Large deflection solve difference using 3D static and 3D nonlinear static solver.

rpalinka

I'm working with a polyurethane closed cell foam spring with 30% compression. I initially ran the solve using the CCX solver with 3D Nonlinear Static. It crashed at about 10% deflection after hours of run time. Then I tried 3D Static with both the CCX and the Internal solver. Both converged in minutes. I'm not complaining. The results looked
correct. Just wondering why the simpler solver worked and the nonlinear one didn't.

Sergio

Have you used the special material *HYPERFOAM in your simulation? Also, maybe using hexa elements with reduced integration can help, 30% of deformation is a lot for the mesh.

Victor

I agree with Sergio that 30% is a lot, especially with a linear material where the results wouldn't be valid anyway. Here's a Neo-Hooke cube deformed into a mushroom shape before it failed. With linear material in non-linear analysis, it failed much sooner.

If there's a problem with the model like runaway loading or insufficient constraints that can fail in nonlinear whereas linear is more tolerant of those things.

Would you be able to share your model?

rpalinka

Not used to sending files. Did this work??

rpalinka

I'm used to analyzing solid hot cast polyurethane parts. I just took a guess at the properties. Solid polyurethane elastomers have a Poisson's Ratio of 0.499. I've worked with both linear properties and Mooney properties with solid elastomers. For the foam, I used a ratio of 0.2. In this case, the 3D Static worked well. Whereas the 3D Nonlinear Static crashed. I guess it's possible that the 3D Static results aren't valid. But they look right.

Sergio

Due to the large impossed displacement, this problem must be solved with geometrical no lineal activated. Your material is a sponge, so a propper hyperfoam material must be defined using CCX custom model definition like this

*SOLID SECTION, MATERIAL=SPONGE, ELSET=SPONGE
**********************************************
*MATERIAL,NAME=SPONGE
*HYPERFOAM,N=2
0.164861E6,8.88413,2.302E-5,-4.81798,0.,0.
**********************************************

And as your part is simetric, you could use also a quarter model, or even axissimetric model.

What kind of results do you need from the analysis?

Victor

I see. Your model is also stopping at a similar strain to mine when I used linear material.

I'd say you need to use a non-linear material here, such as *HYPERFOAM Sergio suggested. It's not in Mecway's GUI but you can define it with CCX cards.

I tried Neo-Hooke with what I guess are similar parameters for the small-strain region:
C_10 = 400 psi
D1 = 2.7e-7 m^2/N to give calculated Poisson's ratio = 0.202
and it solved further, up to 90% but the deformed shape is very different from linear, with a crease near the top.


Linear analysis can happily produce a (wrong) solution for any amount of strain, even less than -100% so it turns inside-out.

disla

EDITED :Erased. I can see you have also enforce radial displacement.

disla

ERASED

rpalinka

Thanks. I'll play around with your suggestions. The radial displacement was imposed because there is a pin that runs through the center when it's in use. But that would only restrict negative radial displacement. These are tested on a machine that drops a weight repeatedly from a specified height. The impact drives the deflection. I haven't seen a failure like I would see from a crease at the top. But that doesn't say that it doesn't happen. The failed parts are pretty messed up.

Sergio

Sometimes you need to include the test devices also in your simulations to take in count the shape and contacts that cannot be represented by simple boundary conditions. Can you extend a little more on the failure modes that you are not seeing in the simulations?

JohnM

My 2 cents. CCX, nonlinear 3D, note settings in Analysis. I used a handy hyperelastic material but your hyperfoam should perform similarly. I ramped your Y displacement, and removed the constraint on the pin surface - if it can slide, it can move normally. You could add the pin and use contact. This ran in 50s so I don't think contact is going to slow you down.

On your note about "results looked correct" - careful! That has been my entire career, knowing the difference between "results look correct" and "correct results"

rpalinka

Thanks for the comments, all. I have been thinking about this foam problem. These jounce bumpers are microcellular closed cell polyurethane foam materials. In compression the CO2 "bubbles" compress to a point that the material almost transforms to a solid elastomer. The bumper goes from a sort of pneumatic structure almost to a solid. You can see this in the load/deflection curves. I'm thinking this material is better simulated by a strain hardening material which I found could be simulated by a plastic which Mecway can simulate. I don't have access to testing this type of foam in compression. But I estimated how the modulus should change with compression. I entered this data into the strain/stress section for strain hardening in the plastic material input and ran the analysis in the nonlinear static analysis. I was able to get almost a one inch deflection on the 2.5 inch high bumper without crashing the analysis. I think that the Mooney and Neo Hookean material model tends to simulate strain softening (slope of the stress/strain decreasing with increased strain). I know the Mecway plastic analysis wasn't intended for this material case. And I could be all wrong. But it seemed to work.

JohnM

For the range of loading we typical use, I find the Mooney Rivlin materials tend to stiffen with load, as shown below. I attached a file with hyper55a properties, you can run this and see the behavior.

rpalinka

John
The problem, at least as I see it, is that the Mooney-Rivlin model is that it is for a solid elastomer which is mostly incompressible (volume conservative). The Poisson's ratio for a neat polyurethane elastomer is 0.499. Your ratio in the file you sent was for a carbon black filled rubber. But it is still quite high. These microcellular materials are very compressible. That's why they are favored for these jounce bumper applications. The second file I sent here is exactly as you set up except that I replaced the Mooney model constants with the strain hardening data I used for the jounce bumper FEM. I imposed a Poisson's ratio of 0.05. You can see in the image files the difference in the volume effects.
The force/deflection will increase for both cases- for the part.

Sergio

For microcelullar rubber I have used in the past (automotive door sealing) Abaqus hyperfoam material. CalculiX also includes this material, take a look at a simple comparation between hyperelastic (solid rubber) and hyperfoam (microcelullar rubber). @Victor, the Solution/Sum feature is great, but can you add the field name to the label of the plot? Something like Sum/External Force/Y

disla

What a nice comparison Sergio.!!
Reading through the Abaqus documentation I have seen that it provides guidance on how to fit your material parameters to experimental data.

https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm?startat=ch04s06ath124.html

Excel itself has a Solver that can find the best parameters combination to fit an objective function (relative error in stress measure E = 0). You would probably be limited to HYPERFOAM N=1 due to lack of inputs. It can sometimes be tricky as you need a good set of initial bounded parameters to help Excel to find a solution but in this case, it seems you have the compressibility behavior clear so...you can play just with two parameters.
That would be the homemade solution.

By other hand, I have also seen some people uses Ogden material model for foams. It has some sense as both energy potentials shares many points in common.

If you want to give it a try, Curve fitter can fit OGDEN to experimental data. webpage says it's still free.

https://docs.welsim.com/curvefitter/curvefit_overview/#hyperelastic-material-model-fitting

Sergio

About the material parameters, we determined in the past for rubber using only compression tests on a simple molded test sample (in fact the same as in the animation) and using a comercial tool. We had tested all our hardness range and determinate Mooney coefficients, and they were very accurate for predicting rubber part stiffness.
I have made a similar work a few years ago using Optimax that is free, coupled with a CalculiX input file.

rpalinka

Sergio
Your hyperelastic vs hyperfoamrison is perfect. You indicate that Mecway can accommodate a hyperfoam material model. I'm not seeing where this kind of data can be entered.

rpalinka

Sergio
Couldn't I do the same by assuming a linear elastic material with a near zero poisson's ratio?

JohnM

I second the Optimax method, it does a nice job finding the coefficients.

Sergio

An hyperfoam material can be defined in Mecway using CCX custom model definition like this

*SOLID SECTION, MATERIAL=SPONGE, ELSET=SPONGE
**********************************************
*MATERIAL,NAME=SPONGE
*HYPERFOAM,N=2
0.164861E6,8.88413,2.302E-5,-4.81798,0.,0.
**********************************************

Sergio

@disla, I have downloaded and tested Welsim Material Editor, and looks great... until you start to try to use it in an eficiently/every day use. There is no thing as a material database, all are saved in individual files. There is no way to quickly compare two materials, or properties at different temperatures. It has a way to enter test engineering stress/strain data, but I didn´t find a way to convert it to true stress/strain.

And for rubber coeficient determination, even if they use the theorical/academic procedure with stress/strain curves as input data, in industrial life what you have is a sample (solid) part, and results from a static test, so the input data is a load/deflection curve. I remember that we have available strain stress traction test data, and could even build the devices for the biaxial stress test, but we keep with the simple compression test on a cylindrical shape. Most of the rubber mounts on the car that you see everyday were developed using that data.