Morphogenesis strategies of hollow plants: avoidance of ovalization

Ovalization of a cross-section is a dominant cause of failure in hollow plants subjected to bending. This study investigates the optimal spatial arrangement of fibers to maximize flexural rigidity during transverse bending by examining the morphology of bamboo. Bamboo, a hollow plant, exhibits self-adaptive properties that potentially account for its distinct vascular bundle distribution. By deriving the volume fraction of fibers in the longitudinal direction and equations for transverse flexural rigidity, the study identifies the optimal fiber distribution. The results indicate that a parabolic distribution of fibers is optimal for avoiding ovalization. Furthermore, a comparison with Moso bamboo reveals that this calculated optimal distribution matches the actual fiber arrangement near the bamboo's base, where the ovalization effect is significant. Moso bamboo behaves like a cylindrical shell, with high bending moments causing pronounced ovalization, while in other regions, it resembles a beam with lower bending moments.