Mechanical Properties and Energy Absorption Characteristics of the Fractal Structure of the Royal Water Lily Leaf Under Quasi-Static Axial Loading

Inspired by the self-organizing optimization mechanisms in nature, the leaf venation of the royal water lily exhibits a hierarchically branched fractal network that combines excellent mechanical performance with lightweight characteristics. In this study, a structural bionic approach was adopted to systematically investigate the venation architecture through macroscopic morphological observation, experimental testing, 3D scanning-based reverse reconstruction, and finite element simulation. The influence of key fractal geometric parameters under vertical loading on the mechanical behavior and energy absorption capacity was analyzed. The results demonstrate that the leaf venation of the royal water lily exhibits a core-to-margin gradient fractal pattern, with vein thickness linearly decreasing along the radial direction. At each hierarchical bifurcation, the vein width is reduced to 65–75% of the preceding level, while the bifurcation angle progressively increases with branching order. During leaf development, the fractal dimension initially decreases and then increases, indicating a coordinated functional adaptation between the stiff central trunk and the compliant peripheral branches. The veins primarily follow curved trajectories and form a multidirectional interwoven network, effectively extending the energy dissipation path. Finite element simulations reveal that the fractal venation structure of the royal water lily exhibits pronounced nonlinear stiffness behavior. A smaller bifurcation angle and higher fractal branching level contribute to enhanced specific energy absorption and average load-bearing capacity. Moreover, a moderate branching length ratio enables a favorable balance between yield stiffness, ultimate strength, and energy dissipation. These findings highlight the synergistic optimization between energy absorption characteristics and fractal geometry, offering both theoretical insights and bioinspired strategies for the design of impact-resistant structures.