On the reduced parameter dependence of the Mori–Tanaka theory

In this paper we study the effective elastic moduli of composite materials and explore the possibility of reducing the number of independent variables. More specifically we consider the results for the effective planar elastic moduli of composites containing circular inclusions. We assume that the interface between the matrix and inclusions is either perfectly bonded or is allowed to slip, and we employ the Mori–Tanaka theory (T. Mori, K. Tanaka, Acta Metall. 21 (1973) 571; Y. Benveniste, Mech. Mater. 6 (1987) 147) to account for inclusions’ interaction. In the analysis we use a recent result in plane elasticity due to Cherkaev et al. (A. Cherkaev, K. Lurie, G.W. Milton, Proc. R. Soc. A 438 (1992) 519) and Dundurs constants (J. Dundurs, J. Comp. Mater. 1 (1967) 310; J. Dundurs, J. Appl. Mech. 36 (1969) 650).