## 2 Materials and Methods
### Experimental Design
The cycling was performed at a fixed temperature of \(\sim\)110 \({}^{\circ}\)C, which was chosen based on a previous study that suggests that the reverse martensitic transformation is fully complete for values of temperature below 110 \({}^{\circ}\)C [29]. The SMA sheets were prepared for tensile cycling using a microcutting machine. The SMA tensile cycling was performed on a calibrated MTS Alliance RF/150 testing system equipped with an environmental chamber used to maintain the constant temperature during cycling. We loaded samples for a series of tensile cyclesfrom 0 to 450 MPa at a rate of 1 mm/min until the stabilization of the SMA hysteretic cycle [30]. The strain during the loading cycles was measured using a strain gauge with a 25 mm gauge length, while the crosshead distance was set to 50 mm. In summary, based on the thermomechanical treatment path and final sheet thickness, the following set of Cu-Al-Mn thin sheets was produced:  
* Hot-rolled (0.4 mm);
* Hot-rolled (2 mm), cold-rolled (0.4 mm);
* Hot-rolled (2 mm), cold-rolled (0.4 mm), grain growth (AGG);  
Once all the samples were treated according to the five thermomechanical paths described above, the final betatization was completed by heating to 900 \({}^{\circ}\)C with quenching in cold water. This final step in the treatment process was necessary to activate the shape memory properties of the SMA sheets. The Cu-Al-Mn sheets were analyzed to determine their chemical composition as well as their phase transformation capacity and phase transformation temperatures. Since multiple different testing methods were involved in this process, each requiring samples of specific shape and size, care was taken that the samples were cut from the same bulk  
Figure 3: Section of the [PERSON] one-dimensional SMA constitutive model showing the pseudoelastic (PE) tensile loading cycle used during the SMA “training process” highlighted by the red arrows for the tensile loading and unloading at a fixed temperature above the A\({}_{\text{f}}\) temperature of phase transformation. Figure 2: Abnormal grain growth (AGG) [25], and betatization (BET) thermal treatments used for increasing relative grain size and obtaining martensite to induce the SME in the SMA sheets, respectively. sheets of Cu-Al-Mn as close as possible to each other. The cutting of sample Cu-Al-Mn thin sheets was performed using a microcutting machine. Samples for microscopy were additionally prepared by polishing and then chemically etched using a FeCl\({}_{3}\) + HCl solution. Subsequently, measurements of the chemical composition of samples used in the study were performed by scanning electron microscopy (SEM) and an energy-dispersive X-ray detector (EDX) analysis. Assessment of the phase transformation capability of the differently treated Cu-Al-Mn SMA sheets and their phase transformation temperatures was performed via differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA). During DSC analysis, phase transformations are marked by the measured changes/peaks in heat flow. Conversely, during DMA analysis, phase transformations were measured through changes in the material's damping capacity, expressed through the loss factor tan\(\delta\), which is calculated as the ratio between the loss and storage moduli E\({}^{\prime\prime}\) [MPa] and E\({}^{\prime}\) [MPa], respectively. During phase transformation, SMAs such as Cu-Al-Mn are expected to show a peak in damping capacity. Both in DSC and DMA tests, care was taken to avoid reaching temperatures above 200 \({}^{\circ}\)C, as previous studies have shown that temperatures in the range of -250 to 300 \({}^{\circ}\)C cause martensitic stabilization and a loss of transformation capacity [22; 31]. DSC testing was performed using samples with mass ranging in the interval between 20 and 100 mg, in a temperature range of -75 to 200 \({}^{\circ}\)C with a heating/cooling rate of 10 \({}^{\circ}\)C/min. On the other hand, each DMA test was performed in the so-called temperature sweep mode.