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Hi

then what does a plot of sigma over epsilon look like ?

And have you tried to look for changes for 1, 2, 4 order integration ?

But, how would you define the ratio of those two tensors to get to assumingly a more or less constant Young modulus ?

Ivar

I think perhaps my first post is too general so i'll simplify and narrow the question a bit (i hope).

Say i've got a rectangular block and am applying pressures to its surfaces and bending it as well.

At any individual point in the block I could extract an sx_smsld value and an ex_smsld value and I'd expect them to be related by the Young's modulus of the material because that is how Young's modulus is defined, though your last comment is making me wonder about how constant it really is.

If I want to know the average x-stress everywhere within the block I run subdomain integration of the variable of interest, sx_smsld or ex_smsld and divide the result by the block's volume. I thought that these average values in a given direction would also be related by Young's modulus.

The block is an anisotropic silicon crystal

[ 194 35 64 0 0 0 ]
[ 35 194 64 0 0 0 ]
[ 64 64 166 0 0 0 ]
[ 0 0 0 80 0 0 ]
[ 0 0 0 0 80 0 ]
[ 0 0 0 0 0 51 ]

but in any given direction there should be a constant young's modulus and stress-strains in basic xyz directions are all i'm concerned with.

Hi

I beleive that a model of the type Hook's law stress=E*strain is somewhat too simple if you use it on a physical case in 3D with some realistic boundary conditions and with an anisotropic media.

Not that the formula is wrong, by no way, but generalised with the full tensor representation it's not that obvious (for me) to see how to verify it with a simple one line expression or plot.

What I have done and it illustrates it well, is to make a 2D structural model with a square of 1m^2, density 1, Young 1000, bottom face FIXED, top face -1N total force (compression along -y). Then I put nu=0 for the Poisson coefficient and I solve and look at "sy" and "ey" and their ratio, I find back my E.

Now if I set nu=0.33 the poisson coefficient, hence coupling sx and sy and solve again, as my lower boundary is fixed, I'm constrining it also in x, hence I get a more complex surface plot of "E", just because my BC is playing me a game. To extrapolate this to 3D and with an anisotropic material, I would not be astonished that the images are confusing. And I trust COMSOL for representing correctly Hooks law, in all generality.

But what I often burn my fingers on, is the definition of the local coordinate system I use for defining my Silicon (or any crystalline structure) as COMSOL in V3.5a does not give you an easy "visual" view of the local coordinate system, so you should plot the different stress tensor (and for PZT material the coordinate transform is the standard IEEE, see the doc, and the indexes are different from the standard crystalline / structural tensor indexes). or define sequentially force along x,y,z in the new coordinate system and turn on the BC visualisation

good luck
Ivar

AHA! That does make a bit more sense, though it does mean I can't use the simple assumption as an error check. Oh well.

Thanks for the heads-up on the coordinate system as well, I'm now going to have to dig into it a bit deeper and be sure that it is doing what I think it is. Results so far imply that I have it correct, but it seems that it is something i'm going to have to triple-check to be sure of.