Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 474, Issue 2220, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rspa.2018.0571
Keywords
Willis coupling; metamaterial; fluid; cylinder; scattering
Categories
Funding
- ONR through MURI grant [N00014-13-1-0631]
- ONR through YIP grant [N0014-18-1-2335]
- U.S. Army Engineer Research and Development Center (ERDC), Geospatial Research and Engineering business area
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A material that exhibits Willis coupling has constitutive equations that couple the pressure-strain and momentum-velocity relationships. This coupling arises from subwavelength asymmetry and non-locality in heterogeneous media. This paper considers the problem of the scattering of a plane wave by a cylinder exhibiting Willis coupling using both analytical and numerical approaches. First, a perturbation method is used to describe the influence of Willis coupling on the scattered field to a first-order approximation. A higher order analysis of the scattering based on generalized impedances is then derived. Finally, a finite-element method-based numerical scheme for calculating the scattered field is presented. These three analyses are compared and show strong agreement for low to moderate levels of Willis coupling.
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