Buckling of geometrically confined shells

Area of Science:

• Materials Science
• Mechanics of Materials
• Soft Matter Physics

Background:

• Elastic shells exhibit complex buckling patterns when subjected to geometric confinement.
• Residual swelling allows access to diverse shell shapes with varying curvatures.
• Understanding these patterns is crucial for designing advanced materials.

Purpose of the Study:

• To investigate the periodic buckling patterns in elastic shells under geometric confinement.
• To identify key geometric parameters that predict buckling behavior.
• To develop a model explaining the relationship between shell shape and confinement.

Main Methods:

• Experimental analysis of elastic shells with varying shapes and curvatures.
• Numerical simulations to model buckling patterns under radial and transverse confinement.
• Development of a theoretical model based on competing bending mechanisms.

Main Results:

• A single geometric parameter (shell radius to unconstrained material ratio) predicts lobe number in radially confined shells.
• The number of lobes decreases with reduced transverse confinement for saddle shapes.
• A unified scaling analysis captures wave number across different confinement scenarios.

Conclusions:

• One geometric parameter effectively predicts buckling wave number, linking shell geometry to confinement boundary.
• Findings are applicable to a broad range of shell shapes and confinement conditions.
• Results have implications for designing shape-shifting materials and understanding biological growth.