Design and study of crashworthiness for square vicsek fractal hierarchical multicellular tubes under axial compression

Through extensive examination of thin-walled structures, the efficacy of enhancing the crashworthiness of thin-walled tubes via layered structures has been confirmed. In this study, we introduce a novel design called the square Vicsek fractal hierarchical multicellular tube (SVFHMT), which integrates principles from fractal science, specifically Vicsek fractals. Unlike conventional layered structures that align along a single direction, our design incorporates layers evenly distributed at five positions throughout the structure, resulting in a more uniform material distribution compared to traditional layering methods. In this paper, the verified finite element model is used to analyze the crashworthiness of the structure, and the effects of levels, wall thickness, wall thickness ratio of different levels and height to diameter ratio on the crashworthiness of the structure are discussed. The mean crushing force (MCF) of SVFHMT is predicted by Simplified Super Folding Element theory. Our findings highlight the significant influence of layering, wall thickness, and ratios of wall thickness between layers on the crashworthiness of the structure. Specifically, for structures of equal mass, the energy absorption of second-order SVFHMTs and third-order SVFHMTs demonstrates substantial improvements compared to square nine-cell tubes, with increases of 51.05% and 91.70%, respectively. Moreover, when maintaining equal mass for second-order SVFHMTs with differing ratios of wall thickness between layers, specific energy absorption ranges from 15.69 kJ/kg to 21.29 kJ/kg. Notably, the maximum error between theoretical and simulated values of the mean crushing force for each order of SVFHMT is only 7.34%. This underscores the effectiveness of our novel layer design strategy, which diverges significantly from conventional approaches and offers valuable insights for advancing layered structures further.