Nodal stress vs Centroidal stress in Plastic analysis

[fl11]

Hi,

In my company we are starting to investigation non-linear FEM. WE encountered some situations that lead us to question the results we are getting. Since then, we have some debates going on and I would like to have your two cents. (We are using mostly Nastran/Patran, but I guess the subjects are more general and apply to any softwares.)

1 - WE defined our true/stress-true/strain curves. After Ftu, the software assumes a perfectly plastic material. Therefore, in the FEM model, there should never be any stresses above Ftu as it is not defined by the material curve. When we look at the results, we can see some stresses way above Ftu. This occurs only when the nodal von mises cauchy stresses (shape function interpolation from gauss points) are plotted (non averaging). When interpolation at centroid is plotted, then it seems that it follows in a better way the material curve. But, I often read that the shape function interpolation was closer to the "real stresses" and was the better interpolation. And I would have tought that for a fine mesh, they would both almost give the same results. Any thoughts about using Nodal shape function stress vs centroidal stresses in non-linear problems?

2 - Following the first question, Von Mises stresses at centroid seem to follow closely the material curve, but when the principal stresses are plotted, again at centroid, then the stresses are so much higher (not following the material curve at all). I always understood Von Mises as a yield criteria so not necessarly usefull after yielding. But another criteria gives very different results. So now, should Von Mises or Principal stress or any other criteria be used for predicting failure for non-linear problems?Any thoughts?

Thanks.

 

[crisb]

I find its better to plot unsmoothed stresses at integration points, for runs with material plasticity.

 

[fl11]

crisb,

Are you plotting Von Mises stresses, principal, just cauchy components?

Do the stresses at integration points can exceed Ftu in a non-linear run? I guess not because the softaware should follow the material curve at least at the integration points. What if the stresses at integration points are not available? What can come closer to those points?

 

[rb1957]

can you control (ie define) the yield criteria in the FEA ? is it fixed ?? do you know what it is ??? (not being snarky)

isn't your stress strain curve the definition of the individual components of stress. you'd (well, i'd) think that the FEA would apply a yield criteria based on say von Mises criteria, which says (doesn't it?) that failure occurs when the combined stress is equal to the critical stress (eg ftu).

IMHO the least "averaged, interpolated" stress is the stress at the integration points. that being said, the element centroid stresses smooth the stress over the element, and the nodal averaged stresses smooth the stress over adjacent elements (different elements will have different stresses at common nodes). so how do you want to smooth your stresses ? i'd've thought that is a plastic analysis there's already alot of smoothing and redistribution going on, so a little more shouldn't hurt !?

 

[IDS]

A non-linear analysis works by iterating linear analyses with adjusted elastic modulus values until the stress/strain in each element is sufficiently close to the input stress/strain curves. Since each element can only have one elastic modulus the adjustment is based on the stress at the centroid. It follows that for elements with a steep strain gradient the stress may be well above the specified yield stress at some nodes or integration points. The answer is to subdivide the elements in question and see if it makes a significant difference.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[crisb]

Doug

"Since each element can only have one elastic modulus the adjustment is based on the stress at the centroid"

Was this intended to refer to one particular program code or more generally?

 

[IDS]

"Was this intended to refer to one particular program code or more generally?"

It refers to the programs I'm familiar with, particularly Strand7, but I imagine it would apply to most if not all general purpose programs.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[fl11]

I agree with a lot that has been said here. The question I have is that the mesh we are using is fine enough (quality check has been performed as well to ensure the element quality) and wether you look at centroid stress interpolation or nodale shape function interpolation, the stresses vary a lot. (50 ksi difference). I am just wondering if we are interpreting the result correctly.

In my mind, the stresses and strain are calculated at the gauss points and the software caculates the state of the elements at those points and then interpolate the results at the node or centroid. The state of those points should be compared to the material curve and should follow as much as possible that curve. So that is why I find very odd that some stresses can be 100 ksi above ftu if the maximum plastic stress that can be achieved is Ftu.

We don't use any predefined failure criteria input. We just define the material curve and by analysing the results, we expect that if some stresses reach Ftu, than the component fails. But we certainly do not expect any stresses to have values way over Ftu as the material is defined with a plateau beyond Ftu.

As I mentioned before, Von Mises at centroid seem to follow the material curve, but Principal stress at centroid shows stresses way above Ftu. And that much difference wether you look at one result or the other is very preoccupying.

 

[crisb]

Have you tried plotting effective (von Mises) stresses at integration (gauss) points without carrying out any interpolation or smoothing? They should match the stress strain curve well, if not exactly.
Interpolation and smoothing will give you spuriously high results as soon as there is a significant degree of plasticity.
I appreciate other peoples point of view but am sceptical that is is sensible to plot values at centroids, or that values at centroids are used by mainstream programs to determine the yield criterian for nonlinear materials.

 

[fl11]

That is something I have to find out how do to with Patran sol600. I don't know if it is an option always available or you have to call something in order to access stresses at integration points.

 

[Pawel27]

Maybe some explanations: When at Gauss point stress is above yield limit, then this value is copied to the nodes
(stress is less or equal yield limit). If at Gauss point stress is below yield limit, then stress value is extrapolated to the node. Then due to extrapolation stress can be above yield limit.

 

[rb1957]

i thought (quite possibly wrongly) that the FE is calculating stresses (x-, y-, xy-) according to your stress-strain curve. in which case these stress components would max out at ftu, and then von mises, being a combination of these stress components, would be higher than ftu.

 

[Pawel27]

rb1957 - tensile test (I mean laboratory test) is performed
in such way that there is only one uniaxial stress - tensile stress. Stresses are reduced (for example by using Huber - Mises hypothesis) in order to have possiblity to compare these uniaxial stress from laboratory test with
reduced stress. Stress reducing means that all x,y,xy stresses are reduced to the on uniaxial. Only reduced stress can be compared with stress - strain curve.