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The correlation between statistical descriptors of heterogeneous materials
Computer Methods in Applied Mechanics and Engineering, Volume: 384, Start page: 113948
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Heterogeneous materials such as rocks and composites are comprised of multiple material phases of different sizes and shapes that are randomly distributed through the medium. The random microstructure is typically described by using various statistical descriptors, which include volume fraction, two...
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Heterogeneous materials such as rocks and composites are comprised of multiple material phases of different sizes and shapes that are randomly distributed through the medium. The random microstructure is typically described by using various statistical descriptors, which include volume fraction, two-point correlation function, and tortuosity, to name a few. Capturing different morphological features, a large number of statistical descriptors are proposed in different research fields, such as material science, geoscience and computational engineering. It is well known that these statistical descriptors are not independent from each other, but until recently it remains unclear what descriptors are more similar or more different. In particular, it is extremely difficult to look for quantified relations between various descriptors, since they are often defined in very different formats. The lack of quantified understanding of descriptors’ relations can cause uncertainties or even systematic errors in heterogeneous materials studies. To address this issue, we propose a novel and generic correlation analysis strategy and establish, for the first time, the quantified relations between various statistical descriptors for heterogeneous materials. Based on data science techniques, our approach consists of three operational steps: data regularization, dimension reduction and correlation analysis. A total of 41 statistical descriptors are collected and analysed in this study, which is readily extensible to include other new descriptors. The generic and quantified correlation results are compared with other established descriptor relations that are obtained from analytical analysis or physical intuition, and good agreements are observed in all cases. The quantified relations between various descriptors are summarized in a single correlation graph, which provides useful guiding information for the characterization, reconstruction and property prediction of heterogeneous materials.
Heterogeneous material, Random media, Morphology, Characterization, Reconstruction, Property prediction
College of Engineering