## 3 Results  
The FEM analysis usually calculates von Mises stress, i.e., equivalent stress, a scalar quantity that characterizes the amount of stress and that is very important in formulating criteria of damage, plasticity, fracture, etc. In this study, this was used to evaluate the effect of loading in the dental implant, prosthesis and surrounding bone. The following will present the results of numerical calculation by FEM by figures representing von Mises stress, displacement and safety factor. In the figures below, the most favorable areas are the minimum values of stress or displacement, while areas with the greatest damage and high risk are characterized by higher values. The safety factor is the ratio of admissible limit values and actual FEM calculated values of stress. The admissible limit values of stress are specific to each material and adopted in specific conditions  
Figure 5: (**a**) The boundary condition; and (**b**) applying axial and non-axial forces. described in the literature. The figures representing the safety factor may indicate the necessity of appropriate design solutions adoption that eliminates risky zones that have a low safety factor. In this study, we performed the calculations for different values of cortical bone Young's modulus, E. The corresponding values of Young's modulus, E lower (E = \(0.2\times 10^{8}\) MPa) refers to the immediate phase after the implant insertion, which simulates a weaker biomechanical implantation medium, more damaged. Increasing values for E means that a gradual osseointegration occurs. Achieving a value of E of intact bone is considered to signify the osseointegration process's completion. We conducted two sets of calculations and summarized the results in the following two tables: Table 3 corresponds to set no.1, when the axial force is 20 N and the oblique force is 20 N, whereas Table 4 corresponds to the set no.2, when the axial force is 30 N and the oblique force is 30 N.  
Tables 3 and 4 present the values of the main quantities calculated during the various stages of osseointegration as simulated in our numerical model, namely considering the damaged properties of cortical bone immediately after implant surgery, and further, as osseointegration progresses, cortical bone becomes stronger, so that in the end its mechanical properties are identical to those of intact bone. The total displacement or resulting displacement \(u_{res}\) is calculated by the formula:  
\[u_{res}=\sqrt{u_{x}^{2}+u_{y}^{2}+u_{z}^{2}}\]  
where \(u_{x}\), \(u_{y}\), \(u_{z}\) are the displacements along the axes \(x\),\(y\),\(z\), while the factor of safety (FOS) is calculated by the ratio allowable stress/calculated stress. The calculated stress can be any considered stress: von Mises (the most used), Tresca and others. As a rule, the calculated stress is that corresponding to a failure criterion. We used von Mises and Tresca criterion and the differences were negligible. We present in this paper the values obtained by the von Mises criterion. The following figures present the cases of maximum values of E (\(8\times 10^{10}\) Pa), corresponding to a full osseointegration and the case of minimum values of E (\(0.2\times 10^{10}\) Pa) corresponding to a time immediately after implant insertion, and therefore an early osseointegration as well. Thus, Figure 6a,b represent the von Mises stress distribution for E minimum (a) and maximum (b), respectively.