Quasi-static crushing analysis and multi-criteria decision ranking of royal lily leaf fractal-vein inspired multi-cell structures: A comparative study

The current study investigated the quasi-static crushing behavior and multi-criteria decision ranking of multi-cell tubular structures inspired by the fractal veins of royal lily leaves using a fused deposition modeling (FDM) technique. Inspired by the hierarchical vein patterns of Victoria amazonica, a variety of tubular configurations were fabricated by altering the number of branches and fractal order. Axial compression of the fabricated tubular samples was applied to evaluate significant crashworthiness metrics like average crushing force (ACF), initial peak crushing force (IPCF), total energy absorption (TEA), and specific energy absorption (SEA). The results revealed that increasing the number of branches and fractal order significantly increased TEA and stimulated more progressive crushing along with improved deformation stability. To identify the optimal design, a hybrid Analytic Hierarchy Process (AHP)–Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) multi-criteria decision-making (MCDM) framework was applied. When compared to single-tubular structures, the bi-tubular structures exhibited 15–25% higher energy absorption, mostly at higher branching levels where multi-cell interactions became dominant. Higher-order, high-branch bi-tubular structures were consistently ranked closest to the ideal solution due to their enhanced crushing stability, balanced peak-force response, and superior energy-absorption characteristics. The highest TEA of 735 kJ and SEA of 7.6 kJ/g were obtained for the 2 nd -order, 8-branch bi-tubular structure. Overall, the research proved that biomimetic fractal-vein reinforcement, combined with multi-cell bi-tubular architecture, provides an effective pathway for developing lightweight, high-performance energy-absorbing structures suitable for crashworthiness applications.