If it is desired to model a material by assuming different shapes for the inclusions and host materials, the Mori-Tanaka and Kuster-Toksöz schemes may be used. Again considering the data of Walsh et al. (1965) for glass foam, suppose that one reasonable model would be spherical glass particles and needle shaped voids. The result of such a calculation is presented in Figure 3. The agreement is somewhat better than that for the spherical inclusions model, although the correspondence between this model and the physical composite seems unclear. In fact, this should be a better model for the sintered glass beads, than for the foam. It seems therefore that a more physically realistic model of the glass foam should be just the opposite: spherical voids and needle shaped glass inclusions. However, when I do this computation for MT and KT, I find that the results in both cases are identical to the results for spherical voids and spherical glass inclusions illustrated in Figure 1 and therefore this model gives no improvement in the estimates. I consider this to be a failure of these theories, because it shows they are not flexible enough to capture differences in the microgeometry of the host. For comparison, I also show in Figure 3 the result obtained using the SC theory assuming needle shaped glass and spherical voids. Although the voids are indeed approximately spherical in the glass foam, it seems that needles should be a poor approximation of the actual glass structure until very high porosities are achieved. This intuition seems to be borne out by the results obtained, which underestimate the strength of the foam at intermediate values of porosity but have the right trend overall.
Considering the data of Berge et al. (1993) again, a reasonable model of a finite permeability granular sample is this: spherical grains and needle shaped voids. This result computed using the SC theory is also plotted in Figure 2. The agreement with the data is comparable to that achieved by the theory assuming spherical grains and spherical voids.