## 3 Results  
The objective of numerical simulations was to model the stress state occurring in the implant and mandible model during the transfer of critical occlusal loads. The analysis focused on the implant's load-bearing capacity depending on the support conditions, while the stress results in bone tissue should be considered indicative due to the lack of mesh densification and reinforcement near the fixation plates. The results of the load-bearing capacity verification of the mandibular implant subjected to four load variants are presented in Figures 6-9. The presentation includes Huber-Mises (H-M) equivalent stresses. A threshold value of 938 MPa was introduced in the stress scale, representing the strength of pure titanium [11]. Figure 6: Simulation results for the model with full implant/bone osseointegration and support in both joints (Variant I): (**a**) Huber-Mises reduced stresses, (**b**) vestibular view with boundary condition, (**c**) lingual view with boundary condition. Figure 7: Simulation results for the model with full implant/bone osseointegration and support in one joint (Variant II): (**a**) Huber-Mises reduced stresses, (**b**) vestibular view with boundary condition, (**c**) lingual view with boundary condition. Figure 8: Simulation results for the model without implant/bone osseointegration and supported in both joints (Variant III): (**a**) Huber-Mises reduced stresses, (**b**) vestibular view with boundary condition, (**c**) lingual view with boundary condition. The analysis of the results allows concluding that Variant IV, as expected, proved to be critical due to the assumed conditions of lack of joint support on the side of the occlusal load and the absence of implant osseointegration with the bone stumps. The highest H-M stress values, excluding artifacts (edges and incoherent finite elements at the mesh connection boundaries in fixations), did not exceed 250 MPa. Figure 9: Simulation results for the model without implant/bone osseointegration and supported in one joint (Variant IV): (a) Huber-Mises reduced stresses, (b) vestibular view with boundary condition, (c) lingual view with boundary condition. The most stressed areas were the fixation plates; however, in variants I and III, they were located on the bite side joint (left), while in variants II and IV, they were on the side closer to the contralateral joint. For better comparison of variants, the values of artifacts \"A\" in singular nodes, located on sharp edges and material or mesh inconsistencies, were indicated, though these were not considered as evaluation criteria. Obtaining an exact stress solution in such areas increases the analysis cost beyond the average available computational power and is therefore not applied, although it is feasible for smaller models [6]. If the mesh in this area is not sufficiently refined to provide a physically accurate stress gradient, in such cases, it is necessary to exclude finite elements containing nodes with artifacts and, based on experience, evaluate the result in the next element not associated with the artifact. Evaluation outside the finite elements affected by artifacts showed that the stress values in the plates were similar to those in the body of the implant. However, in these areas, stress values should not be treated as precise criteria but should be based on the comparative observation of stress trend changes between loading cases. The values in the body of the implant are clearly distinct, as it was significantly more loaded compared to variants I and III. Similar stress values in the body occurred only locally due to bending around the occlusal tooth support or from artifacts at the edges of the fixation plate, whereas in variants II and IV, the highest values were found in areas where, for variants I and III, the stresses did not exceed the lowest threshold of the scale (Figure 10). Figure 10: Comparison of stresses in the critical areas of bone fixation plates and the body of the implant.