## 4 Discussion  
The results in Figure 9 reveal that in the case of non-parallelism of supporting implants (Figure 9b), the level of induced axial stresses slightly increases at both Oral and Buccal surfaces, as compared to the situation of parallel aligned implants (Figure 9a), which results in higher martensite volume fraction evolution. In the non-parallel state (Figure 9b in comparison to Figure 9a) the stress also (thus, the stress-induced martensite) concentrated in a small region where the male part and shaft were joined (Figure 9(b6)). To overcome such stress concentrations and thus, very local cyclic phase transitions, alternative design 1 (Figure 5c) was examined in the non-parallel state (Figure 9c). Due to the increase of the contact area between the shaft and male attachment part, the concentration of stress and volume fraction could be reduced, resulting in a larger active transforming  
Figure 11: The non-parallel case while using titanium instead of NiTi for the shaft: (**a,b**) the compressive stresses and strains at the _Oral Surface_, respectively; (**c,d**) the tensile stresses and strains at the _Buccal surface_, respectively. One can compare (**a–d**) here, to Figure 9(b1,b2,b4,b5), respectively, where the same state has been presented while using NiTi instead of titanium. Figure 10: Stress-strain response corresponding to the case studies from Figure 9a–d. (**a**) reference case study (parallel), (**b**) misaligned, (**c**) misaligned alternative design 1, (**d**) misaligned alternative design 2. The data represent points in the _Buccal Surface_ (black curve) or the _Oral Surface_ (red curve) where the maximum volume fraction of martensite evolves. The blue curve in (**b**) represents the associated response of the case study in which titanium was used instead of NiTi in the misaligned state, for comparative purposes (Figure 11). region in the NiTi shaft. To further increase the deformability of the SMA shaft, and to have enhanced control over the location of the maximum stresses for arbitrary misalignments of supporting implants, the second alternative design was tested, where the SMA shaft was necked in the middle (Figure 6d). This minor reduction of shaft diameter triggered higher stress levels at both Oral and Buccal surfaces, which indeed enabled the system to accommodate higher strains at constant stress by the evolution of a higher volume fraction of martensite under an equivalent loading state. The gradual increase of the evolved (compression- and tension-induced) detwinned martensite from the reference geometry to the optimized design number 2, is well illustrated in Figure 10.  
Under 150 N vertical force, the maximum stress at both shafts could reach very high values close to the yield point of titanium (~1100 MPa) (stress situation Figure 9(b1) vs. Figure 11a, and Figure 9(b4) to Figure 11c), while the evolved strains were equivalent (strains in Figure 9(b2) vs. Figure 11b, and Figure 9(b5) vs. Figure 11d). Comparing the results in Figure 11a,b and Figure 11c,d with the case represented in Figure 9(b1,b2) and Figure 9(b4,b5), respectively, demonstrated the effectiveness of the application of SMA shafts in the attachment system to accommodate high deformations, whereby the martensitic phase transformation prevented overstressing. The use of SMA potentially also reduced the transmitted (reaction) force to the surrounding implant and bone. To better visualize this effect, Figure 12 compares the reaction stresses on the inner surface of the titanium implants (for a non-parallel state), showing a gradual decrease from the case where the male part was made of titanium to the alternative design 2. This higher reaction force may be seen as a cause for wear phenomena at the male/female interface of current attachment systems. It can be anticipated, that the use of SMA reduces wear phenomena, thereby decreasing maintenance costs [20; 21; 22; 23]. Currently, it is not possible to link the simulations carried out to the anticipated clinical performance of the novel attachment system.