Equivalent-inclusion approach and effective medium estimates for elastic moduli of two-dimensional suspensions of compound inclusions

An effective medium scheme is developed to estimate the elastic moduli of two-dimensional macroscopically isotropic suspensions of compound inclusions in a continuous matrix material. The two-phase (coated) compound inclusions are substituted by equivalent one-phase inclusions, using dilute solution results. Then, the available effective medium approximations and bounds are applied to the equivalent medium with homogeneous inclusions. Numerical fast Fourier transform simulations in some benchmark examples are compared favourably with the predictions of the scheme.