## 1 Introduction  
The aerospace industry is facing new challenges related to contingencies of different nature. Climate change, to cite an example, imposes, from one side, the adoption of a series of measures to mitigate the environmental impact of the aircraft and, from the other side, the development of dedicated strategies to deal with the arising weather instability [1]. To cite another example, the extreme competition within the aerospace compartment is a crucial aspect that can dramatically make the difference between the survival or extinction of a market player. This situation is made even more critical by unpredictable events such as the COVID-19 pandemic, which led to a dramatic reduction of passenger-kilometers [2], or the Ukraine-Russia war that imposed longer and, thus, more expensive routes [3]. The policy, on one side, must define dedicated economic strategies and allocate funds for new programs, while the scientific community, on the other side, has to identify new approaches to the problems and develop novel technologies. In this complex scenario, strategies focusing on both aircraft environmental impact and relevant costs are strategically important [4; 5]. The concept of adaptation, that is to say, the capability of changing some features, can be exploited for those design cases not completely covered by the conventional approach [6]. Off-design conditions and flight segments penalized for their incompatibility with other extended ones are just some target applications for adaptivity. Wings for aircraft and main rotors for rotorcrafts can benefit from this approach [7; 8]. In these cases, since the focus is mainly on the geometry change, one uses the word \"morphing.\" This discipline is not so new. Starting from the world of nature up to the early days of aviation, it found several applications. Birds [9] and the flyer plane of the [PERSON] brothers [10], in fact, embody the morphing wing concept. In the following decades of aviation, this approach was not abandoned but revisited to face growing loads [11]: the extremely flexible wing of the first aircraft gave way to more rigid versions equipped with movable parts. However, despite their capability of altering the load distribution, conventional flaps, slats, and ailerons for aircraft and swash plates for rotorcrafts alter the smoothness of the aerodynamic surfaces. Here, both the external kinematic chains needed for actuation and the geometrical discontinuities at the interface with the wing main body dramatically worsen the overall aerodynamic performance. In the last decades, the advent of a new family of materials, namely \"smart\", changed the design perspective. To cite an example, active materials such as shape memory alloys, SMA, have been in the spotlight for their capability to bear loads and their relatively high force and power density. These peculiarities, in fact, make this type of material particularly suited for applications requiring large deformations and, at the same time, provide adequate flexibility to allow the morphing. In line with this trend, different programs were funded to mature morphable wing concepts and fill the gap for their industrialization [12]. Many programs in the last two decades were funded to comprehend the exact limitations of the morphing technology and the materials considered. Starting from the beginning of this century, the 5 th European FPS-GROWTH Program funded the Project \"Active aeroelastic aircraft structure\" (3 AS) to develop concepts able to alter wing mechanical features and achieve optimized configurations under the action of external loads [13; 14]. The next Program, FP6, funded other projects focusing on the topic: the project of \"Integration of technologies in support of a passenger and environmentally friendly helicopter\" (FRIENDCOPTER), focusing on the estimate of the environmental impact of the rotorcraft and on the identification of some strategies of mitigation [15].