PSI - Issue 83

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

220

௡ ൌ൬ 2 2 0 7 ൰ ௡ ଴

(1)

where n is the order of the MF cube, and V 0 is the volume of the solid cube. Fig. 1b represents the volumetric decrease of the MF cube in terms of fractal order.

(a)

(b)

100

Second-order MF cube

First-order MF cube

75

50

25

Volumetric Decrement (%)

0

0

1

2

3

4

Fractal Order

Fig. 1. (a) The first- and second-order MF cube; (b) The variation of volumetric decrease in the MF cube in terms of fractal order.

In this study, the first- and second-order MF tubular structures (MF1 and MF2) were considered for the analysis. Considering the MF cube as a unit cell, the MF tubular structures were generated by three vertically arranged MF cubes, as seen in Fig. 2. The main objective of this study is to determine the dynamic axial crushing behavior of the MF tubular structures and to compare their crashworthiness performance with that of a conventional steel tube of equal mass. Therefore, the dimensions of the removed cubes in the MF structures were modified to obtain approximately equal mass with that of the steel tube, as shown in Fig. 3. The MF1-M and MF2-M represent the modified structures. The materials for the steel tube and the MF structures are HSLA-350 steel (7850 kg/m 3 ) and AlSi7Mg alloy (2650 kg/m 3 ), respectively. All the structures have dimensions of 60 mm × 60 mm × 180 mm.

(a) Steel tube

(b) MF1

(c) MF2

Fig. 2. The steel tube and the MF tubular structures.