Characterizing microstructures with representative tortuosities

This paper addresses the numerical characterization of microstructures by the concept of tortuosity. After a brief review of geometric tortuosities, some definitions are considered for a benchmarking analysis. The focus is on the M-tortuosity definition, which is revised by expliciting the link to percolation theory, among other things. This operator fits with the analysis of real samples of materials whatever their complexity. A contribution of this paper is a new formulation of the M-tortuosity, making it generic to many situations. Additionally, the comparison of the various tortuosimetric descriptors, state-of-the-art definitions and M-tortuosity, is proposed by considering several scenarios thanks to stochastic multi-scale models of complex materials. The relationships with porosity, morphological heterogeneity and structural anisotropy are investigated. The results highlight the similarities and differences between the descriptors while attesting that the M-tortuosity is equivalent to the state-of-the-art definitions, for a potential use in diffusion and conductivity analyses. Moreover, the M-tortuosity handles correctly situations where state-of-the-art algorithms fail. The anisotropic case highlights some limitations of the state-of-the-art definitions behaving differently according to the given propagation direction. In the case of unknown propagation and irregular piece of materials, the M-tortuosity provides a unique tortuosity value representative of the whole microstructure while detecting the anisotropy. These operators are freely available within the \textit{plug im!} platform.