## 4 Discussion  
The present study focused on the evaluation of the stress patterns associated with distal extension removable partial dentures when submitted to static bilateral and homogenous loading of the artificial acrylic teeth. Three models were compared, one featuring a conventional removable partial denture (CONVENTIONAL RPD) and two featuring implant-assisted removable partial dentures, with the implants placed either in the proximal portion (IARPD PM) or in the distal portion of the dentulous areas (IARPD MO). Although some studies addressing the finite element analysis of implant-assisted removable partial dentures have been published [17; 18; 33; 34; 35; 36], the present work is, according to our knowledge, the first non-linear analysis presenting a three-dimensional comparison with conventional extension base removable partial dentures and also the first evaluating the effect of implant position on stress and strain on a patient-based 3-D mandibular model. The 3-D nature of the CONVENTIONAL RPD model of this study provided a better understanding of the mechanics of the conventional extension base RPDs when occluding the acrylic portion of the prosthesis. Moreover, the patient-based construction method together with the geometric complexity associated with the model and the specific material characteristics also allowed pairing with the clinical phenomena taking place in Kennedy class I denture wearers, even though no intra-oral or clinical measurements were taken as part of a validation procedure. The similarity of the tissueward displacements of the denture base at the CONVENTIONAL RPD model with those visually detected by [PERSON] et al. [37] and [PERSON] et al. [38] contributes to the proximity of the FEM results and those reported in clinical and experimental studies. It is the case of the maximum vertical displacements of the framework and denture base of 0.5 mm (500 \(\upmu\)m) observed in the CONVENTIONAL RPD model that is in line with the 400 \(\upmu\)m reported by [PERSON] et al. [39] for the posterior portion of unilateral extension RPDs and superior, but concordant, with the 250 \(\upmu\)m registered for a similar maxillary prosthesis [40]. The pattern, the consistency and the magnitude of the displacements registered to the buccal, mesial and apical directions were not unexpected for a prosthesis with non-rigid retainers. The clasp systems applied to the abutment teeth are usually designed to have a stress-releasing effect, allowing the tissueward rotation of the RPD bases around the axis passing through the occlusal rests, without torqueing the clasped teeth. When the distal extension base is loaded, the occlusal rests of the prosthesis act as hinge support, resisting vertical and horizontal loads, but are unable to resist to the moment generated by the vertical loads. Therefore, the prosthesis and tooth ensemble can be interpreted as a Euler-Bernoulli beam problem [41; 42], represented in Figure 8.  
In the correspondence of mandibular Kennedy class I patients rehabilitated with CONVENTIONAL RPDs to a classic mechanics problem, the angle of rotation of the prosthesis can be related to the cross-section rotation angle (\(\theta\)) of a cantilever beam and the vertical displacements, in any cross-section of the acrylic, can be given by the deflection of the Euler beam at any point in the \(y\) axis by [42]: \(w(y)=qy^{2}/24 EI\big{(}y^{2}+6\ell^{2}-4\ell y\big{)}\), where \(q\) is the load applied, \(EI\) is the beam bending stiffness and \(\ell\) is the total length of the beam. Similarly, the vertical displacement of the acrylic base in the CONVENTIONAL RPD depends on the axial position of the acrylic section and increases as we move away from the support at the occlusal rests. This effect explains the increasing vertical displacement of the CONVENTIONAL RPD from the mesial to the distal portion of the acrylic base, where the maximum displacement is registered. This interpretation of the variation of displacement can also be applied to the IARPD PM model.