Crashworthiness assessment of thin-walled columns with functionally graded stiffness induced by multi-level spherical crush initiators

Abstract This study investigates the crashworthiness performance of thin-walled columns equipped with functionally graded, multi-level spherical crush initiators. The proposed concept extends previous solutions by introducing a sequence of embossments with varying diameters and depths along the column height, enabling controlled variation in local structural deformation resistance and progressive folding under impact loading. Both numerical simulations and experimental tests were conducted to validate the effectiveness of the proposed configurations and to assess the convergence of the computational model with physical experiments. The results demonstrate that the locations of fold formation coincide with the positions of the introduced spherical embossments, confirming their effectiveness as crush initiators. Increasing the diameter of the embossment sequence significantly improves crashworthiness indicators, particularly Peak Crushing Force (PCF), Crush Load Efficiency (CLE), and Total Efficiency (TE). Similarly, greater embossment depth enhances the energy absorption capability of the passive absorber configurations within a mechanically safe range (1.2–4.8 mm), ensuring stable plastic hinge formation in accordance with Super Folding Element (SFE) theory. Under both axial and oblique impacts (5° and 10°), the columns exhibited stable progressive crushing without global buckling. Although oblique loading reduced PCF values and increased overall efficiency, further improvements due to initiator geometry were more pronounced under axial loading. Additionally, larger diameter sequences improved the formation of the lower plastic hinge during lateral impact. Overall, the proposed graded initiator concept effectively enhances the crash performance of thin-walled energy absorbers.