A computational multiscale homogenization framework accounting for inertial effects: Application to acoustic metamaterials modelling

The framework is specifically tailored for modelling the phenomena involved in Locally Resonant Acoustic Metamaterials (LRAM). In this view, several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment of the multiscale problem. On this basis, the issue of numerically capturing the local resonance phenomena in a FE2 context is addressed. Objectivity of the obtained results in terms of the macroscopic Finite Element (FE) discretization is checked as well as accuracy of the homogenization procedure by comparing with direct numerical simulations (DNS). The appearance of local resonance band-gaps is then modelled for a homogeneous 2D problem and its extension to multi-layered macroscopic material is presented as an initial attempt towards acoustic metamaterial design for tailored band-gap attenuation.