Crashworthiness and Multi-Objective Optimization of Concave Tree-Like Bio-Inspired Multi-Cell Tubes

A concave tree-like bio-inspired multi-cell tube (CTBMT) is proposed as a hierarchical energy absorbing structure that integrates a concave honeycomb-derived outer contour, a horsetail-inspired intermediate tubular network, and a tree-like branching core. A validated finite element (FE) model based on published experimental data is used to investigate the crashworthiness of three CTBMT configurations under quasi-static, dynamic, and oblique loading conditions. The results show that hierarchical structural interaction improves
deformation stability by promoting distributed folding initiation, enhancing lateral confinement, and redistributing axial loads during progressive collapse. Among the designs, CTBMT-1 exhibits the most balanced crashworthiness performance. Under equal-mass conditions, it achieves a specific energy absorption (SEA) of 16.93 J/g and a crushing force efficiency (CFE) of 0.73, outperforming representative classical and bio-inspired multi-cell tubes. The study further shows that increasing hierarchical confinement enhances structural stiffness and peak crushing force (PCF) but yields diminishing improvement in SEA due to reduced fold multiplicity and mass efficiency. To quantify the trade-off between energy absorption and peak load, a surrogate-assisted NSGA-II optimisation is performed using the outer width 𝑊1, inner
diameter D, and wall thickness t as design variables. The identified knee point design (W1=64mm, D =55mm, t = 0.94mm) provides an effective compromise between SEA and PCF. The results demonstrate that integrating multiple bio-inspired mechanisms within a hierarchical thin-walled architecture effectively improves crashworthiness in load-limited lightweight structures.