Helicoids, wrinkles, and loops in twisted ribbons

Area of Science:

• Physics of soft matter
• Materials science
• Mechanics of materials

Background:

• Elastic ribbons exhibit complex shape transitions under mechanical stress.
• Understanding these instabilities is crucial for designing novel materials and structures.

Purpose of the Study:

• To investigate the instabilities of a flat elastic ribbon under tension and twist.
• To develop a comprehensive phase diagram of ribbon shapes and transitions.

Main Methods:

• Experimental investigation of elastic ribbon behavior under controlled tension and twist.
• Analysis of buckling modes, shape evolution, and transition points.

Main Results:

• A phase diagram reveals a switch from longitudinal to transverse buckling modes at a triple point.
• Longitudinally buckled ribbons form self-creased helicoids; further twisting leads to anomalous loop formation.
• High tension induces transverse wrinkles due to compressive stresses and higher harmonic development.

Conclusions:

• The study provides a detailed understanding of elastic ribbon instabilities and shape transitions.
• Results offer insights for developing functional structures with tunable properties across various scales.