Effective elastic properties of suspensions of radially symmetric particles

In this work we study the exact solution to the single-inclusion problem in elastostatics for inclusions which have a spherically symmetric elastic profile. We present a systematic scheme by which the so-called intrinsic moduli, which determine the response of a particle to an external field, can be calculated. For that purpose a transfer-matrix method is developed, which enables us to express the intrinsic moduli of the particle in terms of the moduli of its constituent layers. This method works in both two and three dimensions. In the case of two layers the results of the generalised self-consistent scheme of Christensen and Lo could be easily rederived. The calculated intrinsic moduli can be substituted in previously derived mean-field expressions, thus providing us with expressions for the effective elastic moduli of suspensions of layered spheres (or circles).