Scattering from a fluid cylinder with strain-momentum coupled constitutive relations

Abstract

Many important applications of acoustics are associated with the principle of scattering. For example, biomedical ultrasound and sonar both make use of acoustic field scattering for localization, imaging, and identification of objects. While the theory of acoustic scattering from fluid and elastic materials is well established and has been validated with numerical and physical experiments, no work has been published to describe scattering from a more general class of acoustic materials known as Willis materials. Willis materials are characterized by a bulk modulus and mass density as well as a vector that couples the pressure-strain relationship with the momentum density-particle velocity relationship. The coupling vector is the result of microstructural asymmetry. 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.