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Buckling transitions is the term we apply to what happens when we crumple a piece of paper. Where shall we start? Well, let's induce a curvature energy in the presence of a topological constraint. When we crush foil or paper or plastic, we are putting energy into a material and causing parts of the microstructure to fail and/or break. There are loose "connections" between molecules that give the material its strength. The better the interconnections and the more "engineered" the shape of the microstructure, the stronger the material. When we crumple the material up, a bunch of these connections or microsturctural components are broken. If fact, there is wholesale destruction in lots of areas. And with the breaking of the connections comes the "rebound" of the other parts of the microstructure in the area of the break. If we take a piece of uncooked spaghetti and bend it far enough, it snaps. We've applied energy to it and it broke, releasing some of that energy. And the pieces that are left snap back into a shape. Scale that idea waaaay down. Throughout the breakage event there is movement that creates vibration. Vibration is mechanical energy. Sound. We are hearing the little vibrations of zillions of failures in the microstructure and "rebounds" when "broken connections" in the microstructure of the material occur. Hope that makes sense. There is a whole field of physics that deals with elasticity and stress on films of material like foil and paper. It can be interesting, but be warned that a lot of statistical physics is used to "map" the activity. Naturally if a student is interested in physics, that student would be well advised to roll up the sleeves and grab all the mathematics that can be had. Math is the prime mover in physics and engineering disciplines. Who'd get on a commercial airplane if it wasn't?

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