Extraction of structural information from measured transport properties of composites

We describe clearly Milton's bounds on the scalar transport properties of composite materials in the case when no geometrical information is known about the composite, but when a set of measured values of a transport property is available. We consider how the measured values may be used when they are subject to known errors. In this case, a statistical analysis is employed. We illustrate the various conclusions which may result from this analysis by considering six cases involving both two-and three-dimensional composites. In four of the six cases, estimates of the volume fraction of the composite in agreement with the known value are obtained. In the fifth case, the analysis pointed out a possible error in the experimental data, while in the sixth it revealed a critical dependence of transport properties on composite geometry due to filamentary linking between particles.