Origins of Willis coupling and acoustic bianisotropy in acoustic metamaterials through source-driven homogenization

In addition to conventional acoustic properties (mass density and compressibility), recent research has shown that inhomogeneous acoustic media may require coupling tensors between effective volume strain and momentum fields. These coupling tensors imply conversion between monopolar and dipolar motion in the effective material response. Intrinsic coupling between strain and momentum is known as Willis coupling in elastodynamics, and it is analogous to bianisotropy in electromagnetism. This paper investigates the microscale and mesoscale effects that lead to Willis coupling, studies the proper homogenization of acoustic metamaterials with non-negligible Willis coupling, and demonstrates the impact of Willis coupling on defining physically meaningful effective material parameters.