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.

翻译：通过采用等效包含法（一种与Hashin-Shtrikman变分原理密切相关的方法）作为替代模型，我们提出了一种随机复合材料的数值同质化方差缩减策略。这些复合材料由嵌入在均匀基质中的包含物组成（或称非均质物）。在二维线性电导率的框架下，我们证明了此策略的效率，即使在高对比度值的情况下，与全场模拟相比，也可以获得显著的计算收益。我们还展示了我们的策略允许研究微结构参数对宏观响应的影响。我们的策略可以方便地扩展到三维问题和线性弹性问题。我们特别关注替代模型的计算成本。特别地，我们提出了一个廉价的逼近方法来计算所谓的影响张量（这些张量用于计算替代模型）。