Metamaterials, or architected materials, represent a well-established field of applied physics and engineering. The idea of developing artificial materials, which show physical properties that hardly occur naturally, dates back to the late 1960s, but the actual introduction of metamaterials straddles the XX and XXI centuries. The sudden rise of such a research ambit, that shook the field of electromagnetism, was triggered by the substantial improvements in the computational methods and in the manufacturing technology. Those innovations enabled the realization of a new class of rationally designed composite materials, constituted of a periodic repetition of an engineered micro-scale unit cell. More recently, the field of metamaterials was enlarged to encompass mechanical and acoustic features, with several possible applications: from broadband wave attenuation to mechanical energy harvesting, from speech recognition to acoustic cloacking, from enhanced signal processing to innovative mechanical sensing.

The design, the realization and the experimentation of mechanical and acoustic metamaterials require the knowledge of many concepts, that fall within various physical domains, obviously including mechanics, acoustics and thermodynamics but often extending to material science and electronics. The Summer School, embracing such a complexity, aims at providing the fundamentals of the working principle, with advanced description of a few case studies. Starting from the underlying theoretical bases, some specific analytical and theoretical design tools will be described, with an outlook to future developments. Afterwards, the most important experimental procedures will be discussed, with a special interactive session with hands-on testing activity. The most relevant advanced applications will be discussed, with the participation of world-class experts in the field. The importance of advanced multi-physics modeling will be presented to students, with the final day devoted to the development of examples on a Finite Element software.