A Green's function-based method for wave attenuation on random matrix-inclusion microstructures with local isotropy

A numerical Green's function-based approach is developed for attenuation characterization in two-phase matrix-inclusion microstructures. This approach avoids the critical boundary enforcement in plane wave modeling and is extensively tested and compared to current analytical methodologies based on the First-Order Smoothing Approximation (FOSA). Assuming each phase is isotropic with constant density, we examine the effects of varying density and elasticity. When only elasticity differences are present, the numerical and analytical predictions show good agreement. However, the results demonstrate that the FOSA overestimates attenuation when both density and elasticity differences are introduced, leading to a divergence in high wavenumbers. The discrepancies observed in density-related terms under the FOSA underscore its limitations and point to the need for more refined analytical models in multiphase wave propagation.