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Young Modulus Assessment

Posted Jul 6, 2023, 5:35 p.m. EDT Structural & Acoustics, Geomechanics, Structural Mechanics Version 6.1 1 Reply

Ali Madani
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Hi Everyone!

I would like to calculate Young modlus (E) for some 2D porous media images like the following image:Like This

Black parts are solid and white parts are air (Zero velocity). Could you please suggest me a workflow in terms of moduls and boundry conditions? Thank you in advance

1 Reply Last Post Jul 7, 2023, 10:21 a.m. EDT
Jeff Hiller COMSOL Employee

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Posted: 10 months ago Jul 7, 2023, 10:21 a.m. EDT
Updated: 10 months ago Jul 7, 2023, 10:36 a.m. EDT

Hi Ali,

In at least the first image the solids look like they are disconnected so this material would not be able to carry tension and would not follow Hooke's law.

But there's a more fundamental problem/question here that affects all three images. You're proposing to work in 2D, which implies that you either a/ have a situation where the material is independent of the third dimension, in which case it isn't isotropic and doesn't follow Hooke's law (so there's no Young's modulus to speak of), or b/ are talking about a very thin layer of this material being subjected to plane stress under a particular loading/BC combination and only care to determine an equivalent Young's module for that very specific case.

If you're in case b, then you can get inspiration from this model, though it involves different physics. In your case, I would make sure to apply plane stress conditions and apply appropriate material properties to the solid regions (the air region should be removed entirely from the COMSOL geometry), set up BCs to apply an equivalent tensile load on two opposite sides and put the other two sides on rollers. From the results of the analysis you'll be able to compute an equivalent Young's modulus by relating the applied equivalent stress in the loading direction to the resulting equivalent strain in the loading direction. An important caveat here is that based on the images above you will get different equivalent Young's moduli in different directions because the samples are too small to yield equivalent properties that are independent of directions (and to repeat myself, there's no point trying this type of analysis with the first image since the solid phase in it is not even continuous).

Best,

Jeff

PS: Left unsaid above is the fact that you need to know the material properties of the black regions.

-------------------
Jeff Hiller
Hi Ali, In at least the first image the solids look like they are disconnected so this material would not be able to carry tension and would not follow Hooke's law. But there's a more fundamental problem/question here that affects all three images. You're proposing to work in 2D, which implies that you either a/ have a situation where the material is independent of the third dimension, in which case it isn't isotropic and doesn't follow Hooke's law (so there's no Young's modulus to speak of), or b/ are talking about a very thin layer of this material being subjected to plane stress under a particular loading/BC combination and only care to determine an equivalent Young's module for that very specific case. If you're in case b, then you can get inspiration from [this model](https://www.comsol.com/model/pore-scale-flow-488), though it involves different physics. In your case, I would make sure to apply plane stress conditions and apply appropriate material properties to the solid regions (the air region should be removed entirely from the COMSOL geometry), set up BCs to apply an equivalent tensile load on two opposite sides and put the other two sides on rollers. From the results of the analysis you'll be able to compute an equivalent Young's modulus by relating the applied equivalent stress in the loading direction to the resulting equivalent strain in the loading direction. An important caveat here is that based on the images above you will get different equivalent Young's moduli in different directions because the samples are too small to yield equivalent properties that are independent of directions (and to repeat myself, there's no point trying this type of analysis with the first image since the solid phase in it is not even continuous). Best, Jeff PS: Left unsaid above is the fact that you need to know the material properties of the black regions.

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