# In Silico Modeling the Impact of Cartilage Stiffness on Bone Tissue Stress
## 3 Numerical Results and Discussion
### Von Mises Stress in Case of 2 mm Displacement  
Von Mises stress plots in case of running (2 mm displacement) are shown in Figure 10. In the general view of the finite element model, we can see that the \"red\" zones of stress values increased both in area and in numerical values. For the model with mild cartilage stiffness, the maximum stress was 14.7 MPa (Figure 10a); for a model with moderate cartilage stiffness the maximum stress was 18.5 MPa (Figure 10b); for the model with the severe cartilage stiffness the maximum stress was 3.1 MPa (Figure 10c). The model components representing cartilage, as in the previous calculation case, turned out to be painted in blue; however, the stress value in the cartilages became higher. As the stiffness increased in the model, the stress values were 1.1 MPa for the tibia cartilage and 0.8 MPa for the femur cartilage (Figure 10a), 6.7 MPa for the tibia cartilage and 1.4 MPa for the femur cartilage (Figure 10b), and 10.1 MPa for the tibia cartilage and 3.6 MPa for the femur cartilage (Figure 10c). A significant increase in stress was also observed for the meniscus. In the case of mild cartilage stiffness, the value has risen to 4.2 MPa (Figure 10a). In the case of moderate cartilage stiffness, it was 5.1 MPa (Figure 10b), and in the case of severe cartilage stiffness--8.1 MPa (Figure 10c). Figure 8: Von Mises stress plots on contact surfaces of the bones in case of walking: (**a**) With mild cartilage stiffness; (**b**) With moderate cartilage stiffness; (**c**) With severe cartilage stiffness. The section view of the finite element model is shown in Figure 11. The area of zones with high stress values increased as expected. As mentioned earlier, such a distribution of stresses is caused by the external moment. However, from a strength point of view, the areas of the \"red\" zones (especially in the case of severe cartilage, Figure 11c), does not come close to critical stress values. Comparing the obtained values with reported yield strength of the bone (140 MPa), we find that the strength capacity under this type of loading exceeds 80 percent. Figure 10: Von Mises stress plots in case of running. General view of the model: (**a**) With mild cartilage stiffness; (**b**) With moderate cartilage stiffness; (**c**) With severe cartilage stiffness. Figure 9: Von [PERSON] stress plots on trabecular bone in case of walking: (**a**) With mild cartilage stiffness; (**b**) With moderate cartilage stiffness; (**c**) With severe cartilage stiffness. The distribution of stresses on the contact surfaces of the bone is shown in Figure 12. In the case of mild cartilage (Figure 12a), small differences in values occur on the contact surface of the femur; however, they are not too intense, so it is not advisable to consider them as stress concentrators. On the contact surface of tibia, the distribution of stresses is even more uniform, which may indicate a good functionality of the cartilage: in comparison with the first case of loading, the displacement was doubled; however, this did not cause stress concentrators. In the case of cartilage of moderate stiffness, with a supplied displacement of 2 mm, stress concentrators appear on both contact surfaces of the bones. They have a different area and are dispersed over the entire articular surface (Figure 12b). In the case of severe cartilage stiffness, stress concentrators already occupy a significant part of the contact area (Figure 12c). Again, from the strength point of view, the values themselves are safe; however, such pronounced differences in values in the long term may contribute to more intense wear of tissue. The distribution of stresses on the trabecular component of the model is shown in Figure 13. The trends described in the previous subsection are reflected, but it should be noted that in the case of higher displacement (2 mm), the resulting stress values on the trabeculae are percentage closer to the stress values on the cortical bone.