Hashin-Shtrikman bounds on the shear modulus of a nanocomposite with spherical inclusions and interface effects

The recently developed variational framework for polarization methods in nanocomposites is applied to the determination of a lower-bound on the shear modulus of a nanocomposite with monosized, spherical inclusions. This bound explicitly accounts for linear elastic effects in the matrix-inclusion interface. Even if the polarization fields involved in its derivation are much more intricate, this bound is closely related to the classical Hashin-Shtrikman bound, with which it coincides when surface stresses are disregarded. More strikingly, when surface stresses are not disregarded, it also coincides with previously established Mori-Tanaka estimates. This result provides firm ground for the practical use of these estimates, for example for design purposes.