Can't tear something into three pieces

[OranL]

Does anyone know what physical principle theoretically prevents something from being torn into three pieces from two forces being applied? (E.g. pulling on both sides of a piece of paper will never tear it into three pieces.)

 

[Andy Resnick]

Yes, but breaking a piece of spagahetti by bending it will usually result in three pieces (I think Feynman describes this), so your assumption is wrong.

There's some work out there on crack formation and propogation, the main result is that the stress field is locally concentrated near the crack tip, and this localizes the crack by relaxing the stress away from the crack tip.

 

[tiny-tim]

See http://www.exn.ca/Stories/1998/05/06/54.asp (Discovery Channel):

If you were to tape a coin to the middle piece of paper, that would dramatically increase its inertia. It is then it is a fairly simple matter to tear the paper into three pieces. Pull sharply on the two outside edges and both outside pieces split away, because the inertia of the heavy middle piece keeps it stationary while the outside pieces tear off.

This web-page also explains why you can't do it for plain paper:

No matter how small the last remaining vestiges of paper are at the bottom of the tears, one will always be stronger than the other and will remain intact while the other side tears apart. What makes this work, however, is that the centre piece of paper is extremely light and thus has little inertia. It simply tags along with one side or another.