This relates to the extension of a uniform cross-section, homogenous, ideal wire which extends within the proportional limit (Hooke's law). From my understanding, only half of the gravitational potential energy lost when the mass is lowered on the initially un-extended wire, is stored in the wire itself as potential energy which increases the separation of molecules internally as long as the load is maintained. According to my understanding, the remaining half of GPE in fact remains in the mass and this is eventually dissipated as heat (if there is surrounding air to oppose motion) and work is done on the hand which lowers the mass. Why is only half but not all of the GPE stored in the wire? I was told that this is due to the stress-strain relation (straight line through origin) but its not that convincing. Thank you.