We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper treatment of particles intersecting the boundary of the computational cell may affect the accuracy of the computed effective properties. Motivated by recent results on a superior convergence rate of the systematic error for periodized ensembles compared to taking snapshots of ensembles, we conduct computational experiments for microstructures with circular, spherical and cylindrical inclusions and monitor the systematic errors in the effective thermal conductivity for snapshots of ensembles compared to working with microstructures sampled from periodized ensembles.

We observe that the standard deviation of the apparent properties computed on microstructures sampled from the periodized ensembles decays at the scaling expected from the central limit theorem. In contrast, the standard deviation for the snapshot ensembles shows an inferior decay rate at high filler content. The latter effect is caused by additional long-range correlations that necessarily appear in particle-reinforced composites at high, industrially relevant, volume fractions. Periodized ensembles, however, appear to be less affected by these correlations.

Our findings provide guidelines for working with digital volume images of material microstructures and the design of representative volume elements for computational homogenization.

我们研究了用于粒子增强复合材料随机均匀化的体积元采样策略，并通过计算实验表明，对与计算单元边界相交的粒子的不当处理可能会影响计算有效属性的准确性。受近期结果的启发，与拍摄集合快照相比，周期性集合的系统误差具有更高的收敛速度，我们对具有圆形、球形和圆柱形夹杂物的微观结构进行了计算实验，并监测了集合快照的有效热导率的系统误差与使用从周期性集合中采样的微观结构相比。

我们观察到，在从周期性集合采样的微结构上计算的表观特性的标准偏差以中心极限定理预期的比例衰减。相比之下，快照集合的标准偏差在高填料含量下显示出较差的衰减率。后一种效应是由额外的长程相关性引起的，这些相关性必然出现在具有高工业相关体积分数的颗粒增强复合材料中。然而，周期集合似乎受这些相关性的影响较小。

我们的发现为处理材料微观结构的数字体积图像和用于计算均质化的代表性体积元素的设计提供了指导。