Effective properties of periodic media in elastodynamic problems

This paper describes a homogenization model for evaluating the effective elastodynamic properties of acoustic metamaterials in problems involving wave propagation. The methodology is based on determining the constitutive equations in terms of averaged quantities observed at the macroscale. In this sense, the approach very closely follows the pioneering ideas introduced by Willis, and afterwards, followed by several authors in the last ten years. The distinctive characteristic of our approach is that we write the microscale equation in the spatial domain. The model is validated with previous results published in the literature, and our results replicate them almost exactly. The resulting homogenization model could be used as an additional tool for the topology design of acoustic metamaterials.