# Assessment of Contact Pressures between a Mandibular Overdenture and the Prostodontic Area
## 2 Materials and Method
### Finite Element Method Model  
The particular parts described in the previous section were assembled in order to obtain the final finite element (FE) model of the overdenture prosthesis. Within the FE framework, linear 4-node elements [14] were assigned to the housing and linear 8-node brick elements [15] with reduced integration [16; 17; 18; 19] to the prosthesis, bar, implants, clips, and edentulous mandible. The FE mesh was created to obtain a regular node pattern. The total number of model elements amounted to approximately 470 thousand, with the total number of the unknowns around 440 thousand. In order to ensure realistic motion of the implant construction, a special FE technique was applied. Kinematic constraints were assigned to contact surfaces between the implants, bar, and clip matrices; thus, translational and rotational movements between the parts were excluded. No friction or material damping was assumed. A similar stiff connection (kinematic constraints) approach was used between the edentulous mandible and implant pillars; therefore, we considered the possible displacement between the implants and cortical bone (full implant-bone osteointegration) to be insignificantly small. In order to avoid numerical difficulties due to mismatched FE meshes of the mandible and resin prosthesis, additional kinematic constraints were introduced, namely embedded elements [20]. The translational constraints provided (in physical meaning) well-fitted surfaces of the upper mandible and lower prosthesis and (in the mechanical sense) full compatibility of deformation fields. A realistic condition of contact between the touching bodies was ensured. On the prosthesis mandible surface, the stiff (Herz-type) contact with no friction was defined [21; 22]. Contact pressure depends on the normal forces between touching bodies; no influence of tangential forces is included. The separation of contact surfaces is possible due to a progressive deformation of bodies. The coefficient of tangential friction between the prosthesis and mucosa of the mandible is equal to zero under the assumption that saliva is present. Thus, the saliva lubrication gives an ideal slip between the surfaces, i.e., tangential pressures are equal to zero. There was no formal contact defined between the bone and the implant or the implant and the bar. The interactions between those bodies were modeled by tying them to the displacement (see Abaqus FEA documentation). Those connections were modeled as infinitely stiff. In this paper, classical isotropic linear elastic material models were used. Table 1 presents the adopted material parameters (the Young modulus, E; and the Poisson's ratio, v); the values were taken from the literature. In the research, the influence of stiffness on the bar clips was also investigated; therefore, three different Young moduli were used (1.5 GPa, 2.5 GPa, and 3.5 GPa) based on the commercially used materials. The essential part of the numerical model description is the definition of the applied loads and the boundary conditions. Based on the literature and to obtain a realistic outcome of the modeled biomechanical system, we adopted a representative vertical force. The value of the force is equal to 200 N [29; 30]. Three unsymmetrical positions of the occurrence of the force were chosen (three load cases). In each case, force is distributed on the surface of the particular tooth, mimicking occlusion pressure on a single tooth while eating. The canine, central incisor, and first molar were selected, according to Figure 6. The boundary conditions are an integral part of the FE model. In the presented paper, the nodes of the bottom surface of the edentulous mandible were restrained, as shown in Figure 6.  
In the final part, finite element method calculations were performed in Abaqus FEA software (Dassault Systems). Nine linear stress analyses (three load cases, Figure 6, multiplied by three bar clip materials, see Table 1) were submitted.