USING QUASI-CONVEX FUNCTIONALS TO BOUND THE EFFECTIVE CONDUCTIVITY OFCOMPOSITE-MATERIALS

In this paper we establish bounds constraining the effective conductiv ity tensor of composites made of an arbitrary number n of possibly ani sotropic phases in prescribed volume fractions. The bounds are valid i n any spatial dimension d greater-than-or-equal-to 2. The bounds have a very simple and concise form and include those previously obtained b y Hashin and Shtrikman, Murat and Tartar, Lurie and Cherkaev, Kohn and Milton, Avellaneda, Cherkaev, Lurie and Milton and Dell'Antonio and N esi.