MODELING ACOUSTIC SPACE-COILED METACRYSTALS^*

We present an effective model of ``space-coiled metacrystals"" composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry-P\'erot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a one-dimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes.