Effective Elastic Wave Characteristics of Composite Media

TL;DR

This paper develops exact and approximate formulas for the effective elastic wave properties of two-phase composites, incorporating microstructure details and validating predictions with simulations, to aid in designing materials with specific wave characteristics.

Contribution

It extends strong-contrast expansion methods to dynamic elastic properties, providing microstructure-dependent approximations valid beyond the quasistatic regime.

Findings

Hyperuniform systems are less lossy than nonhyperuniform ones.

Stealthy hyperuniform media can be transparent over a range of wavenumbers.

The derived formulas accurately predict wave behavior validated by simulations.

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 [J. Kim and S. Torquato, Proc. Nat. Acad. Sci. ${\bf 117}$, 8764 (2020)] to extend their applicability ${\it beyond ~the ~quasistatic ~regime.}$ 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 wavenumber. Finally, we discuss how to utilize our approximations for engineering composites with prescribed elastic wave characteristics.