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：采用等效夹杂法（一种与Hashin-Shtrikman变分原理密切相关的数值方法）作为代理模型，本文提出了一种针对嵌入均匀基质的夹杂（更准确地说是非匀质体）随机复合材料数值均匀化的方差缩减策略。该策略的有效性在二维线性电导率框架下得到验证，即使在高对比度值下，与全场模拟相比仍能获得显著的计算收益。我们进一步表明，该策略可用于研究微观结构参数对宏观响应的影响。该方法可便捷地推广至三维问题及线性弹性领域。我们特别关注了代理模型的计算代价，并提出了一种估算所谓影响张量（用于计算代理模型）的低成本近似方法。