A metacontinuum model for phase gradient metasurfaces

Acoustic metamaterials and metasurfaces often present complex geometries and microstructures. The development of models of reduced complexity is fundamental to alleviate the computational cost of their analysis and derivation of optimal designs. The main objective of this paper is the derivation and validation of a metacontinuum model for phase gradient-based metasurfaces. The method is based on the transformation acoustics framework and defines the metasurface in terms of anisotropic inertia and bulk modulus. Thermal and viscous dissipation effects in the metacontinuum are accounted for by introducing a complex-valued speed of sound. The model is implemented in a commercial FEM code, and its predictions are compared with numerical simulations on the original geometry and also using an equivalent boundary impedance approach. The results are examined for an exterior acoustics benchmark and for an in-duct installation in terms of transmission coefficient with the four-pole matrix method. The metacontinuum model gives solid results for the prediction of the acoustic properties of the examined metasurface samples for all the analyzed configurations, as accurate as the equivalent impedance model on which it is based and outperforming it in some circumstances.