Branching pattern of flexible trees for environmental load mitigation.

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.