## 3 Results
### Axial Crushing Experiment  
To verify the crushing performance of the CAP produced by this successive partial rubber-bulging method, a crushing test was conducted using an auto-cupping machine (AG-300 KAG, Shimadzu Corp., Kyoto, Japan), as shown in Figure 11. When a compressive load was applied in the axial direction and compression deformation progressed to a certain extent, a naturally formed partial wall structure (PWS) that intersected at right angles the central axis of the CAP was observed. Through mutual support of this PWS, the crushing deformation could be sustained for a long crushing compression distance. This collapse behavior is considered beneficial for improving the crashing energy absorption. The FEM was used to simulate the collision deformation process of the CAP, to verify its crushing performance, as shown in Figure 11. A numerical simulation model is shown in Figure 12. Rigid plates were attached to the upper and lower ends of the CAP, and an evenly distributed displacement load was applied on the upper plate along the axial direction. The CAP was simulated by using four-node curved S4R shell elements. Surface-surface contact was applied between the impacting rigid plate and the CAP. The friction coefficient was taken as 0.3. In order to save computing resources, different mesh sizes, such as 10 mm \(\times\) 10 mm, 8 mm \(\times\) 8 mm, 6 mm \(\times\) 6 mm, and 4 mm \(\times\) 4 mm, were tried to check the convergence of the finite element model. The results show that a mesh size of 4 mm \(\times\) 4 mm can fully meet the requirement of simulation accuracy. Combined with the actual experimental conditions, several simulations were run to conduct a convergence test, and a distance for the displacement load of 180 mm was determined. The dimensions of the numerical simulation model were the same as those shown in Figure 3. The total number of nodes was 3001, and the total number of elements was 2867. The samples used in this crushing experiment were the same as those in the previous processing and so were the material properties. By using a rubber-bulging method, samples of the CAP were manufactured. In the crushing experiments, five samples were tested, and the error rates of the other samples were within 5%. The most similar one was picked as a result in this research. Comparison of the numerical simulation and experimental results for the crushing load as a function of crushing deformation is shown in Figure 13. The numerical analysis shows that, as the compression deformation progressed, PWS were naturally formed, which intersected at right angles along the central axis. This is consistent with the experimental results, which confirmed the general accuracy of the collapse experiment. Figure 11: Photographs showing crushing experimental configuration and various crushed states of the CAP during its deformation. According to Figure 13, in the initial stage of crushing deformation, as the axial compression force continued to increase and the initial buckling occurred, an initial crushing peak load appeared. Thereafter, crushed wrinkles appeared in the bulging part and the unformed part, which acted as inducement to each other during the process. Owing to the mutual support of the subsequently created PWS, the crushing load of the CAP stabilized during this period at about 25 kN. When the crushing deformation distance exceeded 158 mm, the crushing load again increased, when the PWS formed in each stage started to contact each other. The displacement-crushing-load diagram of Figure 13 shows almost the same characteristics as those of the ideal crash absorber shown in Figure 1. In addition, the crushing load increased again in the latter half of the crushing deformation process. To explain this phenomenon in detail, corresponding photos from the experiment will be used for discussion, as shown in Figure 14.  
Figure 12: Model used for simulation of the crushing experiment of the CAP, and its states during deformation.