Characterization of microstructures using contour tree connectivity for fluid flow analysis

Abstract

Quantifying the connectivity of material microstructures is important for a wide range of applications from filters to biomaterials. Currently, the most used measure of connectivity is the Euler number, which is a topological invariant. Topology alone, however, is not sufficient for most practical purposes. In this study, we use our recently introduced connectivity measure, called the contour tree connectivity (CTC), to study microstructures for flow analysis. CTC is a new structural connectivity measure that is based on contour trees and algebraic graph theory. To test CTC, we generated a dataset composed of 120 samples and six different types of artificial microstructures. We compared CTC against the Euler parameter (EP), the parameter for connected pairs, the nominal opening dimension (d nom ) and the permeabilities estimated using direct pore scale modelling. The results show that d nom is highly correlated with permeability (R 2 ¼ 0.91), but cannot separate the structural differences. The groups are best classified with feature combinations that include CTC. CTC provides new information with a different connectivity interpretation that can be used to analyse and design materials with complex microstructures.

Strain heterogeneity and micro-damage nucleation under tensile stresses in an Mg–5Al–3Ca alloy with an intermetallic skeleton

“…the amount of connecting branches of the network, was quantitatively evaluated using the software Avizo Fire 6 9.5 by means of the Euler number, χ as a topological parameter. [36,38]. This parameter reveals changes in local connectivity in complex network structures.…”

“…Variations in the Euler number indicate a change in local connectivity. More specifically, a decreasing Euler number indicates an increase of local connectivity and vice versa [36,38].…”

Influence of 3D connectivity of rigid phases on damage evolution during tensile deformation of an AlSi12Cu4Ni2 piston alloy

“…networks. While the global interconnectivity of a large 3D network might remain constant, variations in the Euler number indicate local connectivity changes such as loss or formation of connecting branches within a 3D network [28,29]. The Euler number is defined as:…”

Topological Characterization of Fractured Coal

“…The static metrics include Euler characteristic, fractal dimension, and percolation characteristics (Robins et al, ; Sahimi, ; Scher & Zallen, ). Euler number is the most widely accepted connectivity measure, which is a dimensionless number characterizing topology (Aydogan & Hyttinen, ). It has been successfully measured based on digital images for topology study (Armstrong et al, ; Liu et al, ; Schlüter et al, ).…”

“…Topology can be quantified using dynamic and static metrics to characterize the connectivity of porous media (Aydogan & Hyttinen, 2014;Renard & Allard, 2013). The dynamic metrics include physical processes of flow or transport (Renard & Allard, 2013), while static methods do not consider a specific physical process (Aydogan & Hyttinen, 2014). The static metrics include Euler characteristic, fractal dimension, and percolation characteristics (Robins et al, 2016;Sahimi, 1995;Scher & Zallen, 1970).…”