Department of Mechanical Engineering, Joint College of Engineering, Florida A&M University-Florida State University, Tallahassee, FL, United States of America.
Bioinspir Biomim. 2022 Jul 13;17(5). doi: 10.1088/1748-3190/ac759e.
Wind-induced stress is the primary mechanical cause of tree failures. Among different factors, the branching mechanism plays a central role in the stress distribution and stability of trees in windstorms. A recent study showed that Leonardo da Vinci's original observation, stating that the total cross section of branches conserved across branching nodes is the optimal configuration for resisting wind-induced damage in rigid trees, is correct. However, the breaking risk and the optimal branching pattern of trees are also a function of their reconfiguration capabilities and the processes they employ to mitigate high wind-induced stress hotspots. In this study, using a numerical model of rigid and flexible branched trees, we explore the role of flexibility and branching patterns of trees in their reconfiguration and stress mitigation capabilities. We identify the robust optimal branching mechanism for an extensive range of tree flexibility. Our results show that the probability of a tree breaking at each branching level from the stem to terminal foliage strongly depends on the cross section changes in the branching nodes, the overall tree geometry, and the level of tree flexibility. Three response categories have been identified: the stress concentration in the main trunk, the uniform stress level through the tree's height, and substantial stress localization in the terminal branches. The reconfigurability of the tree determines the dominant response mode. The results suggest a very similar optimal branching law for both flexible and rigid trees wherein uniform stress distribution occurs throughout the tree's height. An exception is the very flexible branched plants in which the optimal branching pattern deviates from this prediction and is strongly affected by the reconfigurability of the tree.
风致应力是树木失效的主要力学原因。在不同因素中，分枝机制在树木在风暴中承受风致应力的分布和稳定性中起着核心作用。最近的一项研究表明，达芬奇的原始观察是正确的，即分枝节点处的总分支横截面积保持不变，这是抵抗刚性树木风致损伤的最佳配置。然而，树木的破坏风险和最佳分枝模式也是其重构能力和减轻高风致应力热点的过程的函数。在这项研究中，我们使用刚性和柔性分枝树木的数值模型，探索了树木的灵活性和分枝模式在其重构和减轻应力能力中的作用。我们确定了广泛的树木灵活性的稳健最优分枝机制。我们的结果表明，从树干到末端叶的每个分枝水平上树木断裂的概率强烈依赖于分枝节点的横截面积变化、整体树木几何形状和树木灵活性水平。已经确定了三种响应类别：主干中的应力集中、树木高度上的均匀应力水平以及末端分支中的大量应力局部化。树木的可重构性决定了主导响应模式。结果表明，对于柔性和刚性树木，非常相似的最优分枝规律，其中整个树木高度上都存在均匀的应力分布。一个例外是非常灵活的分枝植物，其最优分枝模式偏离了这一预测，并且受到树木可重构性的强烈影响。
