We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.

中文翻译：

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随机复合材料断裂过程区和代表性子空间的统计提取

我们建议通过量身定制的统计工具来识别异质材料中的工艺区域。过程区被重新定义为结构的一部分，其中随机过程不能在低维确定性空间中正确近似。这种低维空间是通过对预先计算的溶液样本进行的光谱分析获得的。提出了一种贪心算法来识别互补区域中解的过程区域和低维代表子空间。除了本文提出的用于分析局部现象的工具的新颖性外，我们还表明，该方法生成的约简空间是构建降阶模型的有效基础。