CONNECTION BETWEEN THE CONDUCTIVITY AND BULK MODULUS OF ISOTROPIC COMPOSITE-MATERIALS

Rigorous cross-property bounds that connect the effective electrical c onductivity sigma and the effective bulk modulus kappa* of any isotro pic two-phase composite are derived when the volume fractions of the p hases are either specified or unknown. These bounds enclose lens-shape d regions in the sigma-kappa* plane, portions of which are attainable by certain microgeometries and thus are optimal. Our cross-property b ounds apply also to anisotropic composites with cubic symmetry. The bo unds are applied to some general situations, as well as to specific mi crogeometries, including regular and random arrays of spheres and hier archical geometries corresponding to effective-medium theories. It is shown that knowledge of the effective conductivity can yield sharp est imates of the effective bulk modulus (and vice versa), even in cases w here there is a wide disparity in the phase properties.