Abstract
Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established. The aim of this study was to develop a new method for 3D reconstruction of actual tree shape and to establish a theoretical formulation for elucidating the structure and function of tree branches. We obtained 3D point cloud data of tree shape of Japanese zelkova (Zelkova serrata) and Japanese larch (Larix kaempferi) using the NavVis Lidar scanner, then applied a cylinder structure extraction from point cloud data with error estimation. We then formulated the mechanical stress of branches under gravity using the elastic theory, and performed finite element method simulations to evaluate the mechanical characteristics. Subsequently, we constructed a mechanics-based theoretical formulation of branch development that ensures constant bending stress produces various branching patterns depending on growth properties. The derived theory recapitulates the trade-off among branch growth anisotropy, stress-gravity length, and branch shape, which may open the quantitative way to evaluate mechanical and morphological rationality of tree branches.
Highlights
Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established
We evaluated the detailed morphology of Japanese zelkova and Japanese larch and constructed two mechanical hypotheses
The first hypothesis was that the trees have different mechanical strategies that determine their shapes; this was supported by the following two mechanical results: (1) The mechanical stress depends on the branch inclination angle
Summary
Trees are thought to have acquired a mechanically optimized shape through evolution, but a scientific methodology to investigate the mechanical rationality of tree morphology remains to be established. The aim of this study was to develop a new method for 3D reconstruction of actual tree shape and to establish a theoretical formulation for elucidating the structure and function of tree branches. We formulated the mechanical stress of branches under gravity using the elastic theory, and performed finite element method simulations to evaluate the mechanical characteristics. We constructed a mechanics-based theoretical formulation of branch development that ensures constant bending stress produces various branching patterns depending on growth properties. Leveraging the recent growth of 3D reconstruction methods to recover accurate tree structures from 3D point clouds, we aimed to unveil the relationship between the morphological and mechanical properties of trees. We hypothesized that the branch-growing process is mechanically unstable in terms of compressive and tensile stresses, and verified it by performing mechanical simulations using the finite element method, which is a similar approach to the recent w orks[24,25]. Information on this type of constraint and the interactions among mechanics, shape, and growth, may provide a solid platform for investigating the mechanical and morphological rationality of tree shape
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