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When a metal or rubber is bent and deformed, it heats up. What is the reason for this?

I know that when deforming it, work is done on the object. If the object is perfectly elastic, all of the energy is stored as elastic potential energy, which is released when the stress is removed. But if it not perfectly elastic, by energy conservation, some of the energy is dissipated as heat.

By what mechanism does the energy stored due to compression/stretching of chemical bonds (e.p.e) end up increasing the temperature (proportional to avg translational k.e of molecules)?

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When you deform a piece of (for example) metal, on the atomic level you are forcing atoms to press against and squeeze past one another and assume new positions within the structure of the solid. And on the atomic level, there are friction forces that oppose that motion, like when you press your hands together and rub them against each other. This is called internal friction and it generates heat as the atoms snap back and rattle around their new equilibrium positions during the slipping and squeezing process.

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Rubber is a bit of a special case, because it is "elastic", it heats up when stretched and cools when un-stretched.

see https://depts.washington.edu/chem/facilserv/lecturedemo/EntropyofRubber-UWDept.ofChemistry.html

As Niels answered, materials heat up when "plastically" deformed, because of "friction" when you drag sheets of atoms across each other. From a materials perspective this is about tearing up dislocations within the lattice, the stronger the dislocations, the more force is required and work = force * distance = heat generated. Slippery materials like axle grease, don't have dislocations, so the lattice layers can slide across each other with near-zero force hence near zero work and near-zero heat.

Regarding "heating ... due to compression/stretching of chemical bond" , Actually bending doesn't heat up perfect materials. Some years back we worked with an extremely sensitive accelerometer system, that used a beam of etched mono-crystalline quartz. It was frictionless (i.e. so didn't generate any heat) if you achieved a perfect vacuum inside, so there was no heat generated by flexure of the beam. The residual gas atoms inside the accelerometer contributed a measurable noise floor, and lowered the Q of the pendulum due to friction of the gas molecules.

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