Homogenization of acoustic metamaterials using retrieval methods

The effective properties of two-dimensional acoustic metamaterials are here obtained by applying two retrieval methods, referred to as the direct inversion method and the differential method. They employ the scattering coefficients at the incidence and transmission sides of the global systems immersed in a fluid. A validation case study on a one-dimensional periodic design is first presented. A two-dimensional design comprising periodic cylindrical steel inclusions in a soft elastic matrix is then examined. Homogenization issues related to different underlying assumptions in the two retrieval methods are discussed. It is shown that one of the retrieval methods (the differential method) well describes the interior of the medium, away from the interfaces, while the other (the direct inversion method) captures the interface effects. The two retrieval methods are used to build homogeneous equivalent media which are used to predict scattering coefficients. A hybrid method is introduced which combines the two methods to create effective media that are accurate approximations of their 2D counterparts.