results can be easily generalized for the three-dimensional composites with arbitrary number of phases. Copyright 0 1996 Elsevier Science Ltd.