Curvature-Regulated Multiphase Patterns in Tori

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.