Simple tension table for hyperelastic material 2

Wake

I successfully used simple tension & planar tension data to calculate the MR-constants in DStar 2006.

In the Material box, select Custom Defined and then Hyperelastic-MR. Then select number of constants to compute and click/check Use Curve Data. Select Tables & Curves tab.

Select type = Simple Tension
You can then manually enter the data points but I preferred to read in a .dat text file. Ensure your data is in the correct units. And remember stretch ratio means you need to add 1 to all elongation values. Stretch ratios must be in increasing order. Thus, your first row should typically be 1,0.

Repeat the above for any other type of curve you have available.

Run the analysis and recover your calculated constants from the .OUT file. Hope this helped.

Please enlighten me on your comment “the simple compression data was used to create the biaxial tension table”. Would be interesting to know how exactly you converted the data (what calcs). Was the simple compression experiment done whilst applying a simultaneous hydrostatic pressure to the sample? If not, what do you think about the idea to simply add the compression data onto the front of your simple tension data? Thanks.

Regards

Thanks gfbotha.

I got it to work now. I was not adding the one to get stretch ratio. Stupidly assumed it was the same as engineering strain. Also found I had to not have input any Mooney-Rivlin coefficients.

Using the simple compression data as biaxial tension works fine if input as positive values. Physically the engineering stress and strain are the same except for their sign and for the compression test friction. I ran analyses to compare with the test data and they match OK. I don't know what the friction coefficient was during the compression test (Santoprene TPV 111-55, unknown lubricant), so of course there will be errors.

I might try adding the compression data to the front of the simple tension data to see what happens. Would I use 1/(1-e) for the stretch ratio for minus strains?

Wake

Stretch ratio = 1+e
Just use the correct sign for strain.
So, for a neg. strain of say 20% the ratio will simply be 0.8

Don't feel stupid/alone - when I 1st had to determine hyperelastic constants, I also ended up looking for assistance. At that time I had to use GEOSTAR which prompted for strain whilst it actually wanted stretch ratios! Pointed out to the developers that we need better documentation.

Regarding the use of simple compression data for biaxial: so you simply changed the sign of the neg. compression values. Well, I also thought so in the past until we once got involved with a skilful Abaqus analyst. Although the strain state is similar, the loading/stresses differ? He pointed out that according to updated Abaqus documentation, one should only do so if a simultaneous hydrostatic pressure was applied during the simple compression test... He then came up with the idea to add the data in front of the simple tension data. The result was increased accuracy under certain conditions plus increased solver stability.

It is reassuring to hear the “compression-for-biaxial” approach indeed yielded good results in your case. Like you, I accept there will be some error. Do you mind indicating what scenario or type of loading you need to simulate? I’m just asking because, as you know, that will be an indication as to what material test type(s) need to be included.

Please let us know about the outcome if you indeed decide to try out the “compression+tension” approach. Sorry for slightly hijacking your thread.

Regards

gfbotha,

I'm new to nonlinear analysis, so I may be wrong, but doesn't the hydrostatic pressure compression equal zero with incompressible materials?

The shape of a biaxial curve, which starts off similar to the uniaxial curve, is different than that of a uniaxial compression curve which starts of nearly linear. But my table with 2 term fit produced nearly the same results as using the two term Mooney-Rivlin coefficients supplied with the test data. I don't know why.

DesignSTAR seems to fit a Mooney-Rivilin to the data, using the number selected in the "Number of constants" box. Is there a way of retriving the constants DesignSTAR calculates?

I have not yet added the compression terms to the front of the uniaxial tension data. I should do that today.

gfbotha,

I added the compression data to the front of the uniaxial data and deleted the biaxial input as you suggested. The results were the same as my using compression data as biaxial data. Even thou they gave the same results, I like your way better and will use it from now on. It may make a difference if I was using a material with significant compressiblity.

Thanks!

Although elastomers are sometimes called “incompressible” it would be more correct to say they are slightly compressible. I would estimate your material to have a Poisson’s ratio of around 0.495 You can use this to calculate the material bulk modulus (K) which dictates actual volumetric strain under conditions of hydrostatic loading. Where did you obtain your Poisson’s value from?

Sometimes it is OK to employ an “incompressible” FE formulation (if your component is not highly confined or hydrostatically loaded). The DStar formulation will indeed consider volumetric strains if applicable. But I do not know the nature of your simulation problem. It is good practice to at least include a material test type which sort of matches your real application.

The 2nd paragraph in your 2nd last post is a bit confusing to me: to the shape of what biaxial curve are you referring? From where – thought you haven’t any? I understood you simple entered compression data for biaxial when determining constants. Or do you mean the shape of a biaxial curve in general? When comparing the curves, be sure you are looking at similar total strain range (“zoomed in” similarly).

It seems you received a set of MR constants from a materials testing lab; if DStar analysis results stay the same, you might be glad because then at least you know DStar calculated similar constants to those supplied. Think you missed it: I indicated how to retrieve the DStar MR constants in my 1st post.

I think you might find the following useful: At the same place in that output file you will find 3 columns of data. Strain / Actual test stress / Theoretical or fitted stress. Plot these two stresses against strain in, say, Excel – the last represents the material approximation used when running your FE analysis… Sometimes (only!) selecting a higher order MR fit (i.e. more constants) might give you a better fit over the complete strain range (e.g. if the test data curve has an inflection point).

Thank you very much for your feedback about the “compression+tension” approach! Interesting. Do you mean the results are the exactly the same, or do you actually mean similar values? You could always compare the MR constants directly. It might be that your loading is such that you have very limited volumetric strains.

Regards

gfbotha,

I am using .4995 for Poisson's ratio. I have no source for that number. It was arbitrary. My material is Santoprene PTV 111-55, and I was unable to find the Poisson ratio.

My application is a gasket, some flat and some with features similar to a "D" shaped O-ring. I figure the compression data most closly matches this application.

The biaxial curve shape I was comparing to is for natural rubber. I assume the shape would be similar for Santoprene.

Yes, I missed your telling me how to retrieve the constant. Thank you. I will look for an .OUT file.

The DS results match so closely whether using the supplied MR coefficients or test data table that I am sure the DS calculated MR coefficients also matches the supplied MR.

However, the match with the test data is a different story. The simulation results only match the test data at strains equal to the peak in the table. With the full table, intermediate compression results can be 28% off, and intermediate tension results 100% off. If I reduce the table lenght (or use the supplied MR coefficients for the reduce range) and simulate a test to the corresponding reduced strain limit, the results will now match at this reduced strain, but not for greater or lesser strains. Is this typical?

Higher order MR fits have only slightly improved the fit of the test data to the simulation results for intermediate strains, and they no longer match at the strain limit.

Wake

I have no specific experience with Santoprene material but 0.4995 for Poisson's ratio sounds in the right ballpark to me (I actually guessed a typ. lower limit value in my previous post). We usually test for bulk modulus and then use that together with the modulus to calculate the Poisson's ratio. Bulk modulus testing is done by compressing a confined specimen (approximate method), or by applying a true hydrostatic pressure to the sample whilst measuring the strain in 3 directions using LVDT probes.

I agree about the relative importance of your compression test. But, if the gasket is well / completely confined, you may want to determine the bulk modulus/ Poisson's ratio more accurately. Depends how accurate your results need to be and what is considered important analysis outputs.

Regarding the deviation from test data: I am sure you will be able to predict & understand that more easily if you plot “Stretch ratio / Actual test stress / Theoretical or fitted stress”, as explained in my previous post. Yes, I found that results will depend on things like the shape of the test curve to be matched (nature of material), strain range used during testing, determining your constants and during application. It depends on material nature but I too did not really benefit from fitting higher order MR functions. Often it is a compromise, you may have to decide in what strain range you desire a good fit (in your case negative strains). You could include or exclude extreme ends of data from your material test to obtain most suitable MR constants for the strain range actually important to your application. It is also typically easier to obtain realistic deformation results than stress results. Once again, it is worthwhile to plot the 2 curves showing the fit.

“I added the compression data to the front of the uniaxial data and deleted the biaxial input as you suggested. The results were the same as my using compression data as biaxial data.” – this is still both interesting and good news...(you do sound quite sure)!

Regards

gfbotha,

I was wrong about using the biaxial data. Although the simulation results were very close, the Mooney-Rivlin coefficients were vastly different. Two term Mooney-Rivlin results:

+.8403/-.2067 MPa from test source;

+.7857/-.1637 MPa DesignSTAR calculation from adding the compression data to the simple tension table;

+.3216/+.3007 MPa from using the compression data as biaxial data.

Adding the simple compression data to the start of the simple tension data is the way to go! Thanks for your help!

Wake

A pleasure... - you supplied good feedback - a benefit to others sharing tips on this forum!

Regards
Gert