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Periodic folding of a falling viscoelastic sheet.
Kui Pan1, A Srikantha Phani1, Sheldon Green1
1Department of Mechanical Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada.
Physical Review. E
|February 20, 2020
Summary
A viscoelastic sheet folding on a plane was studied using particle dynamics. Increased velocity and viscosity reduce fold length and alter folding patterns, offering insights for manufacturing processes.
Area of Science:
- Physics
- Materials Science
- Mechanical Engineering
Background:
- Viscoelastic sheet folding is common in textile and paper manufacturing.
- Understanding folding dynamics is crucial for process optimization.
- Existing models often focus on quasistatic conditions.
Purpose of the Study:
- To investigate the folding dynamics of a viscoelastic sheet using a particle dynamics model.
- To explore the influence of feeding velocity and viscosity on folding morphology.
- To derive scaling laws and construct a phase diagram for folding patterns.
Main Methods:
- Application of a particle dynamics model to simulate sheet folding.
- Analysis of sheet behavior at varying feeding velocities and viscosities.
- Derivation of scaling laws by balancing kinetic and elastic bending energies.
Main Results:
- The model reproduces quasistatic results at low velocities and viscosities.
- Higher velocities and viscosities lead to decreased fold length and loss of 'rolling back' motion.
- A transition from line contact to point contact with lemniscate-like patterns occurs above a critical velocity.
Conclusions:
- The particle dynamics model accurately captures viscoelastic sheet folding phenomena.
- Feeding velocity and viscosity significantly influence folding morphology and dynamics.
- The derived scaling laws and phase diagram provide valuable insights for high-speed manufacturing of sheet materials.
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