## 3 Challenges  
During the last decade, great effort has been made by the research community on the development of acoustic metamaterials and the ability to shape the acoustic field. However, most of the so far presented works, even the concepts selected as the most promising for aeronautical applications, have dealt with quiescent hosting media, and have often focused on the development of noise-reducing material and structures for building acoustics. On the, still, long road towards the application of effective metamaterial concepts in the aeronautical framework for noise reduction, the first issue to be tackled is the inclusion of flows in models and simulations. As a moving fluid fundamentally affect acoustic wave propagation, corrections and modifications in models and concepts that depends on Mach numbers and/or flow field shapes, are expected to make them effective in the aeroacoustic domain. Another challenge to face is the development of suitable numerical methods to simulate the behavior of acoustic metamaterials under aeronautical operating conditions. When it comes to evaluating the system response, one may consider analytical (or semi-analytical) approaches or numerical simulations. The former typically guarantees very fast evaluations, at the cost of a preliminary analytical resolution of the problem, which are not always available, especially for complex geometries and conditions with non-uniform complex background flows. Numerical approaches are more versatile, but versatility comes with a cost as well. Simulating acoustic metamaterials is a non-trivial challenge from the numerical point of view. Many concepts have labyrinthine complex micro-structures with audacious designs, and often, their behaviors rely on acousto-elastic interactions in structures where thermo-viscous losses are not negligible, thus they deeply affect the solution. A direct numerical simulation of such concepts, e.g., using the Finite Element Method (FEM) on fully detailed geometries, would result in computationally-expensive, high resource-demanding calculations, due to the fine mesh needed toaccurately reproduce the smallest geometrical details and solve the frequency of interest. This often does not allow for performance optimization testing, in which simulations are repeated a large number of times. Hence, new efficient and accurate numerical models are needed that can combine advantages from different existing methods. This is the case, for example, of the one proposed in [103] for meta poro-elastic laminates with thin coatings, that couples the FEM, which simulates the response in the poro-elastic medium with inclusions, and the Bloch expansion, which simulates the surrounding media using a technique similar to the transfer matrix method to account for the coatings. Multiscale and homogenization modeling techniques are also attractive ways of addressing the issue when different scales are involved, such as microporous materials where one is interested in the macroscopic effect due to the microstructure of the system [104], and they can be adopted in a metamaterial design process [105; 106]. As a final remark, the actual manufacturing of metamaterial devices poses significant challenges. Often, metamaterials come with complex geometries that are needed to exploit particular physical phenomena, but may increase production complexity and hence, costs. It is obviously of fundamental importance to control the latter aspects to enable the deployment of metamaterial technologies in an industrial context. During the last two decades, additive manufacturing (AM) techniques have experienced a boost in terms of versatility and reliability, and several new processes have been developed that use a large variety of materials, including polymers and metals. The aerospace industry is introducing AM, and through this technique, exploiting the possibilities offered to obtain lighter and still durable components with less geometrical restrictions in the design of the parts.