nonlinear analysis / tangent modulus 5

[ikkedus]

for a project i'm trying to calculate the stresses and deformation of a steel (st52-3) structure with Cosmos.

After conducted a linear analysis the stresses are above the yield strength. I thought it is then usefull to do a nonlinear analysis? After trying a nonlinear analysis i found that the stresses and deformation using the different modules are very different. I'm not sure i'm doing it correctly.

My main 3 questions are:

1) with nonlinear analysis i can choose different material models. I tried linear elastic isotropic and Von Mises plasticity (isotropic). Which one should be used?

2) The value for "Tangent Modulus" has to be given. Does someone know the value or formula that i can use for s355 (st52-3)?

3) with nonlinear analysis i can flag a option "large displacement formulation". When i use this the stresses are lower. Do i need to check this box in order to get an accurate result?

Any info would be very welcome. Thanks in advance.

Ikkedus

 

[feajob]

1) Which one did you use and what was the difference between the obtained stresses? linear elastic isotropic or Von Mises plasticity

2) You may find some information regarding stress-strain curve of your steel in MIL-HDBK-5H. Click on the link of MIL-HDBK-5H:

http://www.geocities.com/fea_tek/asd/

3) If you find the large displacement in your structure then your structure is undergoing through large displacement. If not, you are just dealing with small displacement problems and by using this option, I guess that you will just slow down the analysis process. Compare the largest displacement with the size of your structure.

AAY

 

[TGS4]

I would highly recommend that you find a textbook on the therory of plasticity and read it. This is such a massive topic that cannot be fully appreciated in a forum such as this.

Suffice it to say that LEHI analyses (linear-elastic-homogeneous-isotropic) will give a substantially different result from one that has non-linear effects - they are totally different analyses. One question (of hundreds) that you should know the answer to: do you fully appreciate that a non-linear solution is path-dependant?

Do the research on the subject matter and them get back to the forum with the fruits of your research.

 

[sdm919]

I don’t use COSMOS, but do perform nonlinear structural analysis. There are 3 basic types of nonlinearity: material, geometric, and contact. Material is nonlinear stress-strain behavior, which includes plasticity. Geometric is when the displacements are large enough that the equilibrium equations can’t be written in the undeformed position. Contact is when parts of the structure press together or separate (such as at joints), and the stiffness varies due to the changing contact area. These are separate behaviors, and only one or all 3 may be acting at the same time. Here are my answers to your questions:

1) Material model: Since your stresses from a linear run are above yield, you are interested in plastic behavior; therefore choose von Mises plasticity, not linear elastic. Both of these are for isotropic materials, which I assume is OK for your steel. The von Mises yield criterion is good for ductile metals.

2) Tangent modulus: In general, the tangent modulus is the slope of the stress-strain curve, so it’s equal to E in the elastic region and it varies continuously in the plastic region. Sometimes, a bilinear representation of the stress-strain curve is used, in which case they may be calling the tangent modulus the slope of the plastic region. Then you have to look at the stress-strain curve for your material and approximate it with 2 linear parts. Since the approximation is up to you, this “tangent modulus” is not going to be tabulated as a standard material property. Obviously, it will be less than the initial modulus, maybe up to 10 times less. Some software allows you to input a table of points so you can more closely approximate the curve, in which case you don't have a single tangent modulus.

3) Large displacements: Linear analysis assumes very small displacements so that the equilibrium equations can be written in the undeformed position. Whether this is good enough depends on your problem. The deflections might have to be considered “large” if the shape changes noticeably when the deformations are drawn to a scale of 1 (not exaggerated). Things like cables and membranes are definitely nonlinear in this respect. Assuming there are no other differences, the differences you get between small and large displacement runs are an indication of how important geometric nonlinearity is in your problem.

A good book for plasticity is “Plasticity: Theory and Applications” by Alexander Mendelson. As mentioned previously, nonlinear analysis is much more complicated than linear analysis and you should be very careful. There are many more inputs to define and even the load increments you use can affect the results. Also, a mesh that is OK for linear analysis may not be good enough for a nonlinear analysis, for example if the stresses redistribute due to yielding.

 

[ikkedus]

Hallo,

many thanks for your answers.

faejob:
1) The following stresses were found:
linear: 293MPa | nonlinear: 251MPa | nonlinear with large displacement: 222MPa. These are all with Von mises plasticity.
3) the size of the displacement is about 20mm on a construction with 2 profiles of 30x15x1.5 with a length of 600mm (sort of cantilever construction). I think this would qualify as large displacement?

sdm919:
2) I'm already trying to find a stress strain curve for the materials used so i can guestimate this value. (St52-3 and Domex 700). Thanks for the info.


Gr, Ikkedus

 

[corus]

If you don't know the stress-strain curve then it's common practice to set the tangent modulus to zero above the yield stress. In general if you're using plasticity then it's advisable to use large deformation theory in the solution.

The problem with using plasticity and large deformation is that most design codes rely on stresses that are calculated elastically. Your results will be of little value if you're assessing your calculated stresses against fatigue/design code limits.

corus

 

[ikkedus]

Hallo Corus,

thanks for your answer, but i'm not sure that i understand what you mean. You say it's commom practice to set the tangent modulus "to zero above the yield stress".

If i set it at zero there's no strength whatever left in the plastic regions so they act as swivel points?

The structure doesn't have to be assessed against design code limits. It's merely a study trying to understand where the max. stresses occur and an approximation of how high they are. So thats no problem. We will also do a test in practice.

Gr. Ikkedus

 

[feajob]

ikkedus,

As sdm919 explained, you get the highest stress with linear elastic isotropic option, because Young's modulus is much higher than Tangent Modulus.

Well, I think that Von Mises plasticity match better with your material. But, I am not sure if you can consider a large displacement condition for your problem. Because 20/600 = 0.033 and your final shape is not so different from the initial shape. I don't know how we can explain 251-222=29 (MPa) (which represents more than 10 percent)?

AAY

 

[corus]

If the tangent modulus is zero then this means that the material is prefectly plastic, ie. no strength, so that if the stress was load dependent then the strain would be infinite. If the loading was strain dependent such as in thermal loads, or if the stress was at a notch, then this wouldn't happen.
The plastic regions wouldn't necessarily act as swivel points unless the plastic region was through the full thickness of the material.

corus