PSI - Issue 83

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

224

ܧ ൌ ൈ 100

(5)

First, the EA and SEA values of the MF tubular structures and the steel tube are compared in Fig. 7 for the impact energy of 7.2 kJ to show the relative performance of the original MF structures with respect to the modified configurations. As expected, all the structures absorb nearly the entire impact energy through effective plastic deformation. As noted in Section 2 (Fig. 3), keeping the dimensions of the MF structures the same as the steel tube results in greater mass, about 2 times more for the MF1 and about 1.5 times more for the MF2, and this causes the original MF structures to have less SEA than the other structures. Therefore, the following comparisons are only made between the steel tube, MF1-M, and MF2-M structures.

(a)

(b)

E = 7.2 kJ

Steel Tube MF1 MF2 MF1-M MF2-M

12

8000

11.25

11.18

11.04

7000

10

6000

8

7.51

5000

7.15

7.13

7.11

7.08

7.05

6

4000

5.54

3000

4

2000

Striker Kinetic Energy (J)

2

1000

0

0

0

2

4

6

8

10

12

Steel Tube MF1

MF2

MF1-M MF2-M

Time (ms)

EA (kJ)

SEA (kJ/kg)

Fig. 7. (a) The kinetic energy histories of the striker for the steel tube and the original and modified MF structures; (b) Comparison of the EA and SEA values of the steel tube and the original and modified MF structures. Fig. 8 shows the force-displacement curves and final deformation states of the structures for the impact energy of 7.2 kJ. The steel tube has a typical progressive crushing response and deformation profile of a thin-walled member. The force suddenly increases, reaching its peak at the initial stage of the deformation, until the onset of the first folding. After the first fold due to local instability, the force decreases until the onset of the second fold. Then, it increases again to create the second fold, and as the second fold initiates, the force decreases. On the other hand, the MF structures exhibit notably different crushing response and deformation profiles compared with the steel tube. Both MF structures have a lower peak crushing force than the steel tube, with MF2-M being only about 2% lower. However, the crushing force reaches its peak value at the initial stage of the deformation for the steel tube and the MF1-M, whereas the peak crushing force of the MF2-M occurs at the final stage of the deformation. Except for the initial oscillations, the MF structures do not have a decrease in the force; on the contrary, the force increases gradually, indicating a hardening response due to the cell-collapsing effect. As seen in Fig. 8, the MF structures undergo cell collapse at the midsections of the top, middle, and bottom regions. Although both MF structures have nearly the same crushing displacement, their hardening slopes differ. The MF1-M presents higher forces during most of the deformation range, while the MF2-M exhibits higher forces towards the end of the deformation due to cell collapsing-densification at the midsections. Cell collapsing is less effective in the MF1-M since it has a single cell (void) in each face of the MF cubes, and its cell walls are thicker than those of the MF2-M. Therefore, its resistance to impact load is higher than that of the MF2-M over a large part of the deformation. This is also why the MF1-M has an initial peak force, as does the steel tube, though it is more prominent in the steel tube and particularly undesirable in crash box designs, as it may cause passenger injuries due to the high deceleration. On the other hand,