## 3 Working Principle of the Concept and Main Features
* The skin is screwed to the rib elements and to the main structure; it contributes to keeping the aerodynamic shape under the external loads and the twist action of the actuator. SMA torsional actuators obtained the actuation. The simplicity of the transmission and the possibility of minimizing the number of parts led to the consideration of torsional active elements rather than other shapes and types of actuation (wires, ribbons transmitting axial forces) [47]. Rods and tubes were both candidates. The centrifugation of the areas of a tube assures a higher bending and torque stiffness over mass ratio compared to a rod of the same diameter. The inner cavity, moreover, can be exploited as an inlet for cold air for the refrigeration and the de-activation of the alloy. Furthermore, the pre-twist of an SMA rod cannot produce martensite in the inner core since the stress level does not grow enough, as will be discussed in the next part of this section. This results in a portion of material that cannot be exploited for actuation and must be twisted together with the structure without contributing to the overall stiffness. However, some drawbacks of the tube layout led the designers to consider the rod. First, the structural instability of the wall under the combined action of the pre-twist and the bending and torque coming from conventional loads. Second, the magnitude of the torsion to be applied to the pre-twist tube is relatively higher because of the higher inertia moment. Thus, considering the target TRL of the prototypes [48], conceived for demonstration in facilities with relevant safety factor restrictions, the designers chose the rod shape. The selection of the material was dictated by the elastic properties, the recoverable strain, and the temperatures of activation. These parameters have a relevant impact on transmitted twist, power consumption, and thermal safety. Another not negligible aspect that drove the choice was the availability of products with the required size on the market. The market offers a wide variety of SMA products, usually of relatively small size and derived from wires and sheets. Rod elements are difficult to find since they require dedicated tooling, and the machining forces may alter the microcrystalline composition. Based on a survey of the worldwide market, it was possible to find rod elements of a diameter greater than 8 mm made of NiTiNol alloy with transition temperatures compatible with the requirements. Figure 1: Layout of the device: two cells connected (**top**); detail of the holes within the spar for heating coil supply and the thermocouple (**left**); detail of the ring-like element (**right**). It is worth clarifying a fundamental aspect before illustrating the design approach adopted for the SMA actuators. As already specified, the capability of these alloys to recover strain is strictly related to the transformation of the martensite phase into austenite, obtained by heating. In this sense, the presence of the martensite phase plays a critical role. In fact, the higher the initial martensite percentage, the higher the strain that can be potentially recovered. A certain stress level must be assured to produce an adequate amount of martensite. For this reason, the SMA elements are pre-twisted and mounted onto the structure. Then, they are released to achieve the elastic equilibrium with the structure. The residual stress thus determines the level of martensite. The approach adopted for the definition of the features of the actuator is based on the conceptual scheme illustrated in [47]. The SMA element is initially seen as a 1D actuator, considering only the torsional dof. The element is clamped at one side, and a twist is applied at the other edge. This produces a linear, angular strain along the radius at each cross-section of the SMA element. The corresponding shear distribution is computed using the theoretical model described in ref. [49]. In line with the 1D assumption, both strain and shear do not depend on the tangential or axial coordinates but only on the radius.