## 3 Working Principle of the Concept and Main Features
When the SMA rod is twisted, the three different situations shown in Figure 2 may occur [50]: in case (a), the applied twist is not enough to produce phase transformation, and no activation can be obtained by heating. Meanwhile, in case (b), the twist is higher, and a ring region of phase transition appears; only a partial activation can be obtained. Finally, in case (c), the level of twist (and thus the stress generated) is sufficient to produce an outer martensite region, fully exploitable for activation. The scope of the design is to generate as much martensite phase as possible; this will be transformed into austenite by heating, with the macroscopic effect of recovering strain. The momentum of the shear acting on each elemental ring is then computed with respect to the axis of the rod. Finally, it is integrated towards the entire radius to get the torsional moment. This process is repeated for twist angles ranging between 0 and 90 deg and for values of temperature between 25 and 200 \({}^{\circ}\)C. In this way, all required load-unload torque-twist curves can be built. At this point, the torsional rigidity of the blade structure is computed. This operation, in line with the preliminary level of the design, is addressed considering the geometrical parameters and inertia moments of the cross-section. This allows us to draw the equivalent torsional elastic line of the structure. Figure 2: Stress-strain distribution in the cross-section of a SMA element: full austenite (**a**), austenite core plus transition phase (**b**), austenite, transition phase, martensite (**c**). The last step of the procedure consists of preparing a plot to compare the load-unload torque twist curves and the just-mentioned elastic line. In Figure 3, a qualitative representation of this graph is shown. The load-unload cycles of the SMA at four different temperatures (RT \(<\) T\({}_{1}\)\(<\) T\({}_{2}\)\(<\) T\({}_{3}\)) were plotted. All the cycles arrive at the same maximum angle of twist. At each temperature but the highest one, T\({}_{3}\), phase transformation occurs, as indicated by the hysteretic behavior. However, the areas of the cycles become less and less pronounced as the temperature rises up to collapse to the red straight line at T = T\({}_{3}\). This condition corresponds to case (a) of Figure 2, for which the stress achieved within the twist range is not enough to allow any phase transformation, and the rod remains in pure austenite. The \"pre-load equilibrium\" point represents the equilibrium condition in pre-twist at RT, between the blade and the SMA. As the temperature rises, this point moves upward and leftward on the cycles at higher temperatures to arrive at the \"full activation equilibrium\" on the straight line (T = T\({}_{3}\)). The horizontal distance between the pre-load and the full activation points represents the maximum recoverable twist. This simplified scheme was used to address the preliminary identification of the main features of the SMA actuators, whose complex behavior was investigated through the refined FE models described in the next section. The mentioned SMA components can be heated essentially in two ways: by energy production (Joule effect) and external supply (conduction, convection, irradiation). The first approach is generally preferred for small sizes (wires, ribbons) since the required current is relatively low (<10 A). However, as the cross-section grows, this value becomes prohibitive. Furthermore, to avoid short circuits, the SMA must be adequately insulated from the other conductive parts, but this operation is often difficult to reconcile with the need for a mechanical transmission that requires a strong connection. Due to the diameter of the SMA rod selected for this application (10 mm), the option of the external energy supply was chosen.