Leaf venation angle: The physical origin and bio-inspired application

Biomimetic design has emerged as a valuable approach to enhance the physical and mechanical performance of materials and structures. As a commonly observed object in nature, leaves have inspired numerous interesting practical applications. In this work, through experimental measurements on leaves, we revealed that the angle between the secondary and primary veins in leaves is ∼50°, a feature that is remarkably widespread in nature. Furthermore, based on the principle of energy minimization, we elucidated that this 50° angle minimizes the bending energy of the veins, thereby explaining its prevalence in nature. We then designed a plate structure analogous to leaf venation and discovered that the structure with a 50° angle (mimicking the leaf venation) exhibited a 60% higher flexural resistance compared to that with a 90° angle. This significant enhancement is attributed to the contribution of the bending energy from the vein-like components. The findings of this study hold promising implications for guiding the design of large-area plate structures with enhanced flexural resistance in practical applications.