Analytical and Numerical Investigation of Scattering From Bianisotropic Acoustic Media

Scattering from fluid domains with dissimilar material properties is of foundational importance to many application areas in acoustics and elastic wave propagation. For example, biomedical ultrasound and sonar both make use of acoustic field scattering for localization, imaging, and identification of objects. The theory of acoustic scattering from fluid and elastic materials is well established and has been validated with numerical and physical experiments. Recent work in acoustic and elastic meta-materials has shown that materials with subwavelength asymmetry have a macroscopic response characterized by a scalar bulk modulus, a tensorial mass density, and a vector that couples the pressure-strain relationship with the momentum density-particle velocity relationship. This type of constitutive behavior is the acoustic analogue of bianisotropy in electromagnetism and has come to be known as Willis coupling in acknowledgement of the first description of this material response by J.R. Willis [Willis, Wave Motion 3, pp. 111 (1981)]. We present a theoretical description of acoustic scattering of a plane wave incident upon a cylinder exhibiting weak Willis coupling using a perturbation approach. The scattered field depends upon the orientation of the Willis coupling vector and is therefore anisotropic despite the symmetry of the geometry. The analytical model is validated through comparison with a finite element-based numerical experiment where the bianisotropic material response is introduced using a weak formulation of the constitutive equations.