Stress Analyzes, sigmaEq and Von Mises

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 June 30, 2015, 10:46 Stress Analyzes, sigmaEq and Von Mises #1 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Tussenhausen Posts: 2,699 Blog Entries: 6 Rep Power: 51 Hi all, I am a bit confused at the moment. Using the solver solidDisplacementFoam and a simple test case (beam with tension; fixed pressure) leads to a sigmaEq which should be the von Mises stress. I have to check it in my book tomorrow but up to know I checked the "wikipedia" where I get the equation for calculating von Mises like: Code: ```sigma_vonMises = sigmaEq = sqrt(3*I) where I is the invariant of the stress tensor deviation: I = 1/2 * s_ij * s_ij``` I think the deviation of the stress tensor is calculated by using the following code: Code: `magSqr(dev(sigma))` At least the code (I think you know it), looks like: Code: `sigmaEq = sqrt((3.0/2.0)*magSqr(dev(sigma)))` The problem now is the following. If I compute the stresses in all directions with Code: `foamCalc components sigma` I get all stresses that can be used to calculate the von Mises stresses again (see here for the general eqn. https://en.wikipedia.org/wiki/Von_Mises_yield_criterion) If I do this in paraview I get a complete different result from the equivalent von Mises calculated by FOAM and by the general eqn. Both should be the same if I understand it correct. All hints are welcomed. __________________ Keep foaming, Tobias Holzmann

 June 30, 2015, 15:26 #2 Super Moderator     Philip Cardiff Join Date: Mar 2009 Location: Dublin, Ireland Posts: 1,082 Rep Power: 33 Hi Tobias, I tried this using the plateHole tutorial case and the results were almost the same using both methods (I assume the small difference was due to precision). If you were looking at a 2-D case, you need to be careful for the plane stress cases as sigma_ZZ is not directly forced: it is instead implied through manipulation of mu and lambda lame parameters: this means sigmaEq will not be correct. For 2-D plane strain and 3-D, everything should be fine. Philip

 June 30, 2015, 15:55 #3 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Tussenhausen Posts: 2,699 Blog Entries: 6 Rep Power: 51 Hi Philip, thanks for your replay. I already saw today, that you are using stress solver within openfoam. I will check it out tomorrow but in my case it was a 3d cylinder with a tension force. Maybe I will upload the case tomorrow. Are you using extend for stress analyzes or the standard version? I should simulate the stresses in a disc with a borehole. Imagine that there is a screw in the borehole with tension force. Then I wanna know how the strain is. It should be possible with FOAM (maybe with Extend). Can you confirm that? __________________ Keep foaming, Tobias Holzmann

 July 1, 2015, 02:50 #4 Super Moderator     Tobias Holzmann Join Date: Oct 2010 Location: Tussenhausen Posts: 2,699 Blog Entries: 6 Rep Power: 51 Hi, I also checked the von Mises at the plateHole but did not get same results. Using that formula: I get different values for the von Mises stresses. I assumed tau as zero here. Any suggestion would be appreciated. Thanks in advance. __________________ Keep foaming, Tobias Holzmann

July 20, 2015, 23:26
#5
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Philip Cardiff
Join Date: Mar 2009
Location: Dublin, Ireland
Posts: 1,082
Rep Power: 33
Quote:
 Originally Posted by Tobi Hi, I also checked the von Mises at the plateHole but did not get same results. Using that formula: I get different values for the von Mises stresses. I assumed tau as zero here. Any suggestion would be appreciated. Thanks in advance.
Why do you assume tau is zero? The XY shear stress (called sigmaXY in ParaView) in the plateHole case will not be zero.
You could try prepare a simple 3-D block case and apply simple principal stresses to check your calculations.

Philip