PSI - Issue 83

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

227

M has relatively more stable crushing efficiency. Moreover, the MF2-M also exhibits more stable and uniform axial deformation since the MF1-M shows a global buckling mode for the impact energy of 7.2 kJ.

(a)

(b)

E = 7.2 kJ

E = 16.2 kJ

400

300

375.65

350

254.94

249.42

329.10

250

300

207.15

262.24

200

181.33

250

174.18

231.89

226.45

200

150

129.91

150

100

120.74

87.54

69.83

100

68.81

50.96

61.73

50

46.04

50

0

0

Steel Tube

MF1-M

MF2-M

Steel Tube

MF1-M

MF2-M

PCF (kN)

MCF (kN)

CFE (%)

PCF (kN)

MCF (kN)

CFE (%)

Fig. 11. The performance indicators of the structures: (a) 7.2 kJ; (b) 16.2 kJ.

6. Conclusions This study aims to investigate whether Menger fractal tubular structures could serve as a crashworthy alternative to conventional tubular structures under dynamic crushing loads, performing finite element simulations, with particular emphasis on the force-displacement response, energy absorption characteristics, crushing efficiency, and deformation stability. The numerical model was first validated against relevant results available in the literature, and both first- and second-order Menger fractal configurations were considered in the analysis. The dimensions of the removed cubic elements were adjusted to obtain fractal structures with approximately the same mass as the reference steel tube, thereby enabling a more meaningful comparison of energy absorption performance. The results demonstrate that Menger fractal-based architected geometries can significantly enhance energy absorption performance through their hierarchical cell-driven deformation mechanisms. Among the investigated configurations, the modified second-order structure (MF2-M) exhibits the most favorable overall response, owing to its more stable and uniform axial deformation mode, its progressive force increase associated with simultaneous cell collapse and densification, and its ability to eliminate the undesirable initial peak crushing force observed in both the steel tube and the MF1-M. Although the MF1-M shows competitive energy absorption capability, its tendency toward global buckling and the presence of an initial peak force indicate lower crushing stability. Unlike the steel tube, which deforms through a sequential progressive folding mechanism, the fractal structures exhibit a hardening type response governed by simultaneous cellular collapse and densification. Overall, the preliminary findings suggest that Menger fractal-based structures, particularly higher-order configurations, offer a promising alternative to conventional energy absorbers and have strong potential for advanced crashworthiness applications in automotive, aerospace, and impact protection systems. References Abedrabbo, N., Mayer, R., Thompson, A., Salisbury, C., Worswick, M., van Riemsdijk, I., 2009. Crash response of advanced high-strength steel tubes: Experiment and model. International Journal of Impact Engineering 36(8), 1044–1057. Abramowicz, W., Jones, N., 1984. Dynamic axial crushing of square tubes. International Journal of Impact Engineering 2(2), 179–208. Abramowicz, W., Jones, N., 1984. Dynamic axial crushing of circular tubes. International Journal of Impact Engineering 2(3), 263–281.