Abstract
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the ‘strong-contrast’ expansion formalism that was previously applied to the static problem. These strong-contrast expansions explicitly incorporate complete microstructural information of the composite via an infinite set of n-point correlation functions. Utilizing the rapid-convergence properties of these series expansions (even for extreme contrast ratios), we extract accurate approximations that depend on the microstructure via the spectral density, which is easy to compute or measure for any composite. We also investigate the predictive power of modifications of such approximation formulas postulated elsewhere (Kim and Torquato 2020 Proc. Natl Acad. Sci. 117 8764) to extend their applicability beyond the quasistatic regime. The accuracy of these nonlocal microstructure-dependent approximations is validated by comparison to full-waveform simulation results for certain models of dispersions. We apply our formulas to a variety of models of nonhyperuniform and hyperuniform disordered composites. We demonstrate that hyperuniform systems are less lossy than their nonhyperuniform counterparts in the quasistatic regime, and stealthy hyperuniform media can be perfectly transparent for a wide range of wavenumbers. Finally, we discuss how to utilize our approximations for engineering composites with prescribed elastic wave characteristics.
Highlights
The theoretical determination of the effective elastic wave characteristics of multiphase composite media is of great importance in geophysics [1, 2, 3], exploration seismology [4, 5], diagnostic sonography [6], crack diagnosis [7, 8], architectural acoustics [9] and acoustic metamaterials [10], among many examples
The exact series expansion (31) accounts for complete microstructural information and multiple scattering to all orders in the quasistatic regime
Closed-form approximations of the effective dynamic elastic moduli derived previously only apply at long wavelengths and for very special macroscopically isotropic disordered composite microstructures [16], namely, nonoverlapping spheres or spheroids in a matrix
Summary
The theoretical determination of the effective elastic wave characteristics of multiphase composite media is of great importance in geophysics [1, 2, 3], exploration seismology. We verify the accuracy of the postulated approximations via full-waveform simulations for certain benchmark models This validation allows us to use them to predict the effective elastic wave characteristics accurately well beyond the quasistatic regime for a wide class of composite microstructures without computationally expensive full-blown simulations. The accuracy of these nonlocal approximations is verified by comparison to full-waveform simulations for certain benchmark models.
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