# Mechanical Strength Study of a Cranial Implant Using Computational Tools
## 3 Results and Discussion  
### Case Study I  
The maximum values of von Mises stress and displacement were nearly identical in all models except the one with five screws, which delivered higher peak stresses nearby the placed screws. As expected, high stresses were verified in the zone where the impact occurs. Furthermore, the holes situated near the impact zone led to increased stress concentrations near these holes, which is explained by the principles of fracture mechanics. Another element that is implicit in these results is that the maximum von Mises stresses verified in the model are in different zones depending on the number of the screws. For the models with five, six, and seven screws, the maximum von Mises stress was in the implant near the interface between implant and skull, while for the models with eight and nine screws, the maximum von Mises stress was in the region nearby the impact zone. This is a piece of clear evidence that, as expected, the number of screws is a parameter that may significantly change the stress field on the regions nearby the interface between implant and skull. The higher the number of screws, the lower the stress concentrations in the interface. Figure 4 contains the von Mises stress fields of the different models. When it comes to the displacement, Figure 5 shows that it is impossible to minimize the maximum displacement in the impact zone, whatever the number of screws in use. This happens because, in the region where the impact occurs, the influence of the screws and the interface contact can be neglected, mainly because it is a very central zone of the implant. However, significant differences were verified in the displacement of the interface between implant and skull; the higher the number of screws, the lower the displacement verified in this region. The graphic of Figure 6 exhibits the maximum values of von Mises stress obtained for the implant and the skull, respectively, for the various models studied. For the implant, and as mentioned early, the maximum stresses were obtained near the interface between implant and skull for the cases when five, six, and seven screws were used. In contrast, the maximum von Mises stress was obtained near the impact region in the other two cases. Recording the material constitutive behavior, the initial yield strength at a quasi-static  
Figure 4: Von Mises stress fields for the models with different screws configurations [MPa]: (**a**) configuration with five screws; (**b**) configuration with six screws; (**c**) configuration with seven screws; (**d**) configuration with eight screws; (**e**) configuration with nine screws. strain rate was 132 MPa. This stress value was outdated only in the model with five screws, which reinforces the reasoning presented. In short, two critical zones can be identified: the region nearby the impact and the interface between the implant and skull. Since changing the number of screws does not modify the behavior of the central zone of the implant where the impact occurs, the key for choosing the best option is to consider the von Mises stress and displacement near the interface between bone and implant. The models with six, eight, and nine screws are preferable regarding the von Mises stress. However, the significant displacements verified for the model with six screws ranging from the central zone to the interface are a possible explanation that the stresses are lower in these regions and make this model unusable. Since the models with eight and nine screws provide identical solutions and, as mentioned  
Figure 5: Displacement field for the models with different screws configuration [mm]: (**a**) configuration with five screws; (**b**) configuration with six screws; (**c**) configuration with seven screws; (**d**) configuration with eight screws; (**e**) configuration with nine screws. Figure 6: Maximum von Mises stress verified on the implant and the skull for the various models. earlier, the lower the number of screws, the better, the model used in the further analysis is the one with eight screws.