EXACT EXPRESSION FOR THE EFFECTIVE ELASTIC TENSOR OF DISORDERED COMPOSITES

We derive new, exact series expansions for the effective elastic tenso r of anisotropic, d-dimensional, two-phase disordered composites whose nth-order tensor Coefficients are integrals involving n-point correla tion functions that characterize the structure. These series expansion s, valid for any structure, perturb about certain optimal dispersions. Third-order truncation of the expansions results in formulas for the elastic moduli of isotropic dispersions that are in very good agreemen t with benchmark data, always lie within rigorous bounds, and are supe rior to popular self-consistent approximations.