# Simulation Analysis of Knee Ligaments in the Landing Phase of Freestyle Skiing Aerial
## 3 Results
### Finite Element Simulation Results  
Combined with the three landing conditions described in Section 3.1, the external constraint conditions of the model were adjusted and finite element analysis performed on the ACL, PCL, MCL, and LCL. Time-stress curves were calculated according to the results of the analysis.  
In forward landing (Figure 7), deformation of the front of the skis was minimal with elastic force in the balancing stage that could be ignored. According to the results of the analysis, due to the tendency of the tibia to move rearwards, the position of stress concentration was at the lower end of the posterior bundle of the ACL with a maximum stress value of 4.01 MPa. The position of stress concentration on the PCL was at the upper end of anterior bundle, with a maximum value of 6.81 MPa. The position of stress concentration on the LCL was in the middle, with a maximum stress value of 1.60 MPa. Maximum stress on the MCL was 1.96 MPa, with stress concentration in the middle and on the lower section. As the center of gravity was adjusted rearwards, the medial meniscus became squeezed, resulting in a region of stress concentration in the middle of the MCL.  
In neutral landing (Figure 8), the skis were parallel to the landing slope and so elastic force in the balancing process was ignored. Although the impulse from the femur had a forward component at the tibial plateau, the tibial plateau also moved synchronously with flexion of the knee joint and so relative motion of the femur and tibial plateau were not apparent. According to the results of the finite element analysis, the position of stress concentration was at the lower end of posterior bundle of the ACL with a maximum stress of 3.16 MPa. Stress was concentrated in the upper part of the posterior bundle of the PCL to the lower end of anterior bundle with a maximum stress of 6.61 MPa. Maximum stress on the MCL was 2.49 MPa which was concentrated in the middle region. Stress concentration was in the middle of the LCL, to a maximum stress value of 1.67 MPa.  
Figure 6: Force curve of a single knee joint in the balancing phase.  
During backward landing (Figure 9), elastic force from deformation of the tail of the skis provided an additional elastic force. Deformation of skis extended the duration of the balancing phase and reduced vertical impact force on the tibial plateau. According to the results of finite element analysis, maximum stress was experienced at the lower end of the posterior bundle of the ACL, at 4.52 MPa. On the PCL, stress was concentrated from the upper end of the posterior bundle to the lower end of anterior bundle, with a maximum value of 6.99 MPa. The middle of the MCL and LCL endured maximum stress, with values of 3.46 MPa and 1.39 MPa, respectively.  
Figure 8: Stress distribution and stress–time curve of the ligaments in neutral landing.  
Figure 7: Stress distribution and stress-time curve of the ligaments in forward landing.  
Simulation of stress at the tibial plateau are displayed in Figure 10, where the position of stress concentration was obvious. When the tibia moved rearwards relative to the femur, as in forward landing (Figure 10a), a region of stress concentration was observed at the front of the menisci and the middle of the medial meniscus. When the tibia is relatively immobile, such as during neutral landing (Figure 10b), the position of stress concentration was in the middle of the medial meniscus and the center of the lateral tibial cartilage. As the tibia moved forward relative to the femur such as in backward landing (Figure 10c), stress became concentrated in the middle of the medial meniscus and central position of the lateral tibial cartilage. Compared with neutral landing, the position and value of stress concentration in backward landing were relatively small and located towards the rear.