Dynamic homogenization of heterogeneous piezoelectric media: A polarization approach using infinite-body Green’s function

Dynamic homogenization theories are powerful tools for describing and understanding the behavior of heterogeneous media such as composites and metamaterials. However, a major challenge in the homogenization theory is determining Green’s function of these media, which makes it difficult to predict their effective constitutive relations, particularly for the finite-size and/or non-periodic media in real-world applications. In this paper, we present a formulation for finding the elastodynamic effective constitutive relations for general heterogeneous media, including finite-size and non-periodic ones, via a polarization approach based on the Hashin–Shtrikman principle along with Green’s identities. Our proposed formulation relies on the infinite-body Green’s function of a homogeneous reference medium, making it free from the difficulty of determining Green’s function even for the homogenization of finite-size and/or non-periodic media. Additionally, we demonstrate the universal applicability of this formulation for both random and deterministic heterogeneous media. This work contributes to a better understanding of the homogenization theory and the design of next-generation metamaterials that require the accurate prediction of effective material characteristics for dynamic wave manipulation under desired operating environments.