IMPROVED BOUNDS ON THE CONDUCTIVITY OF COMPOSITES BY INTERPOLATION

Different bounds on the conductivity of a composite material may impro ve on each other in different conductivity regimes. If so, the questio n arises of how to efficiently interpolate between the bounds. In this paper I show how to do an interpolation with a two-point Pade approxi mation method. For bounds on two-component composites the interpolatio n method is shown to be, in a sense, the best possible. The method is discussed in the context of equiaxed polycrystals where the classic Ha shin-Shtrikman bounds and the more recent null-lagrangian bounds, part ly improve on each other. Denoting the principal conductivities of the crystallite sigma(1) less than or equal to sigma(2) less than or equa l to sigma(3), the method gives;improved lower bounds for equiaxed pol ycrystals which have sigma(2)(0.77 sigma(1) + 0.23 sigma(3)) greater t han or equal to sigma(1) sigma(3). The method also gives improved uppe r bounds.