Numerical Simulation to Determine the Effect of Topological Entropy on the Effective Transport Coefficient of Unidirectional Composites

Abstract

The influence of topological entropy (TS) on the effective transport coefficient (ETC) of a two-phase material is analyzed. The proposed methodology studies a system of aligned bars that evolves into a stochastic heterogeneous system. This proposal uses synthetic images generated by computational algorithms and experimental images from the scanning electron microscope (SEM). Microstructural variation is imposed for statistical reconstruction moments by simulated annealing (SA) and it is characterized through TS applied in Voronoi diagrams of the studied systems. On the other hand, ETC is determined numerically by the Finite Volume Method (FVM) and generalized by a transport efficiency of charge (ek). The results suggest that our approach can work as a design tool to improve the ETC in stochastic heterogeneous materials. The case studies show that ek decreases when TS increases to the point of stability of both variables. For example, for the 80% surface fraction, in the particulate system of diameter D = 1, ek = 50.81 ± 0.26% @ TS = 0.27 ± 0.002; when the system has an agglomerate distribution similar to a SEM image, ek = 45.69 ± 0.60% @ TS = 0.32 ± 0.002.

Keywords

• effective transport coefficient
• topological entropy
• aligned composites