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Curvature-Regulated Multiphase Patterns in Tori.

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  • 1Institute of Mechanics and Computational Engineering, Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, People's Republic of China.

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Summary
This summary is machine-generated.

Biological toroidal structures exhibit complex wrinkling patterns due to varying curvatures. A new core-shell model predicts these patterns based on stiffness and curvature, aiding in designing functional surfaces.

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Area of Science:

  • Morphoelasticity
  • Materials Science
  • Biological Physics

Background:

  • Biological functions are linked to geometry and morphology.
  • Toroidal structures in nature display complex curvatures (positive, zero, negative).
  • Varying curvatures influence morphogenesis during growth or dehydration.

Purpose of the Study:

  • To understand the morphoelastic mechanisms governing toroidal structure patterning.
  • To identify key factors controlling instability patterns in toroidal systems.
  • To develop a predictive model for wrinkling patterns in curved biological structures.

Main Methods:

  • Development of a core-shell model for toroidal structures.
  • Derivation of a scaling law for growth- or dehydration-induced instability.
  • Construction of a phase diagram based on dimensionless parameters (stiffness, curvature).
  • Experimental validation of the phase diagram and predicted patterns.

Main Results:

  • Wrinkling patterns are determined by two dimensionless parameters: stiffness and curvature.
  • A phase diagram illustrates multiphase wrinkling pattern selection.
  • Experimental observations confirm the model's predictions.
  • Hysteresis loops and Maxwell equal-energy conditions provide insights into transitions and bistable modes.

Conclusions:

  • A universal law for morphology selection in core-shell structures with varying curvatures has been established.
  • The model accurately explains and predicts wrinkling patterns in diverse toroidal structures.
  • This research offers a foundation for designing functional surfaces based on morphology control.