标题： 中脉调节干燥叶片的形状形成 显示英文标题

标题： Midveins regulate the shape formation of drying leaves

摘要： 自然中的干叶通常表现出卷曲和皱缩的形态，通常归因于内部应变梯度产生类似圆顶的形状。然而，这些应变梯度的起源仍然不为人所知。尽管叶脉——尤其是中脉——被认为会影响形状形成，但它们的机械作用尚未被系统研究。在这里，我们证明中脉施加的机械约束在叶片干燥过程中产生多种形态中起着关键作用。结合数值模拟和理论分析，我们表明由非收缩中脉约束的均匀收缩叶片会引发两种不同类型的构型：以卷曲为主和以折叠为主。在以卷曲为主的区域，S形卷曲和C形卷曲形状都会出现，由于C形卷曲构型具有较低的弹性能量，因此更常被观察到。相反，在以折叠为主的区域，折叠伴随着边缘波纹。理论模型揭示了中脉曲率与失配应变之间的线性关系，这与模拟结果一致。此外，我们发现形态结果由叶片和中脉的弯曲刚度比决定。我们构建了一个不同构型之间转换的综合相图。这些发现为理解干燥叶片中的形状形成提供了一个机械框架，为自然变形过程提供了新的见解，并指导了仿生可变形结构的设计。 显示英文摘要

摘要： Dried leaves in nature often exhibit curled and crumpled morphologies, typically attributed to internal strain gradients that produce dome-like shapes. However, the origin of these strain gradients remains poorly understood. Although leaf veins--particularly the midvein--have been suggested to influence shape formation, their mechanical role has not been systematically investigated. Here, we demonstrate that mechanical constraints imposed by the midvein play a crucial role in generating the diverse morphologies that emerge during leaf drying. Combining numerical simulations and theoretical analysis, we show that a uniformly shrinking leaf lamina constrained by a non-shrinking midvein gives rise to two distinct types of configurations: curling-dominated and folding-dominated morphologies. In the curling-dominated regime, both S-curled and C-curled shapes emerge, with C-curled configurations more commonly observed due to their lower elastic energy. In contrast, the folding-dominated regime features folding accompanied by edge waviness. Theoretical modeling reveals a linear relationship between midvein curvature and mismatch strain, consistent with simulation results. Moreover, we find that the morphological outcome is governed by the ratio of bending stiffnesses between the lamina and the midvein. We construct a comprehensive phase diagram for the transitions between different configurations. These findings provide a mechanical framework for understanding shape formation in drying leaves, offering new insights into natural morphing processes and informing the design of bio-inspired morphable structures.