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How to explain the expression of von Mises Yield criterion in v4.1
Posted May 2, 2011, 9:27 a.m. EDT Materials, Parameters, Variables, & Functions, Structural Mechanics Version 4.1 5 Replies
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Hi,
Before going into my question, I must admit that I am a relatively new user of COMSOL.
I have been attempting to understand variable definitions in yield criterion for an elastoplastic material in Structural mechanics module. Upon examining the equation structure for the already existing von Mises yield function, I seemed to be unfamiliar with the expression there, which reads as
solid.sEff =
sqrt(1.5*((solid.SX-(solid.SX+solid.SY+solid.SZ)/3)^2+2*solid.SXY^2+2*solid.SXZ^2+(solid.SY-(solid.SX+solid.SY+solid.SZ)/3)^2+2*solid.SYZ^2+(solid.SZ-(solid.SX+solid.SY+solid.SZ)/3)^2)+4*solid.sigmags^2*eps)
My only problem is with the last term under the square root: 4*solid.sigmas^2*eps.
Why should it be there at all?
Furthermore, the variable eps appears neither defined in the same list nor in any of the documentation files for v4.1. If it were the EPSILON of machine precision variable, then what is the necessity of the last term? What is the point in having a factor 4 when multiplying with eps?
Could this be a mistake of having this last term? or I am missing some thing?
Best,
Kodanda
Before going into my question, I must admit that I am a relatively new user of COMSOL.
I have been attempting to understand variable definitions in yield criterion for an elastoplastic material in Structural mechanics module. Upon examining the equation structure for the already existing von Mises yield function, I seemed to be unfamiliar with the expression there, which reads as
solid.sEff =
sqrt(1.5*((solid.SX-(solid.SX+solid.SY+solid.SZ)/3)^2+2*solid.SXY^2+2*solid.SXZ^2+(solid.SY-(solid.SX+solid.SY+solid.SZ)/3)^2+2*solid.SYZ^2+(solid.SZ-(solid.SX+solid.SY+solid.SZ)/3)^2)+4*solid.sigmags^2*eps)
My only problem is with the last term under the square root: 4*solid.sigmas^2*eps.
Why should it be there at all?
Furthermore, the variable eps appears neither defined in the same list nor in any of the documentation files for v4.1. If it were the EPSILON of machine precision variable, then what is the necessity of the last term? What is the point in having a factor 4 when multiplying with eps?
Could this be a mistake of having this last term? or I am missing some thing?
Best,
Kodanda
5 Replies Last Post May 3, 2011, 3:56 a.m. EDT
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Posted:
1 decade ago
Hi
This is no mistake. Try to write "eps" in a parameter value and you will see what it gives you: (just as for matlab) the smalles number you can differenciate from 1, on the PC's binary representation of floating point values.
Bit I accept that its some of the "black magic" of numerical calculations, how to avoid square root of negative values, or dicision by "0" or other INF generating error conditins. Anytme you see an "eps" it is there to avoid a numerical instaility or a poure dicison by "0" or a INF trap generation
--
Good luck
Ivar
This is no mistake. Try to write "eps" in a parameter value and you will see what it gives you: (just as for matlab) the smalles number you can differenciate from 1, on the PC's binary representation of floating point values.
Bit I accept that its some of the "black magic" of numerical calculations, how to avoid square root of negative values, or dicision by "0" or other INF generating error conditins. Anytme you see an "eps" it is there to avoid a numerical instaility or a poure dicison by "0" or a INF trap generation
--
Good luck
Ivar
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Posted:
1 decade ago
Hi Ivar,
thanks for your reply.
It is still surprising, since firstly, the terms under the sqrt are squares, so no negative numbers. Secondly there is no condition of dividing by 0. Third, all the squared terms are added up. So I could see no problem.
Above all, the factor 4 in front of the term with "eps" is very strange, isn't it? For a safety mechanism with eps, multiplying with 4 (along with MPa s of stress) does not appear to be plausible.
Best,
Kodanda
thanks for your reply.
It is still surprising, since firstly, the terms under the sqrt are squares, so no negative numbers. Secondly there is no condition of dividing by 0. Third, all the squared terms are added up. So I could see no problem.
Above all, the factor 4 in front of the term with "eps" is very strange, isn't it? For a safety mechanism with eps, multiplying with 4 (along with MPa s of stress) does not appear to be plausible.
Best,
Kodanda
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Posted:
1 decade ago
Hi
AI agree that looking only into this equation it looks strange, but it depends what is happening with the final variable, perhaps it's used in a situation with a 1/0 possibility, then it makes sens and if you take the set all other variables to "0" you end up with a 2*sigma ...*sqrt(eps). One should never judge a system on an individual element
be aware that as most physical equations are 2nd order equations, the minimum numerical value that has any sense is hence not "eps", but mostly sqrt(eps) which is not that small (and this in double precision). we really need 512 bit floating point representation soon ;)
--
Good luck
Ivar
AI agree that looking only into this equation it looks strange, but it depends what is happening with the final variable, perhaps it's used in a situation with a 1/0 possibility, then it makes sens and if you take the set all other variables to "0" you end up with a 2*sigma ...*sqrt(eps). One should never judge a system on an individual element
be aware that as most physical equations are 2nd order equations, the minimum numerical value that has any sense is hence not "eps", but mostly sqrt(eps) which is not that small (and this in double precision). we really need 512 bit floating point representation soon ;)
--
Good luck
Ivar
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Posted:
1 decade ago
Hi Ivar,
Thanks for the reply. I agree more on your lines. This would also suggest that if I were to define my own yield function, it is safe to add this term.
Now, I tend to think that to have a user defined yield function, it may not be so simple just to define an alternate expression but one should better look into the exact algorithm in COMSOL.
Another example where there is a lack of proper documentation... I will contact support.
Best regards,
Kodanda
Thanks for the reply. I agree more on your lines. This would also suggest that if I were to define my own yield function, it is safe to add this term.
Now, I tend to think that to have a user defined yield function, it may not be so simple just to define an alternate expression but one should better look into the exact algorithm in COMSOL.
Another example where there is a lack of proper documentation... I will contact support.
Best regards,
Kodanda
Please login with a confirmed email address before reporting spam
Posted:
1 decade ago
Hi
have you checked the elasto-plastic material properties, perhaps that is already what you are looking for ?
I know COMSOL is working on the documentation, as there are several thousand pages to update, COMSOL covers more physics field than what I covered over 4 year at the university so this needs some time, specially since they changed to v4. But you should find the references for the articles used behind the theory, in the doc.
another tip, index your pdf doc and use the index searcher to find your way therein
--
Good luck
Ivar
have you checked the elasto-plastic material properties, perhaps that is already what you are looking for ?
I know COMSOL is working on the documentation, as there are several thousand pages to update, COMSOL covers more physics field than what I covered over 4 year at the university so this needs some time, specially since they changed to v4. But you should find the references for the articles used behind the theory, in the doc.
another tip, index your pdf doc and use the index searcher to find your way therein
--
Good luck
Ivar