Multi-element metamaterial's design through the relaxed micromorphic model

Exploring the dynamical response of mechanical metamaterials has gathered increasing attention in the last decades, enabling the design of microstructures exotically interacting with elastic waves (focusing, channeling, band-gaps, negative refraction, cloaking, and many more). Yet, the application and use of such metamaterials in engineering practice is still deficient due to the lack of effective models unveiling metamaterials' interactions with more classical materials at finite scales. In this paper, we show that the relaxed micromorphic model can bring an answer to this open problem and can be effectively used to explore and optimize metamaterials' structures consisting of metamaterials' and classical materials' bricks of finite size. We investigate two examples, namely a double-shield structure that can be used to widen the frequency range for which the internal region can be protected and a multiple-shield structure that optimizes both the screening of the regions internal to the single shields and of the zones exterior to the shields themselves. The exploration of these complex meta-structures has been enabled by the finite element implementation of the relaxed micromorphic model that predicts their response at a fraction of the computational cost when compared to classical simulations.