  Using the equivalent inclusion method (a method strongly related to the
Hashin-Shtrikman variational principle) as a surrogate model, we propose a
variance reduction strategy for the numerical homogenization of random
composites made of inclusions (or rather inhomogeneities) embedded in a
homogeneous matrix. The efficiency of this strategy is demonstrated within the
framework of two-dimensional, linear conductivity. Significant computational
gains vs full-field simulations are obtained even for high contrast values. We
also show that our strategy allows to investigate the influence of parameters
of the microstructure on the macroscopic response. Our strategy readily extends
to three-dimensional problems and to linear elasticity. Attention is paid to
the computational cost of the surrogate model. In particular, an inexpensive
approximation of the so-called influence tensors (that are used to compute the
surrogate model) is proposed.
