Universal phenomenon of an elastic coiling plate

JUNG-TZU CHANG^1*, JENG-YI LEE¹

¹Department of Opto-Electronic Engineering, National Dong Hwa University, Hualien, Taiwan
²Department of Opto-Electronic Engineering, National Dong Hwa University, Hualien, Taiwan

* Presenter:JUNG-TZU CHANG, email:611025017@gms.ndhu.edu.tw

In 2008, Enrique Cerda of the University of Santiago in Chile observed that when a piece of elastic papers is rolled into a tube, the angle of final side of elastic system with respect to tube is always 24.1 degresses, irrespective of thickness, tube radius, and Young's modulus[1]. They also performed theoretical analysis based on elastic Kirchhoff's continuum theory, that agrees with experimental observations. Due to modern electronic devices, such as display and solar cells, toward flexible and thin property, this undashted phenomenon is expected to occur at such electronic systems. In this representation, we first investigate force and moment equations based on Kirchhoff's continuum theory as well as proper boundary conditions to calculate the force, moment and geometry of this universal phenomenon. Then we also design consequent experiments with a variety of materials to verify the universal phenomenon. In order to solve this universal angle, we formulate the bending coefficient be non-uniform to let the undetashing part lying down the interior tube.
In this way, we can eliminate this undetashing part. With the help of 3D print, we also design modified elastic plate with non-uniform thickness to verify our developed theory.

Reference:
[1] Philip Ball, ``Universal law of coiling,'' Nature volume 453, page966 (2008)

Keywords: Universal angle of an elastic coiling, Elastic beam, Kirchhoff's continuum theory