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Using the equivalent inclusion method (a method strongly related to theHashin-Shtrikman variational principle) as a surrogate model, we propose avariance reduction strategy for the numerical homogenization of randomcomposites made of inclusions (or rather inhomogeneities) embedded in ahomogeneous matrix. The efficiency of this strategy is demonstrated within theframework of two-dimensional, linear conductivity. Significant computationalgains vs full-field simulations are obtained even for high contrast values. Wealso show that our strategy allows to investigate the influence of parametersof the microstructure on the macroscopic response. Our strategy readily extendsto three-dimensional problems and to linear elasticity. Attention is paid tothe computational cost of the surrogate model. In particular, an inexpensiveapproximation of the so-called influence tensors (that are used to compute thesurrogate model) is proposed.

A variance reduction strategy for numerical random homogenization based on the equivalent inclusion method