## 4 Discussion  
The results obtained in this study were in full compliance with the clinical practice and with the results from the literature [5; 9; 10; 28], as it follows. As implant osseointegration develops, the rigidity of the peri-implant bone grows, so that in the end (healing) we can observe that the cortical bone is the one that provides the rigidity and stability of the implant, and the cortical bone stress reaches highest values, placed at the level of the mandibular ridge. During the period after the osseointegration process, the displacements are lower and they are placed only in the cortical bone area [1; 29]. The oral implant insertion implies the incurrence of a microcracking field in the bone tissue at the implant-bone interface [30]. This leads to the mechanical properties' damage of the cortical bone and the decrease in the bone tissue stiffness around the implant. This is illustrated by the stress field aspect which is characterized by low stress values and their distribution extends along the implant [9]. It also finds that the bone-implant interface displacement has the highest values [10]. The limitations of the study were caused by several aspects, as it follows. Ossoeintegration is a growth-increased change of bone structure between implant surface and bone tissue, and in the change of the osseointegration were included both the structure distribution and bone quantity to reflect the stability of the dental implant. This study partially took into account the complexity of the osseointegration progress modeling. The results of the FEM analysis cannot be implemented directly in clinical situations, but one can design a model such that to simulate a real situation as well as possible [4]. Simplifications and method assumptions are, however, some limitations of studies using FEM. FEM analysis should be interpreted carefully. In most cases, the numerical studies of oral implantology, e.g., using homogeneous, elastic and isotropic materials, which remain after the loading to which they are subjected, do not reflect the real situation. Taking into account these issues, it would require very laborious calculations and complicated laboratory tests to determine the material constants for a biological material, which behaves as nonlinear, heterogeneous, etc. [31]. As the cortical layer is an important structure that affects the stress distribution and stress shielding for a dental implant, the thickness of the cortical layer should be considered as a study issue, for instance. The effect of the cortical layer would be discussed as a relationship between the osseointegration progress and the biomechanical influence. On the other hand, to work with a simpler model, we adopted damaged mechanical properties for the entire cortical bone layer in the geometric model for the initial period after implant surgery, although for a more realistic approach, only a smaller area around the implant. Figure 8: Distribution of the safety factor for the minimum E (**a**) and maximum E (**b**). We used the von Mises stress as a stress representation, considering it rather a convenient one, rather than an appropriate one, especially for bone and ceramic materials that are not at all ductile as the von Mises criterion requires. Moreover, as the trabecular bone possesses weaker mechanical properties, it plays a secondary role in approaching the progress of osseointegration from a biomechanical point of view, so that the effect on the calculations would be negligible. The problem domain could be considered small, but enough to have a correctly defined problem. The domain is chosen correctly, as long as the interaction of the neighborhood does not exist. That was proven in our model by the results and can be observed in the figures representing the stress, for instance. The fact that we obtained almost zero stress at boundaries shows the correctness of the choice of the domain, as well as of the boundary conditions. The influence of implant surgery is small and does not affect large areas of bone.