J. Helsing, IMPROVED BOUNDS ON THE CONDUCTIVITY OF COMPOSITES BY INTERPOLATION, Proceedings - Royal Society. Mathematical and physical sciences, 444(1921), 1994, pp. 363-374
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.