Number of inhomogeneities at which the effective moduli of a heterogeneous material stabilize

When the effective elastic moduli of heterogeneous materials containing inhomogeneities are numerically calculated, one of the issues is the number of inhomogeneities at which the effective moduli stabilize. This number may depend on the shape and distribution of the inhomogeneities. In this study, circular holes of the same size are considered. Two distributions of holes, equilateral triangular and random ones are analyzed. It is found that the effective moduli associated with the two distributions stabilize for the samples with seven and nineteen holes, respectively.