As an advanced flexible dynamic sealing technology, the leakage characteristics of a finger seal (FS) is one of the key research areas in this technology field. Based on the fractal theory, this paper establishes a mathematical model of the FS main leakage rate considering the fractal wear effect by taking into account the influence of the wear height on the basis of the eccentric annular gap flow equation. Based on the Hagen-Poiseuille law and the fractal geometry theory of porous media, a mathematical model of the FS side leakage rate considering the fractal porous media seepage effect is developed. Then, a mathematical model of the FS total leakage rate is established. The results show that the mathematical model of the FS total leakage rate is verified with the test results, the maximum error rate is less than 5%, and the mathematical model of the FS total leakage rate is feasible. With the gradual increase in working conditions and eccentricity, the FS main leakage rate gradually increases. In addition, the effects of the fractal dimension, fractal roughness parameters and porosity after loading on the FS main leakage rate are negligible. As the fractal dimension of tortuosity after loading gradually decreases, the fractal dimension of porosity after loading gradually increases, and the FS side leakage rate gradually increases. As the porosity after loading gradually increases, the FS side leakage rate gradually increases. Under different working conditions, different fractal characteristic parameters and different porosities after loading, the weight of the FS main leakage rate is much greater than that of the FS side leakage rate by more than 95%.

To investigate the synergistic regulatory mechanism of vein structure and temperature on crack propagation behavior in plant leaves, this study conducted systematic tensile tests to determine the fracture behavior of leaves with different numbers of veins (0, 1, and 2) at various pretreatment temperatures (35–55 °C). A fractal-corrected fracture energy model was subsequently developed. The results show that both the crack fractal dimension and fracture energy first increase and then decrease with rising temperature, peaking at 45 °C. Fracture energy decreases as the number of veins increases: by approximately 60% for a single vein, and nonlinearly for two veins (synergy factor ranging from 0.59 to 0.71), indicating diminishing toughening returns. When the angle between the crack propagation direction and the vein is less than 90°, veins do not provide a toughening effect but instead act as preferential failure pathways, although they prolong the overall crack propagation duration. Crack propagation velocity exhibits intermittent fluctuations. In the temperature range of 50–55 °C, toughness increases and velocity fluctuations diminish. For double-vein leaves, velocity fluctuations are mild in the early stage, but a pronounced peak occurs later upon interface breakthrough. This model provides a reference for the quantitative analysis of fracture behavior in plant leaves.