Remarks on wave propagation in an acoustic metamaterial modeled as a relaxed micromorphic continuum

Abstract

In order to describe elastic waves propagation in metamaterials, i.e. solids with heterogeneities or microstructure, it is necessary to consider non-local or higher-order models. The relaxed micromorphic model (RMM) proposed here can describe these effects as a continuous material with enriched kinematics. We present a new unit cell giving rise to a metamaterial for acoustic application. The microstructure is engineered to show a band-gap in the low acoustic regime (600-2000 Hz) for which waves cannot propagate through the material. We concentrate on the size effects to make full advantage of the particularly beneficial structure that the model provides. The RMM material parameters are fitted using a new algorithm relying on cutoffs and asymptotes (obtained via a Bloch-Floquet analysis). In particular, by enhancing the kinetic energy of the model with a new inertia term, we enable decreasing curves (modes with negative group velocity).