Crashworthiness of Bionic Fractal Multi-Cell Circular Tubes under Axial Load

Inspired by fractal theory and biological structures, bio-inspired fractal tubes exhibit exceptional crashworthiness. This study constructs bio-inspired fractal multi-cell circular tubes with inscribed regular quadrilaterals, pentagons, and hexagons, and systematically investigates the influence of their mass, fractal dimension, and the number of sides of the inscribed regular polygon on crashworthiness through numerical simulation. The results indicate that the crashworthiness of the bio-inspired fractal multi-cell circular tubes improves with increasing mass. As the fractal dimension increases, the crashworthiness initially decreases and then improves. Furthermore, crashworthiness enhances with an increase in the number of sides of the inscribed polygon, although the variation in the number of sides has a minor impact on the peak crushing force. Based on the super folding element theory, a theoretical model is developed to predict the mean crushing force of the bio-inspired fractal multi-cell circular tubes, and the theoretical predictions show good agreement with the numerical simulation results.