The dynamics behind how Mylar sheets crumple is reported online this week in Communications Physics. These findings reduce the complexity involved in understanding exactly how sheets of paper crumple into a ball.
The act of crumpling a sheet of paper into a ball is simple, but the dynamics of crumpling are complex. When paper crumples, an intricate network of creases forms. Although sheets will preferentially bend along existing creases, unless folding occurs in the exact same order as before, new creases must be formed each time a sheet is crumpled. It is unknown whether it is possible to predict the way a smooth sheet of paper will crumple into a ball.
Omer Gottesman, Shmuel Rubinstein and colleagues repeatedly crumpled single, thin sheets of Mylar that have been rolled into cylinders. Flattening out the sheets, the authors analysed how the crease patterns had evolved. They found that the total length of all creases does not evolve randomly, but changes in a manner determined by the length of the creases at the given instant - regardless of how many times the sheet has already been crumpled or the structure of the existing crease pattern. The authors were then able to define a quantity that characterizes the “crumpledness” of a given Mylar sheet.
The authors suggest that this finding could provide a model for characterising the dynamics of other systems that evolve under geometric and mechanical constrains - such as the folding of proteins or the geological fault systems that can cause earthquakes.