Concerning bounds on the transport and mechanical properties of multicomponent composite materials

The Hashin-Shtrikman and Walpole bounds for the transport properties and bulk modulus of multicomponent composite materials are shown to be attained in a wide range of cases. Thus in these cases the bounds are the best possible bounds that can be given in terms of the properties of the components and the volume fractions. For three-component materials new bounds are conjectured. The conjectured bounds are presumed to apply in the cases where the Hashin-Shtrikman and Walpole bounds are not attained.