Mechanics-based classification rule for plants

The height of thick and solid plants, such as woody plants, is proportional to two-thirds of the power of their diameter at breast height. However, this rule cannot be applied to herbaceous plants that are thin and soft because the mechanisms supporting their bodies are fundamentally different. This study aims to clarify the rigidity control mechanism resulting from turgor pressure caused by internal water in herbaceous plants to formulate the corresponding scaling law. We modeled a herbaceous plant as a cantilever with the ground side as a fixed end, and the greatest height was formulated considering the axial tension force from the turgor pressure. The scaling law describing the relationship between the height and diameter in terms of the turgor pressure was theoretically derived. Moreover, we proposed a plant classification rule based on stress distribution.