# A Morphing Deployable Mechanism for Re-Entry Capsule Aeroshell
## 5 Morphing Tab Concept
### SMA Modelling Approach
To model the system, the non-linear MSC/Nastran SOL400 solver was used in combination with an SMA dedicated card, collecting all the information for the alloy constitutive law (austenite, martensite elastic modulus, Poisson ratio, transformation stresses at reference temperature, maximum recoverable strain, material density, transformation  
Figure 10: Architecture of the SMA morphable tab. stress/temperature gradients). The data collected in Table 3 were used for the simulation and hereafter presented. A non-linear static analysis was implemented to simulate the different working steps of the SMA (pre-stretching and connection to the structure, upward activation, reverse to neutral position, downward activation, reverse to neutral position). A uniform incremental temperature load was assigned to the SMA material, passing from the initial value to the final one foreseen, per each step of the simulation. The finite element model shown in Figure 11 was realized. The root region was not modelled; in fact, being remarkably more rigid than the other parts, it was replaced by constraints. The flat plate was simulated through beam elements. For the two SMA rods, hexahedral parabolic elements were considered; solid non-linear elements are, in fact, mandatory for the implementation of the SMA constitutive law. Finally, the tip was simulated through rigid connections among the edges of the SMA rods and the flat plate. Three moments of the life of the system were simulated:  
* Integration of the SMA rods. * Activation/heating of the upper SMA and then restoring/cooling into the neutral configuration. * Activation/heating of the lower SMA and then restoring/cooling into the neutral configuration. The integration of the SMA rods, originally in the austenite phase, consists of clamping the SMAs at the root region and stretching them up to bring the edges at the tip connection. During this operation, the applied load causes martensite production. Displacements along the rod axes were imposed during the simulation; as the edges coincided with the tip rigid connection, multiple constraints were imposed to pin the overlapping nodes. Then, the  
Figure 11: Finite element model of the SMA morphable tab. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Parameter** & **Value** \\ \hline \multirow{6}{*}{SMA rods} & Austenite, Martensite elastic modulus & 25 GPa, 10 GPa \\  & Austenite, Martensite Poisson ratio & 0.33 \\  & Density & 6500 kg/m\({}^{3}\) \\  & Max recoverable strain & 0.023 \\  & Martensite start and finish & 150 MPa, 325 MPa \\  & transformation stresses at 25 °C & 175 MPa, 45 MPa \\  & Stress/strain gradients for forward & 6.8 MPa/\({}^{\circ}\)C, 7.6 MPa/\({}^{\circ}\)C \\  & and rearward phase transformations & 6.8 MPa/\({}^{\circ}\)C, 7.6 MPa/\({}^{\circ}\)C \\ \hline \hline \multirow{2}{*}{Tab} & Steel elastic modulus & 210 GPa \\  & Steel Poisson ratio & 0.32 \\ \cline{1-1}  & Density & 7700 kg/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material features used for the simulation. edges of the SMA were released to allow their elastic recovery and to achieve equilibrium with the tab structure. In Figure 12, the initial configuration (SMA before stretching) and the fully integrated configuration (SMA stretched, connected, and in equilibrium with the flat plate) are illustrated. The stress level within the components was assumed as design constraint. 1/3 of the ultimate stress was assumed as allowable for the structure material; the allowable arose to the 80% of the ultimate stress for the SMA material; this choice is justified by the necessity to exploit as much as possible the SMA actuation capability, strictly related to the amount  
Figure 12: Integration simulation steps: SMA rods before stretching (**top**), connected to the flat plate (**middle**), and fully upward deflected (**bottom**). of martensite generated during the pre-load. Another design constraint considered was represented by structural instability.