Equivalent-inclusion approach and effective medium approximations for elastic moduli of compound-inclusion composites

Abstract

Effective medium approximations are developed to estimate the elastic moduli of macroscopically isotropic suspensions of compound inclusions in a continuous matrix material. The two-phase compound (coated) inclusions are substituted by equivalent one-phase inclusions, using the respective dilute solution results. Then, the available effective medium approximation schemes for homogeneous-inclusion materials can be applied to the equivalent medium to estimate the effective moduli of original composites. Since the compound-inclusion dilute solution for the shear modulus is rather involved, a simplified approximation is also proposed. Numerical simulations by finite element method in some benchmark examples are compared favorably with the predictions of the scheme.