Morphoelastic ribbons: Differential-growth-induced curvature and torsion
Phys. Rev. Applied 25, 024021 – Published 6 February, 2026
DOI: https://doi.org/10.1103/t5fq-h7kq
Abstract
Natural slender structures, such as plant leaves and petals, exhibit complex three-dimensional (3D) morphologies—including twisting, helical coiling, and saddle bending—driven by differential growth. The resulting internal stresses are partially relieved through the development of intrinsic curvature and torsion. The fundamental challenge lies in effectively correlating microscopic growth fields to the macroscopic shapes and mechanical responses of the ribbon structures. However, existing ribbon or shell models struggle to directly link growth gradients to macroscopic curvature and torsion, necessitating a reduced-dimensional framework. This work establishes a unified one-dimensional morphoelastic ribbon model derived asymptotically from 3D finite elasticity theory via a rigorous dimension reduction framework. The reduced-order model captures growth-induced nonlinear strains and finite rotations asymptotically. We obtain analytical solutions for saddle-bending and twisting configurations induced by specific growth gradients. Furthermore, numerical continuation traces the postbuckling evolution into helical morphologies. This framework explicitly links growth fields to ribbon curvature and torsion, providing fundamental mechanics insights into the morphogenesis of slender plant organs and offering potential for bioinspired soft robotics design.
