Magnetic Force-Based Simulation and Experiment Differ by scaling of (length)^2 for geometries with changing (length)

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My team is trying to 2D model a short (~50um) post (10 x 10 um) with a single cube (sizes from 10-40um) at the top that bends at its fixed base in the presence of slowly rotating (1Hz) magnetic field. The system is also in a fluid medium, so there is fluid structure interaction. The model is compared to experiment and we find that

(exp value) = (Constant) * (sim value) * (L^2)

where "exp value" and "sim value" are the deflection of the cube's leading corner from experiments and simulations, respectively, over a range cube sizes defined by L. "Constant" is a fixed value of 2.5 that was chosen beause it makes the magnitudes of the results agree with minimized R^2 error ~=0.85; the Constant used has the same value no matter what cube size we model.

Even more interesting, the exp results are parabolic (the deflection peaks at an intermediate value of L and drops by ~30 and 70 % at the low and high cube sizes) which this particular scaling matches suprisingly very well. It would seem very odd that this particular scaling matches the data so closely over the wide range of L without some underlying reason since the parabolic nature is tied to simulation geometry. The required Constant could come form material property measurements, or experimetnal field values being off due to fixed machine calibrations and is not seen as a major issue (although 2.5 is an oddly round number).

We've sat with this for months doing hand calculations and simpler models to tease out whether this is an issue with the 2D sim, our application of the Force calculation, Comsols force calculation itself, experimental data collection, some thickness effect that is/not acounted for, and the list goes on.

Anyone have any ideas or threads to pull to help us figure this out? All thoughts are appreiated.


1 Reply Last Post 2024年5月16日 GMT-4 10:49
Jeff Hiller COMSOL Employee

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Posted: 1 month ago 2024年5月16日 GMT-4 10:49
Updated: 1 month ago 2024年5月16日 GMT-4 15:31

Hello Paris,

My initial reaction is to wonder whether the discrepancy may be coming from the model being made in 2D. If I understand correctly, the post has a 10um by 10um square cross-section and is 50um tall. It seems too thick for plane stress yet too thin for plane strain. Not too mention the cube on top, and the FSI, and the rotating EM field, all of which also put the 2D assumption in doubt. Have you tried modeling this in 3D? What happens?

Jeff

PS: Why does this thing deform in the first place? You didn't indicate the materials of the cube and post. Are they both responding to the magnetic field, or only one of them?

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Jeff Hiller
Hello Paris, My initial reaction is to wonder whether the discrepancy may be coming from the model being made in 2D. If I understand correctly, the post has a 10um by 10um square cross-section and is 50um tall. It seems too thick for plane stress yet too thin for plane strain. Not too mention the cube on top, and the FSI, and the rotating EM field, all of which also put the 2D assumption in doubt. Have you tried modeling this in 3D? What happens? Jeff PS: Why does this thing deform in the first place? You didn't indicate the materials of the cube and post. Are they both responding to the magnetic field, or only one of them?

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