Size-curvature constraint in the closing motion of Venus flytrap leaves

Among carnivorous plants, the Venus flytrap (Dionaea muscipula) is known for its rapid (<1 s) trap closure. Although buckling instability, hydrostatic pressure, and hydroelastic coupling have all been proposed to be involved, the nature of this process and the relationship between trap size and curvature remain elusive. Here, we monitored the closure of Venus flytraps and performed micro-CT scanning and 3D reconstruction, revealing that increasing angular velocity was correlated with higher values of a non-dimensional shape index. Based on these experimental data, we constructed a geometric model of the trap that takes leaf orientation into account. We found that leaf curvature is dependent on leaf size, a relationship we denote as a size-curvature constraint. We further propose a curvature design derived from differential deformations of a two-layer model of the leaf, which could be a powerful tool to control the curvatures of soft and bending surface structures in the field of biomimetics.