Morphogenesis of Infinite Plant Ribbons Under Longitudinal Intrinsic Curvature

Ribbon-like plant organs such as leaves, petals, and tendrils frequently exhibit complex three-dimensional morphologies arising from intrinsic curvature generated during growth. Although previous studies have addressed growth-induced deformation in plants, the mechanistic role of longitudinal intrinsic curvature and its interaction with material anisotropy remain poorly understood. This study presents an integrated analytical–numerical framework to investigate infinitely long orthotropic ribbons subjected to prescribed longitudinal intrinsic curvature. Based on two-dimensional orthotropic hyperelastic thin-plate theory, the analysis shows that curvature-induced bending moments can drive bifurcations into either saddle-like or filamentary morphologies. Unlike classical buckling, these bifurcations resemble dynamic transitions in soft matter systems. Perturbation analysis establishes scale-dependent onset criteria, while numerical solutions obtained with MATLAB’s bvp5c solver capture nonlinear transitions under transverse shear-constrained boundary conditions. The results demonstrate that, under free boundaries, ribbons deform primarily through intrinsic curvature with little sensitivity to anisotropy, whereas residual transverse shear forces along longitudinal edges markedly alter the bifurcation pathway and may even reverse bending direction. These findings position intrinsic curvature as a fundamental link between growth, strain, and emergent morphology in ribbon-like structures, while providing design principles for curvature-programmed materials, soft robotic actuators, and deployable morphing systems.