Prediction of Elastic Wave Propagation Characteristics of Composites via Strong-Contrast Expansions

The preponderance of previous treatments to predict the effective elastic properties of composites assume the purely static limit. Here we derive exact expressions for effective elastodynamic properties of two-phase composites at intermediate wavelengths by extending the "strong-contrast" expansion approach previously applied to the static problem. The resulting series expansion explicitly incorporates complete microstructural information about the composite via $n$-point correlation functions and is endowed with excellent convergence properties, even for high contrast ratios of phase moduli. The fast convergence of this series enables us to extract an accurate approximation that depends on the microstructure via the two-point correlation function or its Fourier counterpart, which we call the "spectral density." Our formula thus extends previous "mean-field" treatments that typically do not account for nontrivial microstructural information and/or are limited to small phase contrasts. We apply our spectral-density formula to a variety of models of disordered composites and discuss how to engineer composites with prescribed attenuation properties for elastic waves.