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More specifically, where does it go after it destroys the crumple zone? My assumption is that after a collision most of the kinetic energy will be transferred into the metal in the crumple zone (the rest being sound/heat), making it bend and deform. But what happens after it crumples? Was all the energy simply released as sound and heat? Or does the bent and deformed scrap contain some elastic energy?

I can't believe that the ~250kJ of kinetic energy in a car is all converted to sound and a little bit of heat after a crash. Or maybe sound requires a lot more energy than I'm thinking.

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  • $\begingroup$ I've always wondered this myself. The "classical" answer is that it goes into the "crumpling" of the sheet metal. This would actually be a great question to ask a chemist, as it involves changes that are associated with the potential energy stored in the configuration of a crystalline solid. (bonds are broken/rotated etc). $\endgroup$ – David Reed Nov 13 '17 at 3:08
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when metal is crumpled, work is performed on it. Part of that work is dissipated as heat, which warms the metal slightly, as the metal yields under the applied stresses and deforms plastically. You can demonstrate this yourself by rapidly bending a piece of coat hanger wire back and forth, and then feeling it at the bend. The rest of the work input gets stored as strain energy in the deformed metal itself. this strain energy increases the hardness and subsequent yield strength of the deformed metal, which you can also demonstrate to yourself by trying to unbend the bent portion of the coat hanger: it takes less work to bend an unbent segment of the wire adjacent to the bent part than it does to unbend that bent part.

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  • $\begingroup$ It's primarily the increased dislocation density, not strain energy, that results in increased hardness / yield strength. The plastic deformation of a metal creates untold numbers of additional dislocations that serve as an impediment to future dislocation motion, thus strengthening the material. "Strain energy" generally refers to elastic strain energy, which is recovered when the load is removed. $\endgroup$ – Chemomechanics Nov 13 '17 at 6:07
  • $\begingroup$ thanks. In my own view of this process, I always included the self-energy of the dislocations themselves as repositories of the strain energy stored in the deformed lattice. is this picture inaccurate? -Niels $\endgroup$ – niels nielsen Nov 13 '17 at 8:23
  • $\begingroup$ Dislocations are associated with strain energy, but not all strain energy increases the hardness. $\endgroup$ – Chemomechanics Nov 13 '17 at 19:02
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Can model this as a ball colliding into a stationary spring compressing it. The spring has a latch mechanism which engages and holds the spring in its state of max compression. If the collision and spring and latch are non-dissipative, all the (kinetic) energy of the ball is converted into the potential energy locked in the spring. If a fraction of the energy is dissipated into heat and sound, that much less will end up locked into the spring in its final configuration. The spring latch may never unlock -analogous to the metal of the car folding into a fixed shape. The mass of the car will increase according to m = e/c^2.

Beyond that: Kinetics of stored and dissipated energies associated with cyclic loadings of dry polyamide 6.6 specimens studies where the energy goes for a particular polymer. From the abstract:

From a thermodynamic viewpoint, it was shown that the dissipated energy per cycle was always less than the mechanical energy that could be associated with the area of the hysteresis loop. This energy difference reflects the significant contribution of the stored energy associated, cycle by cycle, with the microstructural changes.

The area under the stress strain curve is the energy absorbed during deformation. They made infrared observations of the heat dissipated, and could see how much less this was than the total energy absorbed during deformation (and unloading as they tracked around an entire Hysteresis loop).

A heuristic model here: the canonical metastable potential, where the compression is initially non-dissipative / reversable / elastic as one roles the ball up the hill, then becomes plastic / non-reversable as the ball roles into the higher little stable valley. The difference in energy between the initial and final potentials of the ball correspond to increased internal energy in the crystal lattice who's structure has changed(compressed). Some of the balls energy may also go into heat.

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