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.

在本文中，我们提出了一个在较低声域中显示带隙的晶胞。相应的超材料由一个单元晶胞的周期性排列组成。我们严格表明，只要足够大，松弛的微形态模型就可以用于大规模的超材料​​设计考虑标本。我们通过应用于钛板的金属蚀刻程序制造超材料，以表明其生产用于实际应用是可行的。还进行了实验测试，证实超材料的响应与理论设计非常吻合。为了证明我们的微形态模型在超结构设计中开辟了前所未有的可能性，我们构想了一种有限尺寸的结构，能够将弹性能量集中在受限区域中，从而使其可能随后用于优化复杂结构。事实上，由于引入了一组适定的微形态边界条件，我们可以结合不同的超材料和经典的柯西材料，使振动源产生的弹性能量集中在特定的收集点。这种结构的设计本来是不可能的（通过例如，直接模拟），由于元结构的大尺寸，数以百计的单位单元。