Paper Crumpling Dynamics

Crumpled paper A crumpled piece of paper is a familiar everyday object for most people, especially for anyone doing research. In addition to their role as graves for failed theories and ideas, the shape of crumpled papers and their networks of creases hold many mysteries. In our group we are mostly interested in the dynamics of the crumpling process; understanding how the shape of a crumpled sheet at any given time will determine its crumpled shape in the future. Apart from being fascinating in their own right, understanding the way a multitude of random creases interact and affect each other can help shed light on the behavior of many other disordered physical systems.

For information: Omer Gottesman


Days of Gold - Richard De Wolfe The shape of a crumpled paper ball can be described by a network of straight folds, connected at point defects termed 'd-cones'. When the ball is opened up, the sharper folds leave the familiar plastic creases seen in crumpled papers (right image - 1). Upon closer inspection, a different type of crease can be observed; considerably sharper and more ragged than the usual creases (right image - 2). They are created when a d-cone propagates across the sheet and 'plows' the paper, leaving a sharp furrow like scar in its wake. We are interested in the formation dynamics of these creases, which bears many similarities to the propagation of cracks in solids. Another question regarding these odd creases is what role do they play in determining the full pattern of creases formed in a crumpled sheet of paper.


Extra furrows stuff:

Furrows creation in crumpled paper:  Paper kvetch

A d-cone propagating in a Mylar sheet - notice the abrupt sharpening of the d-cone accompanying the initiation of propagation: D-cone propagating in Mylar

Furrows in the wake of propagating d-cones (PDF)

Maximally crumpled paper

Experimental ninjasDisturbing philosophical fact #1 - You can never cross the same river twice.

Disturbing philosophical fact #2 - You can never crumple the same paper twice. Believe us, we tried!!! Despite the apparent similarity of all uncrumpled sheets, and no matter how accurately the crumpling protocol is repeated, minute differences in the crumpling process grow rapidly, leading to completely different creases patterns for different paper sheets. Once a paper is crumpled and opened up, any subsequent crumpling will tend to happen along the existing creases where the paper is weakened. Once again, however, the paper refuses to crumple in exactly the same way, and new creases appear with successive crumplings. (A fact which greatly upsets our pet ninjas!)

We are working to understand what the asymptotic behavior of a sheet crumpled repeatedly many times is. Can the sheet be trained to crumple under a certain protocol without creating new creases, or will creases continue to appear indefinitely? The answer to this question, apart from putting our ninjas' minds at ease, can help shed light on the behavior of other disordered physical systems and their approach to steady state under periodic loading.

The following images show the creases in a Mylar sheet after being crumpled once, twice and three times. The bottom set shows the extracted creases, where red lines denote the creases which appeared in previous crumplings, and blue lines denote new creases.

Repeated crumpling

Other fun paper stuff

Another good motivation for studying the crumpling of paper and thin sheets is that it is extraordinarily fun. Here is more fun stuff we did while playing with paper:

First attempts at kvetching papers, and a good use for the leftovers of all the coffee we drink:  Kvetching a paper with a coffee can