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<p>Leaf morphology is strongly influenced by internal structures, with the mid-vein providing both nutrient transport and mechanical reinforcement. It introduces a transverse thickness gradient that affects mechanical stability and triggers growth-induced buckling, including wrinkling and saddle-shaped deformations. Despite extensive biological studies, the mechanical role of this feature remains underexplored. Here, leaves are modeled as two-dimensional orthotropic hyperelastic plates with a power-law thickness distribution. Incorporating geometric nonlinearity, St. Venant–Kirchhoff constitutive equations are used to analyze filamentary and saddle-shaped buckling in infinitely long ribbons, solved via MATLAB’s Bvp5c solver. Finite-length blades are further examined through Abaqus simulations, where growth-induced strains are modeled as anisotropic thermal expansion. Results show that mid-vein-induced thickness gradients significantly influence buckling evolution: increasing the thickness power-law exponent enhances bending stiffness and buckling resistance, though the effect exhibits diminishing returns at higher values. These findings elucidate the mechanical function of mid-veins in natural morphogenesis and provide guidance for designing bioinspired thin structures with non-uniform thickness.</p>

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Mechanical influence of mid-vein-induced thickness gradients on buckling and morphological evolution in growing plant leaves

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Di-Quan Wu,
  • Ling Liu,
  • Qi-Ling Jiang,
  • Mohamad Ikhwan Zaini Ridzwan

摘要

Leaf morphology is strongly influenced by internal structures, with the mid-vein providing both nutrient transport and mechanical reinforcement. It introduces a transverse thickness gradient that affects mechanical stability and triggers growth-induced buckling, including wrinkling and saddle-shaped deformations. Despite extensive biological studies, the mechanical role of this feature remains underexplored. Here, leaves are modeled as two-dimensional orthotropic hyperelastic plates with a power-law thickness distribution. Incorporating geometric nonlinearity, St. Venant–Kirchhoff constitutive equations are used to analyze filamentary and saddle-shaped buckling in infinitely long ribbons, solved via MATLAB’s Bvp5c solver. Finite-length blades are further examined through Abaqus simulations, where growth-induced strains are modeled as anisotropic thermal expansion. Results show that mid-vein-induced thickness gradients significantly influence buckling evolution: increasing the thickness power-law exponent enhances bending stiffness and buckling resistance, though the effect exhibits diminishing returns at higher values. These findings elucidate the mechanical function of mid-veins in natural morphogenesis and provide guidance for designing bioinspired thin structures with non-uniform thickness.