Computation of effective electrical conductivity of composite materials: a novel approach based on analysis of graphs

TL;DR

This paper introduces a novel graph-based method for calculating the effective electrical conductivity of composite materials, leveraging stochastic homogenization and connectivity analysis to account for complex microscopic geometries.

Contribution

The paper presents a new approach that uses graph analysis and adjacency matrices within stochastic homogenization to compute electrical properties of composites.

Findings

Graph-based method effectively models complex microstructures.

The approach accurately predicts conductivity variations due to micromorphology.

Method demonstrates potential for improved composite material design.

Abstract

In this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called 'stochastic homogenization'. In this approach, the classical deterministic homogenization techniques and procedures are used to compute the macroscopic parameters of a composite starting from its microscopic properties. The stochastic part is due to averaging over some series of samples, and the fact that these samples fit into the concept of RVE (Representative Volume Element) in order to reduce the variance effect. In this article, we present a novel method for computation of effective electric properties of composites -- it is based on the analysis of the connectivity graph (and the respective adjacency matrix) for each sample of a composite material. We describe how this matrix is constructed in order to take into account complex microscopic geometry. We also explain what we mean by homogenization procedure for electrical conductivity, and how the constructed matrix is related to the problem. The developed method is applied to a test study of the influence of micromorphology of composites materials on their conductivity.