## 2 Materials and Methods
### Numerical Models  
Each one of the three model files was imported into the ADINA system for linear and nonlinear finite element analysis (ADINA AUI version 9.3.1, ADINA R&D Inc., Watertown, WA, USA) including the following bodies: cortical bone and non-abutment teeth; individualized abutment teeth (34; 33; 43; 44); individualized periodontal ligaments of the abutment teeth (34; 33; 43; 44); cancellous bone; soft tissue (3 rd and 4 th quadrants); metal framework of the removable partial denture (including 2 matrices in the case of the Models IARPD PM and IARPD MO); acrylic denture bases with the missing teeth (3 rd and 4 th quadrants); implants and ball attachments (Models IARPD PM and IARPD MO); loading plate. In both numerical models of the IARPDs the implants were assumed bonded with cancellous and cortical bones, simulating complete osseointegration. Moreover, the glue mesh option was also used to model the attachment of other pairs of components to remain perfectly bonded together, such as the inner surfaces of the cortical bone and the outer surfaces of the cancellous bone or the inner and outer surfaces of the periodontal ligament and the teeth and bone, respectively. Nevertheless, the Lagrange multiplier technique was used to impose contact constraint conditions, assuring the possibility of relative motion between the surfaces of the following contact pairs: implant/soft-tissue; soft-tissue/acrylic; soft-tissue/framework; framework/teeth; teeth-premolar/teeth-canine; teeth/cortical; and acrylic/implant. Assignment of the mesh density to the solid bodies of each model was made by promoting equally spaced subdivisions of the bodies using the desired element edge length. In some cases, the subdivision of specific faces was recalculated with smaller lengths to promote a more refined mesh in areas requiring higher precision of the results. Table 1 presents the mesh density attributed to each body and the refinement areas. Discretization of the domains was assured by the Delaunay free-form meshing algorithm to generate 8-node hexahedral (brick) elements with mixed interpolation formulation (displacement and pressure-based), considering a constant pressure (1 degree of freedom). For elements with linear elastic material properties, additional displacement degrees of freedom were allowed by selecting the incompatible modes option. The total number of nodes and elements of each model are detailed in Table 2.  
### Numerical Models  
This study assumed isotropic linear elastic properties for the cortical and cancellous bones, teeth, framework, acrylic, implants, ball attachments and loading plate but not for the oral soft tissues. These, i.e., oral mucosa and periodontal ligament, were modelled considering non-linear hyperelastic properties. Several models have been proposed to model the hyperelastic effects of biological soft tissues [21]. Nevertheless, the approximation proposed by [PERSON] [22; 23] provides the closest matching to experimental data and was herein considered for the modelling of both the oral mucosa and the periodontal ligament. The mechanical properties of the materials displaying a linear force-displacement relationship as implied in [PERSON]'s law are presented in Table 3.  
The nonlinear constitutive models of the oral mucosa and of periodontal ligaments were derived from a strain energy density function (SEDF), W, which is defined per unit of reference volume (ADINA R&D 2012). This model is based directly on principal stretches instead of invariants to determine the deviatoric strain energy function (WD) and accounts for volumetric compressibility by the inclusion of a term for the volumetric strain energy density (ADINA R&D 2012). In the case of the oral mucosa, the strain energy density function was set based on the fitting of a uniaxial stress-strain curve from experimental data reported by [PERSON] et al. in 1972 cited in [PERSON] et al. [30], using a Ogden 9 th