7. Generalized Differential Effective Medium Method for Simulating Effective Physical Properties of 2D Percolating Composites

In this paper, we propose an approach for calculating the effective physical properties of composite materials taking into account the percolation phenomena. This approach is based on the Generalized Differential Effective Medium (GDEM) method and, in contrast to the commonly used self-consistent methods, allows us to incorporate the percolation threshold into the homogenization scheme for simulation of the effective elastic moduli and electrical conductivity of a 2D medium. In this case, the composite is treated as a conductive elastic host where elliptical inclusions of two types are embedded: (1) non-conductive soft inclusions and (2) conductive elastic inclusions that have the same properties as the host. The comparison of theoretical simulations with the experimental data for metal plates containing holes has shown that the proposed GDEM approach describes well the elastic moduli and electrical conductivity of materials of such type in the wide range of hole concentration including the area near the percolation threshold.