The Elastic and Thermo-elastic Properties of Composite Media

In a continuation of a previous paper, it is shown here how the gross bulk and shear moduli of a composite material consisting of a suspension of grains or a compact of grains may be deduced. The grains are assumed to be perfectly bonded to the suspending medium or to each other, and are taken to be spheres in the mean. By using an averaging procedure due to Bruggeman, and analysing the effect of a uniform hydrostatic compression and of a uniform tension on an average grain, a pair of de-coupled equations for the gross moduli is found for suspensions. When the suspending medium vanishes and the grains are packed, these equations become coupled and there is exhibited a discontinuity in the gross moduli. The bulk coefficients of linear expansion of the two kinds of composites are found from an analysis of the dilatation and bulk stress for average spherical grains when the composite as a whole is subjected to some small temperature change. All results are free of any limitation on the number of components.