Also, I don't know that hysteresis is an unlikely candidate for energy loss. I think about multiple laminations as having multiple compression and tension surfaces, each with their own neutral plane. Of course any internal tension surface is backed and so supported such that failure at the tension line is unlikely, and similarly the compression face is supported by the next tension surface down. The forces going into each of these laminations, and interacting between them, are just multiple places to lose efficiency when you release the string. Heat loss is a possible energy sink (and yes, I am guessing), but so is reformation of the material surfaces.
SOM