# Hooke's law limitation question

Let's consider a spring. I am a strong man(well, lets assume) and I am pulling the spring. the work I do is being stored in the spring in the form of its elastic potential energy. Then suddenly, elastic limit is crossed and the spring reaches to the yielding region. then, at that very moment, i become exhausted and release the spring. then I realise that the spring doesn't budge. the energy i stored is lost. its gone. Nowhere to be found. Mind helping me find it?

• It's been used to deform the spring permanently. Apr 10 '13 at 15:49
• in what form it will store then? Apr 10 '13 at 15:51
• Each arrangement of atoms in a material has a certain amount of energy stored in it (call it the structural energy) which basically comes down to the electrostatic energy of the atoms and their electrons. When deforming a material, you change the arrangement and thus change the electrostatic energy. By pulling our your spring too hard, you bring the atoms in a new "metastable" state where they won't revert to the old position on their own, but still have a higher energy than before. Apr 10 '13 at 15:56
• ah, nice answer man Apr 10 '13 at 15:57

That said, if you continue deforming the material beyond the yield point of the material, any extra work ($\dot{W} = \sigma:\dot\epsilon$ assuming a perfectly plastic material) will be dissipated as heat. The energy is spent rearranging the microstructure of the material, and it cannot be recovered.