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The numerical characterisation of microstructures is of paramount interest in a wide range of applications, such as battery manufacturing, which relates to porous materials. Extracting reliable and relevant features that accurately describe the multi-scale morphology of materials is a delicate task. Tortuosity [1], a multifaceted concept, is one of the key structural characteristics of materials in the broadest sense. Indeed, this concept is considered in materials analysis, as well as in the characterisation of live cells. In this study, tortuosity is defined as the ratio of geodesic to Euclidean distance, providing a morphological depiction of microstructures [2].
Despite this concept playing a central role in numerous applications, numerical methodologies that aim to quantify it continue to focus on scalar descriptions, which limits our understanding of how materials behave [3]. More specifically, the underlying assumptions of state-of-the-art algorithms do not reflect the complexity of real materials, particularly with regard to heterogeneity. To overcome this limitation, a stochastic approach is proposed [4, 5]. Furthermore, the definition is extended to grayscale scenarios by leveraging the versatility of the geodesic distance transform. This paves the way for further improvements in the structural characterisation of heterogeneous microstructures. Finally, these developments are combined to propose an extension to M-tortuosity: a manifold definition of tortuosity.
This extension of the original M-tortuosity enables the analysis of non-segmented images of real materials and binary microstructures enriched with local feature maps, such as those quantifying local narrowness and constrictivity [6]. M-tortuosity is compared to state-of-the-art methodologies, and its efficiency is demonstrated by applying it to random models that are traditionally utilised to simulate complex materials (see Fig. 1). The synthetic microstructures that serve as examples of applications are those that are considered to simulate alumina catalysts or fuel cell components [7]. This innovative solution is accessible via an easy-to-use plug-in for free software called Plug-in!.
[1] Clennell, M. B. (1997). Geological Society, London, Special Publications
[2] Peyrega C et al. (2011). Advanced Engineering Materials
[3] Chaniot J et al. (2024). Science and Technology for Energy Transition
[4] Chaniot J et al. (2019). Image Analysis & Stereology
[5] Chaniot J et al. (2020). Image Analysis & Stereology
[6] Chaniot J et al. (2022). Computational Material Science
[7] Batista A.T.F., […] Chaniot J et al. (2020). ACS Catalysis
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