## 4 Modelling Approach  
The advanced design was addressed by means of a dedicated finite element model. In compliance with the architecture of the real prototype, the model was structured in different cells independent of each other for activation and were connected along the span. Two versions, made of 3 and 4 cells, were considered, representing the prototypes for the whirl tower and wind tunnel facilities, respectively. Different constraint conditions were implemented. The model for the whirl tower was clamped at one edge, namely the root, and left free on the other edge. Differently, the model for the wind tunnel was clamped at one edge while all linear and angular dofs of the other edge were locked, except the ones along the span direction. This configuration was chosen to reproduce the mounting asset in the wind tunnel test room, which foresees one edge of the model clamped onto a motorized shaft for setting the AoA and the other edge hosted within the opposite wall of the test room and free of rotation to avoid any obstacle to the SMA twisting action. In Figure 5, the blade segment was represented as a beam, with the just mentioned constraint conditions. The MSC/Nastran solver was used for the simulations. The nonlinear behavior of the SMA and its dependence on stress and temperature was handled using the SOL400 solver, which also implements the Auricchio SMA constitutive model through a dedicated card entry, the MATSMA [56]. The models reproducing the whirl tower and wind tunnel demonstrators were made of different elements, with the most solids for the main structure and the SMA and a minority of plates for the sensor supporting beam and the skin. In Figure 6, the two FEM are illustrated. On the top, the naked view of the whirl tower demonstrator is reported, together with the details of the connection flange to the facility. On the bottom, the wind tunnel 4 pays model with the lateral flanges is shown. In Table 9, a summary of the main features of the two models is provided. Figure 5: Constraint conditions simulated for the whirl tower (**top**) and wind tunnel (**bottom**) tests. \begin{table}
\begin{tabular}{l l} \hline \hline
**Feature** & **Value** \\ \hline Number of bays & 4 \\ Total length (flange connection excluded) & 880 mm \\ Connection flanges & 2, one per side of the demonstrator \\ Connection flanges material & 15–5 PH steel alloy \\ Connection pins material & 15–5 PH steel alloy \\ Balancing masses & 8 (2 per bay) \\ Strain gages installed onto the supporting plate & 24 (3 per side of each plate) \\ Fiber grating sensors & 24 (3 per side of each plate) \\ Inclinometers & 4 inclinometers (1 per bay counted in Table 2) + \\  & one at the root as reference \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Wind tunnel demonstrator. Rigid elements were also used to simulate the built-in connection between the SMA and the main structure. In more detail, they were used to reproduce the embedding of one edge of the SMA at one side of the main structure, the connection of the other edge of the SMA to the crown, and the connection of the crown itself to the other side of the main block. The schematic of Figure 7 provides details of the rigid spider elements used for the pre-load simulation. A yellow spider is used to pre-twist the SMA rod; this twist is transmitted to the crown component using a second rigid element, highlighted in red. Finally, the connection of the crown with the main structure is obtained through a third rigid element, highlighted in red. All the spider elements have the central nodes placed in the middle of the SMA cross-section; in this way, their relative motion can be altered, passing from one simulation step to another and linking through MPC entry the involved dofs. Figure 6: Naked view FEM of the whirl tower demonstrator with detail of the connecting flange (**top**); FEM of the wind tunnel demonstrator (**bottom**).