How to destroy/destabilize a structure that's been flux-pinned?

This technique has been discussed on this site before as a method for creating nearly indestructible super-materials that can absorb as much energy from violent impacts as you can feed into the electromagnetic field holding it together (this same field also necessarily makes it impervious to the effects of electromagnetic pulses or fields weaker than its own). But of course having a truly indestructible super-material is boring, and it becomes even more boring if the only way to beat it is "hit it harder until it breaks".

So, since I'm not an expert in physics or material science, I'm asking those more knowledgeable than I if a method exists to destroy something reinforced with flux pinning/quantum locking that doesn't involve bashing it with repeatedly more force like an angry caveman. Can it be destabilized with a more fine-tuned, technical approach or is it basically just always going to be a matter of bashing your head against the quantum-locked wall until it breaks?

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How to destroy/destabilize a structure that's been flux-pinned?

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