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Effective Young's modulus used by comsol for simple uniform loading

Posted 31.03.2014, 15:40 GMT-4 Structural Mechanics Version 4.3 6 Replies

Lionel Wong
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Hi,

I have some fundamental problem with the solid mechanics problem. I have a square and would like to exert uniform load on the top surface. The simulated results give the correct y-stress (which is expected since this is y input), but the y-strain obtained is slightly smaller, which means that the modulus used is not the same as the material input young's modulus.

Hand calculated: y-stress:26250Pa ystrain: 8.47e-6 given E=3.1e9Pa
Comsol: y-stress: 26250Pa ystrain: 7.43e-6

Could it be that my boundary conditions are wrong and over-restricting the model. I have checked the Young's modulus after simulation and it is the same as the input value. Also, the strain in the x direction is wrong as I would expect it to be y-strain multiply by the poisson ratio, but it is not the case too. I have use a point fixed constraint at the bottom left point and also a "roller" for the bottom line.

Please advise. Thanks.

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6 Replies Last Post 01.04.2014, 10:27 GMT-4
Jeff Hiller COMSOL Employee

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Posted: 1 decade ago 31.03.2014, 15:49 GMT-4
It sounds like your pen-and-paper calculations assume plane stress. Your file is set up in plane strain. Once you switch to plane stress, you do get a y strain of -8.46e-6.
Jeff
It sounds like your pen-and-paper calculations assume plane stress. Your file is set up in plane strain. Once you switch to plane stress, you do get a y strain of -8.46e-6. Jeff
Lionel Wong
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Posted: 1 decade ago 31.03.2014, 16:27 GMT-4
Hi Jeff,

Changing to plane stress works for the strains. However, the x-stress result is still wrong. In theory, it should be x-strain multiply by E, which should yield about 9000Pa, but the result i'm getting is 4e-10, which is weird. Also the values fluctuates and there is no smooth data. Could this be a resolution problem? Please advise. Thanks.
Hi Jeff, Changing to plane stress works for the strains. However, the x-stress result is still wrong. In theory, it should be x-strain multiply by E, which should yield about 9000Pa, but the result i'm getting is 4e-10, which is weird. Also the values fluctuates and there is no smooth data. Could this be a resolution problem? Please advise. Thanks.

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Jeff Hiller COMSOL Employee

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Posted: 1 decade ago 31.03.2014, 17:11 GMT-4
Please check out this link for the relation between stresses and strains in plane stress: en.wikipedia.org/wiki/Hooke%27s_law#Plane_stress .
Theoretically, Sigma_xx should be exactly zero. COMSOL returns a value of the order of 10^-10 because of finite numerical accuracy. In other words, the Sigma_xx plot shows you numerical noise. Your mesh is actually much finer than really needed for this application.
Jeff
Please check out this link for the relation between stresses and strains in plane stress: http://en.wikipedia.org/wiki/Hooke%27s_law#Plane_stress . Theoretically, Sigma_xx should be exactly zero. COMSOL returns a value of the order of 10^-10 because of finite numerical accuracy. In other words, the Sigma_xx plot shows you numerical noise. Your mesh is actually much finer than really needed for this application. Jeff
Lionel Wong
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Posted: 1 decade ago 31.03.2014, 17:38 GMT-4
Hi Jeff,

I'm a little confused. I agree with the z-stress (sigma33) to be zero which is the case in the sim. and also the link that you provided. However, x-stress should not be zero (sigma11), which is what is stated in the link too. Also, given that I have a proper value for x-strain (non zero), it should be inferred that x-stress cannot be zero too. Please advise on this.

Another thing is, is there a way to hand calculate the results when we use the plane-strain option. Thanks.
Hi Jeff, I'm a little confused. I agree with the z-stress (sigma33) to be zero which is the case in the sim. and also the link that you provided. However, x-stress should not be zero (sigma11), which is what is stated in the link too. Also, given that I have a proper value for x-strain (non zero), it should be inferred that x-stress cannot be zero too. Please advise on this. Another thing is, is there a way to hand calculate the results when we use the plane-strain option. Thanks.
Jeff Hiller COMSOL Employee

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Posted: 1 decade ago 31.03.2014, 18:25 GMT-4
If you compute the expression at the link above you will find that it results in Sigma_xx=0. This is also trivial if you think about it: your model is invariant in the x direction so if you imagine taking a vertical cut in that part there cannot be any net force exerted by one side onto the other.
Jeff
If you compute the expression at the link above you will find that it results in Sigma_xx=0. This is also trivial if you think about it: your model is invariant in the x direction so if you imagine taking a vertical cut in that part there cannot be any net force exerted by one side onto the other. Jeff
Lionel Wong
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Posted: 1 decade ago 01.04.2014, 10:27 GMT-4
hi Jeff,

Thanks. I understand that now.
hi Jeff, Thanks. I understand that now.

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