For linearly elastic heterogeneous solids, averaging theorems are developed by Nemat-Nasser and Hori (S. Nemat-Nasser, M. Hori, Micromechanics: Overall Properties of Heterogeneous Solids, Elsevier, Amsterdam, 1993; and S. Nemat-Nasser, M. Hori, J. Eng. Mater. Technol. 117 (1995) 412), using a multi-inclusion model. This model is based on the observation that the average strain and stress in any...