Polydisperse structures of composites with random elastic properties of inclusions

A generalized self-consistent method [1, 2] is developed and applied to the boundary-value problems of composites with random elastic properties of inclusions. The approach suggested makes it possible to allow for a random mutual arrangement, statistical dispersion of elastic properties and sizes of the inclusions, and their mutual correlations in terms of special homogenized indicator functions. For comparison, the analytical solutions and those obtained from a corresponding sequence of H + 1 (H = 0,1,...) linked homogenized problems of the self-consistent method for the strain distribution in the inclusions and for the tensor of effective elastic properties of the composite are given. A numerical calculation of the effective transversely isotropic elastic characteristics for an undirectional polydisperse fibrous composite is also presented.