A new class of extremal composites

The paper presents a new class of two-phase isotropic composites with extre mal bulk modulus. The new class consists of micro geometrics for which exac t solutions can be proven and their bulk moduli are shown to coincide with the Hashin-Shtrikman bounds. The results hold for two and three dimensions and for both well- and non-well-ordered isotropic constituent phases. The n ew class of composites constitutes an alternative to the three previously k nown extremal composite classes: finite rank laminates, composite sphere as semblages and Vigdergauz microstructures. An isotropic honeycomb-like hexag onal microstructure belonging to the new class of composites has maximum bu lk modulus and lower shear modulus than any previously known composite. Inspiration for the new composite class comes from a numerical topology des ign procedure which solves the inverse homogenization problem of distributi ng two isotropic material phases in a periodic isotropic material structure such that the effective properties are extremized. (C) 2000 Elsevier Scien ce Ltd. All rights reserved.