Unfolding engineering metamaterials design: Relaxed micromorphic modeling of large-scale acoustic meta-structures

In this paper, we present a unit cell showing a band-gap in the lower acoustic domain. The corresponding metamaterial is made up of a periodic arrangement of one unit cell. We rigorously show that the relaxed micromorphic model can be used for metamaterials' design at large scales as soon as sufficiently large specimens are considered. We manufacture the metamaterial via metal etching procedures applied to a titanium plate so as to show that its production for realistic applications is viable. Experimental tests are also carried out confirming that the metamaterials' response is in good agreement with the theoretical design. In order to show that our micromorphic model opens unprecedented possibilities in metastructural design, we conceive a finite-size structure that is able to focus elastic energy in a confined region, thus enabling its possible subsequent use for optimizing complex structures. Indeed, thanks to the introduction of a well-posed set of micromorphic boundary conditions, we can combine different metamaterials and classical Cauchy materials in such a way that the elastic energy produced by a source of vibrations is focused in specific collection points. The design of this structure would have not been otherwise possible (via e.g., direct simulations), due to the large dimensions of the metastructure, counting hundreds of unit cells.