This study examines a hierarchical vertex-based structure that improves the crashworthiness of the conventional multi-cell square, a biological hierarchy of natural origin with exceptional mechanical properties. The vertex-based hierarchical square structure (VHS) is explored for its geometric properties, including infinite repetition and self-similarity. The cut-and-patch method is used to derive an equation for the material thicknesses of different orders of the VHS based on the principle of the same weight. A thorough parametric study of VHS was conducted using LS-DYNA, which examined the effects of material thickness, orders, and various structural ratios. The results were evaluated based on common crashworthiness criteria and demonstrated that the total energy absorption (TEA), specific energy absorption (SEA), and mean crushing force (Pm) of VHS exhibited similar monotonicity concerning the orders. SEA of the first-order VHS with λ1=0.3 and the second-order VHS with λ1=0.3 and λ2=0.1 are improved by at most 59.9% and 102.4% respectively; the second-order VHS with 0.2≤λ1≤0.4 and 0.1≤λ2≤0.15 have the better overall performance of crashworthiness. Then, the half-wavelength equation of VHS and Pm of each fold was established based on the Super-Folding Element method. Meanwhile, a comparative analysis with the simulation results reveals three different out-of-plane deformation mechanisms of VHS. The study indicated that material thickness had a greater impact on crashworthiness. Finally, the comparison with conventional honeycombs demonstrated that VHS holds great promise as a structure for crashworthiness. These results provide a solid foundation for further research and development of new bionic energy-absorbing devices.
Keywords: crashworthiness; energy absorption; fractal geometry; hierarchical structure; super-folding element; vertex-based.