Constructive Homogenization Of Dispersed Random Composites. Part II. Computer Simulations

Consider a two-dimensional, two-component composite consisting of non-overlapping, identical circular disks embedded in a uniform host. The effective conductivity of these dispersed random composites can be determined using constructive homogenization theory, which assumes a strictly stationary distribution of inclusions. The Eisenstein summation method is applied to analyze conditionally convergent sums that arise during the homogenization process. Additionally, the Clausius-Mossotti approximation, which is valid for two-dimensional composites up to O(f3), is justified for random composites. This approach provides a robust framework for understanding the behavior of such materials and offers insights into the computation of their effective properties.