## 5 Results and Discussions
### Impact Force Time-History  
When a car collides with a column, contact force, also known as impact force, is generated at the collision point. Figure 11 shows the impact force-time histories generated during car-column crushes at various car-crashing velocities. The typical impact force-time histories for car crushing velocities of 35 and 40 km/h are shown in Figure 11a. There are stages of impact events. The first stage is soft impact, where the soft frontal part of the car absorbs impact energy by deformation. The second stage can be termed as hard impact, where the car engine gets in contact with the column and pushes it laterally. The last stage (stage 3) is termed as the unloading or rebounding stage of the impact event. As anticipated,  
Figure 10: Column (C400) damage contour for car impact velocity of V = 40 km/h: (**a**) impacted by Economic and (**b**) Explorer. Figure 9: Column (C300) damage contour for car impact velocity of V = 40 km/h: (**a**) impacted by Economic and (**b**) Explorer. the maximum impact force (PIF) increases with the increase in car-crashing velocity, as shown in Figure 11b. This is because of the relationship between kinetic energy and impact velocity for a constant mass. In Figure 11b, it can also be seen that as the impact velocity increases, the duration of peak impact force decreases. The structure may not be able to respond to this short-duration impact force. For this reason, the concept of equivalent static force is developed. In FE analysis, it was found that up to a car-crashing velocity of 20 km/h, the soft frontal part of the car is damaged and the hard part of the engine box does not come into contact with the column. For this reason, the generated impact force remains below 160 kN. When the crashing speed is increased to 30 km/h and above, the hard part of the engine box comes into contact with the column. As a result, the generated impact force becomes higher than 400 kN, as can be seen in Figure 11b. Figure 12 shows the relationship between peak impact forces (PIFs) and the car-crashing velocity. Rates of PIFs increase linearly until the impact speed reaches 20 km/h. At this crashing speed limit, the car experiences deformation in the soft frontal part (distance between the car engine and bumper). In addition, the spring stiffness in this area of the car is nearly constant. As a result, up to a collision speed of 20 km/h, the correlations between PIFs and vehicle speed are almost linear. In contrast, PIF values are increasing in power at twice the speed when the car-crashing speed is from 30 to 60 km/h. Over this impact speed range, the car engine, which is a rather rigid portion of the passenger car, collides with the column. As a result, when the collision speed exceeds 30 km/h, there is a significant increase in impact force. For comparison reasons, in addition to C300 and C400, two more column sizes (C500 and C600) were studied. The size of the cross-section of the column affects the PIF value, as illustrated in Figure 12. Up to a car crushing velocity of 30 km/h, the difference in PIF curves for different column sizes is negligible. Meanwhile, as the column size was reduced, the PIF values increased slightly at car-crashing speeds ranging from 30 to 60 km/h. For example, at a car-crashing velocity of 40 km/h, column C400 produced higher PIFs than C500 and C600. This is due to the fact that reducing the column size reduces the contact area of the crashing point, which results in the deeper penetration of the column inside the vehicle's frontal part. It should be noted that the impact force increases as the penetration depth increases. This pattern indicates that the stiffness of a  
Figure 11: Impact force-time histories at the event of car–column collision: (**a**) typical impact force-time history showing different stages of the impact event; (**b**) impact force-time histories for different car crashing velocities. vehicle is not constant all over the length of the frontal part.