基体-夹杂复合材料的代表性体积元--系综周期化的计算研究
Representative volume elements for matrix-inclusion composites -- a computational study on periodizing the ensemble
摘要：
我们调查体积元素采样策略的随机均匀化的颗粒增强复合材料，并显示，通过计算实验，一个不适当的处理粒子相交的计算单元的边界可能会影响计算的有效属性的准确性。最近的结果周期性合奏的系统误差的收敛速度优越的合奏相比，以快照的启发，我们进行计算实验的微结构与圆形，球形和圆柱形夹杂物和监测系统误差的合奏快照的有效热导率相比，工作与微结构采样周期性合奏。我们观察到，从周期性的合奏采样的微观结构上计算的表观性质的标准偏差衰减在从中心极限定理预期的缩放。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速率。后一种效应是由附加的长程相关性引起的，这些长程相关性必然出现在颗粒增强复合材料中的高的、工业相关的体积分数。然而，定期合奏，似乎不太受这些相关性。我们的研究结果提供了指导方针，与数字体积图像的材料微观结构和设计的代表性体积元素计算均匀化。
英文摘要：
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.
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