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.

11/17/1997