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Hi

I have a few comments on your model ;)

1) the error message comes from the fact that your model is "floating in thin air" : you have NOT defined any fixed point so there is a constant that the solver will integrate until numerical overflow. Fix at least one point fully, or better use 2 planes of symmetry and a roller condition to fix Z height
You must always respect the rule: all dependent variables should have enough defined BC to give an unique solution for all integrations

2) your mesh is not sufficient to correctly resolve any local effects in your thin layer. To overcome this you can either use "thin layer physics" and ignore the thickness (and disable the heigh extrusion of your Al layer, keep it as a boundary only, and set the material properties of Al to the "boundary") or you mesh with at least 3 elements in the thickness.
To obtain that I suggest you to cut your SiO2 layer at the hight of the Al layer, this internal boundary in the SiO2 (you will have 3 SiO2 domains like that, but then you can also apply sweep mesh: select the Si to SiO2+AL boundary mesh it with more: triangular mesh, then select the domains above the Si and use sweep mesh with at least 3 to 5 elements in the thickness. Finish of with normal "thet" for the Si. Another way, by using thets all over, is to , once you have cut up your SiO2, to use the manual mesh and advanced tab and scale the Z direction by a factor 10 at least for your meshing node of the Al and the SiO2 layers

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Good luck
Ivar

I applied the sweep mesh as you've suggested, and the compute result had much clearer boundaries, and lateral stress distribution. Thanks for the advise.

Yet, I still can't see clear stress gradient in vertical direction.
I expected a stress by thermal expansion mismatch to be generated above the Aluminum strip: a stress that will be the greatest right above the Al strip, and decay as it propagates upward.

But the compute results display a stress distribution plot that seems to have only point-like stress sources at the edges of the Al strip. I guess there still are some missing points in the model.

I would really appreciate it if you look over my model once again.

Hi

how dense is your mesh ? you need at least 3-5 elements correctly placed across a thin layer if you really want to resolve the details, normally one often assume the transverse gradient are "0" and one use "thin film physics to model thin layers

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Good luck
Ivar

The model that I attached is a 2-D model with 10 elements across the thin Aluminum strip. Yet, I still can't obtain the appropriate stress gradient above the Aluminum strip in veritcal direction.

I checked the stress distribution above the Al strip using 1-D graph; it turned out the stress increases as it gets further from the Aluminum, which means there must be something wrong about the Physics module that I applied. But the problem is, I really can't figure out what the missing points are. I guess the mesh is dense enough and it's not the problem with mesh density. Can you help me out with this?

Thanks.

Hi

I do not believe there is something wrong in the physics module, to many people use it so that would have been reported before.
It's rather that you have missed some specific boundary condition, or some hypothesis that is not respected.

But like that I really cannot tell, one must dive into the model, plot out more views etc.

This is traditional model V&V so I can only say that it's good practice for any FEM model to be sure one validate what one get

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Good luck
Ivar

Dear Ivar.

Thanks for helping me so far.

I wanna know more about so called "thin layer physics".

I eliminated SiO2 domain just left and right sides of Al strip, it sure is ridiculous and far from reality anyway.
Also one time I just attach Al strip on top of SiO2 domain.

From this I wanna see what happens there is no stress accumulation from Al strip pushing away SiO2 domain to horizontal direction.)

Then whole stress distribution looked like what I expected.

Stress distribution looks like elliptic gradient through medium.

I attached pictures.

So from this I have little bit of doubt that volumetric pushing away stress is largely over estimated than thermal expansion mismatch stress. So stress distribution what I expected was actually happened but it was screened by other factor.

In this manner "thin layer physics" way might be the proper solution to this problem. So can you explain little bit about that to this model?

Thanks.

Hi

analysing the stress means more than just plotting out the von Mises values (which are a combinations of the stress tensor components). Then do not forget that the Poisson coefficient changes the stress distribution if you looking at the far edge with material on only one side, or if you are looking at a cut in the middle of the material.

Check out the different stress tensor components too.

And do not forget to have a reasonable representation you need at least 3-5 mesh elements across the thickness of your layers. so check carefully the mesh dependence of your mode. (for that 2D is easier as this allows far denser mesh for a reasonable time to solve. I have just seen the video on 4.3b there seem to be now some new features allowing to easily cut a 3D model and run a 2D simulation on the cut plane, that I have been waiting for now for several years, finally, we will gain quite some time, and no need to go back to the CAD and save in the unstable DXF format ...

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Good luck
Ivar

Dear Ivar.

Thanks for the input. I understand your concerns and you are right.

But there might be a misunderstanding due to my lack of explanation, sorry about that.
Because previous pictures that I attached few week ago were von mises and I forgot to mention that my last two pictures were x component of stress tensor.
I wanna see some lateral direction stress distribution.

As you can see stress in al strip is lower than SiO2 because it suffer from compressive stress. In von mises case Al region would be highest region.

I tried various kind of stress component and formats but in every cases left and right edge of strip have dominance over total stress distribution(and it decay relatively fast).

Also I use mapped mesh to give dense layer to the Al strip and near regions but main behavior was the same.

I tried a little bit with 3D model, still got the same results but I will try further soon.

Maybe my simple notion that "I would see elliptical stress distribution around Al strip" is too naive and results from COMSOL is actually accurate for situation.

Anyway I am happy to get more comments and any corrections.

P.S can you give me some direction(or where I can look for e.g. manual) for "thin layer physics" ?
If that dose not cause you too much trouble and affecting your own businesses.
I always admire your enthusiasm for this forum.
Thanks for sharing your time with us.


Myung Rae.

Hi

analysing stress, as for any multicomponent tensor is often tricky, and we often have very simplified approaches, issued from thinking in 2D cut view for full 3D models. But there again, it depends on your experience, I'm always very prudent when it comes to state how a stress distribution really is, I notice I always forget some effect ;)

for the thin film physics, really the doc is the easiest, it's essentially the same hypothesis a for 2D that the third direction has no significant gradients and can be extracted from the formulas ans replaced by y d_thickness of the layer simple multiplier

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Good luck
Ivar

Hi,

I built my geometry with Silicon rectangular frame. On the top of the frame, I attach silicon nitrite cross bridge. After heat up the whole geometry, the resonant frequency is increasing 1Hz per 10 degC and then drop down. I'm thinking the reason is because the frame is heating up firstly, which will cause residual stress on the cross bridge. When the temperature goes higher, the bridge's resonant frequency will drop down. On the comsol I use thermal expansion and external stress. It seems to me the resonant frequency never goes up after heating up the frame. Can some one tell me why this happen?

Thanks

Wenyuan