## 1 Introduction  
Nickel-Titanium (NiTi) shape memory alloys (SMAs) belong to the group of metallic alloys known as smart functional materials. Their functional behaviors cover mainly superelasticity, shape memory effect, and shape memory actuation. Superelasticity is related to the cyclic recovery of large thermo-elastic transformation strains on unloading, the shape memory effect is correlated to the recovery of large thermo-elastic transformation strains upon heating, and shape memory actuation describes the cyclic recovery of large thermo-elastic transformation strain upon heating under an external bias load [1, 2]. The superelastic property of NiTi shape memory alloys is based on the induction of phase transformation during mechanical loading and has recently been shown to arise from its microstructure [3]. Their promising biocompatibility [4] allows for applications in the design of many novel biomedical devices and implants [5, 6, 7]. Prior to entering costly prototype fabrication for such novel applications, Finite element analyses could enhance understanding of their physical responses under biomedical loading scenarios [8, 9, 10]. A novel application for NiTi may be seen in dental implant prosthodontics for compensating shortcomings with respect to the parallelism of supporting implants as well as transfer inaccuracies between the patient situation and the laboratory working cast. The use of two dental implants in the interforaminal region and corresponding attachments for stabilizing complete dentures (Figure 1) is a frequently applied [11] and cost-effective treatment option [12], which is well documented in the literature. The use of prefabricated attachment systems such as locators (Zest Dental Solutions, Carlsbad, CA, USA), instead of utilizing individually fabricated attachments such as telescopic crowns or bars, drastically reduces the initial treatment costs in the edentulous mandible [13; 14]. Several studies have shown that maintenance frequency [15] and associated costs [16] in such restorations are quite high, equaling or even exceeding initial treatment fees [14; 17]. In particular, loss of retention and fractures of the prostheses in the area of the attachment constitute the two main technical complications [18; 19]. From a biomechanical perspective, the non-parallelism of supporting implants and transfer inaccuracies between the clinical and the laboratory situation may be seen as major reasons for wear phenomena occurring at the retentive interface of the attachment system [20; 21]. This assumption is supported by clinical studies showing that inter-implant angulation resulted in a greater amount of wear of the attachments used [22; 23]. Two in vitro studies showed that retentive forces deteriorated faster when the attachments were supported by angulated implants as compared to implants with a strictly parallel orientation [24; 25]. Coatings of the male attachment parts [22], as well as the use of different plastic inserts in the female parts, seemed to have only a minor effect on wear phenomena. Compromised clinical results have been reported for maxillary full arch restorations supported by two to four implants arguing that potentially detrimentally high levels of moment loading transferred via a stiff attachment system were a co-factor in these cases [26; 27]. To compensate for the non-parallelism of implants and transfer inaccuracies, as well as to avoid excessive moment loading of supporting implants under dynamic masticatory loading, an attachment system has recently been described [28] incorporating a superelastic Nickel-Titanium (NiTi) element (Figures 2 and 3).