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.
翻译:我们调查了粒子合成合成材料同质同质化的体积抽样战略,并通过计算实验表明,不适当地处理粒子交叉计算细胞边界的粒子可能影响计算有效特性的准确性。我们受到最近的结果的推动,即相对于采集聚合物的相片而言,周期性集合的系统误差的高度趋同率比采集粒子合成合成合成物的相近率高,我们进行微结构的计算实验,以循环、球体和圆柱体融合为对象,并监测与从周期性集合中抽取的微结构相比,对聚合物的切片的有效热传导率的系统错误。我们观察到,在从周期性集合中抽取的显微结构中计算出的显性特性与预期从中央限制值中采集的衰减率相比,标准偏差表明,在高填充物含量时,光团的衰减率较低。后一种影响是由于在高度、工业性组合体的微集成像中出现的其他长期关联性关系,而在高度、工业性混合的微粒合成合成中出现。我们这些设计成型的成型的成型的成型的成型的成型的成型图则会影响较小。