These distortions, unlike simple harmonics, are non-mathematically correlated, and occur in time AFTER the musical signalQuite so. However, and apparently, these can be modelled -- but only with reference to electromechanical properties in each specific application. Unfortunately, I can't find a ref you may be interested in.
BTW, a simple experiment with very hard cone material coupled to powerful electromagnetic support, may reveal an "overdamping" effect (i.e. relative spl drops faster than projected -- further i.e., what we call "decay" is truncated, becoming "sub-audible" if I may coin the ugly word).
A very interesting viewpoint, Martin.