Morphological phases of crumpled wire

The loops and folds that result when a sheet, tape, or wire crumples are of practical and theoretical interest. Engineers want to predict how structures deform under stress; physicists want to reduce diverse crumpling behavior to a few simple principles. Toward that second aim, Norbert Stoop, Falk Wittel, and Hans Herrmann of ETH Zürich have conducted an experimental study of one elementary system: a length of metal wire stuffed from two opposing directions into a cylindrical container so shallow that the crumpling is two-dimensional. At the start of each run, the wire spanned the container in a straight line. Two counterrotating drums then pushed more and more of the wire into the container until, having bent to form a loop, the wire touched the side. What happened next, the researchers found, depended on the wire’s elasticity and on the friction between the wire and the container. When friction is high, the wire adopted nearsymmetric looping patterns, which the researchers termed classical. When friction is low and the wires are stiff and springy (the researchers used steel), the wire adopted spiral patterns. Floppy, soft wires (solder) adopted messy, asymmetric patterns, which the researchers termed plastic. By adjusting the elasticity and friction in their experiment, the researchers could delineate the three regimes in a morphological phase diagram. And, as the figure shows, they could reproduce the three phases with a simple continuum model. The ETH team anticipates their phase diagram could prove useful in characterizing the packing of DNA inside viral capsids and other crumpling systems. (N. Stoop, F. K. Wittel, H. J. Herrmann Phys. Rev. Lett. 101 , 094101, 2008 http://dx.doi.org/10.1103/PhysRevLett.101.094101 .)