Numerical analysis for the growth of tendril of cucumber using elasticity theory on Riemannian manifolds

Abstract

In this study, we investigate the helix formation mechanism of cucumber tendrils using elasticity theory on Riemannian manifolds and the Material Point Method (MPM). During growth, cucumber grows an organ called a tendril, which forms a characteristic helical structure. This helical structure is expected to be applied to biomimetic technology such as torsion-free spring design, but its formation mechanism has not been clarified yet. We developed a mechanical model that takes into account the original geometry and internal organization of the tendril as well as its contact with the support. We then applied non-uniform axial contraction to the internal part of the tendril and performed a quasi-static dynamics analysis using the finite element method to confirm the formation of spiral and inverted helical structures.