A COMPUTATIONAL METHOD FOR CALCULATING THE ELECTRICAL AND THERMAL PROPERTIES OF RANDOM COMPOSITES IN 3 DIMENSIONS

This paper presents a novel three-dimensional computational methodology for determining the electrical (DC) and thermal conductivity of multiphase random composite materials. Expanding upon previous two-dimensional work, this approach integrates percolation theory with a numerical algorithm, offering an efficient alternative to traditional continuum methods. At the microscale,Representative Volume Elements (RVEs) are stochastically generated.Conductive pathways are identified using the Depth-First Search (DFS) algorithm, and their lengths and resistances are quantified via a modified Lee algorithm. The effective RVE conductivity is derived by considering the number of paths, their mean path length, and, where applicable, employing mixture rules. For macro-scale property prediction, a two-step Monte Carlo procedure incorporates microscale percolation probabilities and averages properties of percolating RVEs, further incorporating a correction to account for tortuosity and incomplete connectivity in an effectively infinite medium. The methodologydemonstrates accuracy comparable to Finite Element (FE) and Finite Difference (FD) methods but achieves significantly reduced computational cost without requiring external field application. Convergence analysis validates the method’s stability, and scale effect studies confirm expected power-law behavior near the critical percolation threshold. Simulations in a random binarymedium showed that electric and thermal conduction follow a scaling law with an exponent value of approximately 2.0, aligning with established literature.It was also found that the number of conductive paths, their average length, and their effective width follow scaling laws with exponents of 1.87 ± 0.01, −0.43 ± 0.01, and −0.33 ± 0.01, respectively. Furthermore, applications to continuous percolation problems with conducting spheres (critical exponent t ≈ 2.13) and cubes (critical exponent t ≈ 2.3) validate the methodology’scapability to accurately predict conductivity and critical exponents across relevant volume fractions.