PSI - Issue 83

Kemal Arslan et al. / Procedia Structural Integrity 83 (2026) 218–228

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the MF2-M eliminates the initial peak force due to the gradual cell collapse and the triggering effect of secondary cells to initiate the deformation. Another difference between the MF structures lies in their deformation profiles. As seen in Fig. 8, the MF2-M presents a more stable and uniform deformation, whereas the MF1-M tends to global buckling.

Steel tube

MF1-M

MF2-M

Steel Tube

MF1-M MF2-M

300

250

200

300

150

250

100

200

Contact Force (kN)

150

50

100

0

50

0

10

20

30

40

50

60

Displacement (mm)

0

0

2

4

6

8

10

Fig. 8. The force-displacement curves and final deformation states of the structures for the impact energy of 7.2 kJ.

The force-displacement curves and final deformation profiles of the structures for the impact energy of 16.2 kJ are shown in Fig. 9. The steel tube undergoes nearly full compaction, while the deformation mode of the MF1-M transforms from global buckling to more uniform axial deformation compared with the impact energy of 7.2 kJ, and the MF2-M shows further cell densification at the midsections of each region. The steel tube presents approximately the same initial peak force as it does at the impact energy of 7.2 kJ, and it exhibits a plateau region after the initial peak force with fluctuations due to the progressive folding mechanism and a second peak force at the end due to nearly full compaction. As observed at the impact energy of 7.2 kJ, the MF structures again show a hardening response; however, in this case, with higher peak crushing forces than that of the steel tube. The MF1-M exhibits higher forces during approximately the first half of the deformation, whereas the MF2-M dominates in the second half since the densification of the secondary cells in the MF2-M forms earlier due to the higher loading rate. As in the case of the impact energy of 7.2 kJ, an initial peak force is observed in the steel tube and the MF1-M, while the MF2-M is capable of getting rid of it. To illustrate and understand the deformation patterns of the structures over time in detail, the comparative sequential deformation images of the steel tube and the MF2-M are presented in Fig. 10 for randomly selected time steps. The steel tube has local instability regions at its top and bottom sections, and folding initiates at its top section. The folds occur sequentially and are stacked one above the other along the tube length, and finally, nearly full compaction of the tube is observed. On the other hand, cell collapse occurs at the midsections of each MF cube in the MF2-M, as previously indicated; however, it initiates and propagates simultaneously. Therefore, the entire structure undergoes more stable crushing deformation through the simultaneous collapse of multiple cells rather than the sequential progressive folding, seen in the steel tube.