I once tested a ferrite core for A_L and saturation, using a pulsed test. On adjusting the PRF, *tick* -- and now way higher current draw? I touch the core, it falls apart -- the core had shattered into regular sized hunks, because I hit an acoustic resonant frequency (and the air gap drew extra magnetizing current).
Magnetostriction is very real, and significant for some materials.
Some datasheets warn not to hit an acoustic resonant frequency, and most warn not to saturate, shock or heat-treat some materials (NiZn I think is particularly susceptible?), lest the B-H curve change.
And of course, the mechanical property of magnetic steel is well known. Supposedly, a hard enough whack, to a piece of metal aligned N-S, will magnetize due to Earth's magnetic field, and subsequently serve as a compass needle. Although I've never seen that presented as any more than an urban legend, no data to back it up. I've not observed it myself, at least with modern alloys. Physically speaking, I could imagine it being something like, crystal slippage causing magnetic domain shifting, serving much the same purpose as mechanical dithering or AC bias, momentarily overcoming the material's hysteresis. The consequential work hardening also creates hard traps that can pin domains. But I'm not aware that anyone's actually tested this.
For ferrite, it would of course be rather difficult to have slippage planes, without the mass falling apart from fracture -- but perhaps a smaller scale effect applies, whether microfractures, or something more basic.
Tim