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Yes that would be the stuff and other than recognize what they are dealing with I don't know a huge amount of material science stuff. Basically they would be attacking the orbital stability within the lattice structure in the normal QM realm.

At a guess they will model it as lots of little harmonic oscillators so you have atom oscillations and the lattice oscillations superimposed over the top. Ultimately the atoms around on the surface wont be fully balanced so you need to model them and superimpose that over the top of the internal result. What you end up with is a model of seething vibrating complex oscillations in quantum fields and you and I would see the result as a solid in classical physics. It is probably a lot worse than that and I will have missed important stuff but that would be my initial guess.

In sort of layman terms those larger resonances will have a sort of inertia effect and resist the solid changing shape the old conservation of energy again. It would really only want to change shape if it was energy effective to do so as the resonance has to collapse to a new one.

That is why you can do weird things with metamaterials as there is a pronounced composite effect as well as an atomic effect and that isn't obvious when you look at it from a classical viewpoint. Your are also getting into areas as superconductive materials etc and it's not fully complete yet.