FEA OF RUBBER LIKE MATERIALS 10

[Bhat165]

Hi, I am trying to do a finite element analysis of neoprene rubber. My problem is like this: I have a layerd elastic system where one of the layer is a rubber layer of neoprene with 10 MPa modulus (very low!). A surface load from a car tire is acting on it with 690 kPa pressure. What kind of analysis techniques I have to consider to model a rubber like material? Does a simple elastic analysis works? I tried a simple elastic analysis with ALGOR and the result shows badly deformed elements.

Thanks.

Sudip

 

[elogesh]

Hai bradh,

Thanks for correcting me.

Better way to show thanks is adding a star for Helpful/expert post.

Regards,
Logesh.E

 

[Mrmech]

Hai Bradh/corus !
Nice to see your answers to the thread thrown over here.After reading this question and answer for FEA for rubber, i have a query . i have carried out Linear static FEA and fatigue analysis on Plastics( 4Gpa is 'E' taken from text book) using IDEAS. This linear analysis will fetch any meaning since this material is PLASTICS( Delrin, Cecon M90)? can you tell me approximate poisson's ratio for these material?. Because we know for rubber it is 0.5, Metals and alloys 0.2 to 0.3

Regards,
mrmech

 

[Bhat165]

E
K = -------. so when pr -> 0.5, K -> infinity, that means
3(1-2*pr) incompressible. Is this correct?
E
From the relation G = -----, we see that for E>0 and G>0,
2(1+pr)
the lowerbound of pr is -1. That is -1 < pr < 0.5
Can any one suggest any material with negative poisson ratio?

Thanks.

Sudip

 

[ifegermany]

regarding the choice of software, I'd like to point to ANSYS besides ABAQUS & MARC. ANSYS has the same variety of available Elastomer/Hyperelastic laws as ABAQUS & MARC.

The classic laws like Mooney-Rivlin have been in the code long since, new variants to better cover different strain ranges, model foams, viscoelastic effects are there, fully incompressible/highly confined rubbers can be dealt with, as can temperature dependend material data.

Seen that ANSYS has a variety of solvers, also large/3D modells can be solved efficiently on multi-cpu hardware.

We work exclusively with ANSYS, true, but it's worth a product to evaluate besides those mentioned, especially as ANSYS based FEA is growing and so is the software capability, multiphysics included. So if one considers fluidodynamics, elctromagnetics and their interactions with mechanical/thermal analysis valuable, ANSYS might turn out the right choice.

Well.. sounds like I am from PR/advertising, but I'am not : )

Frank Exius

Frank Exius
IFE Bonn Germany

http://www.ife.subito.cc

Dienstleistung in ANSYS
numerische Simulation FEM Berechnung
digital/virtual Prototyping Outsourcing

 

[EnglishMuffin]

In reply to Bhat165

Yes, there are a number of them. They are called auxetic materials - for example auxetic polypropylene or auxetic polyethylene (see konyok.hostmb.com/List.htm). This is cutting edge stuff. It is also possible to have a poissson's ratio above .5 (for example, our muscles) but this can only be true for non-isotropic materials. Some materials, like Beryllium, have a Poisson's ratio of almost zero. If memory serves me correctly, one of the things that was shown originally by Poisson was that all materials should have a Poisson's ratio of .25 if they are composed of atoms with simple central forces between them. Not bad for a guy who could only read and write at the age of 15 and only then had a chance to study math!

 

[Bhat165]

Thanks EnglishMuffin.

 

[GSC]

It might be late, but let me add some thoughts...
I was modelling Neoprene rubber before finally with LS-Dyna (we finally wrote our own hyperelastic material, but your problem is not so complex, so don't give up , well, here are what I experienced...

Rubber behaves differently subjected to tension than in compression!, this is an important issue when you have cyclic loading with both tension and compression. You also have to bear this in mind if you have tension only data, but compressive loads.

The characteristics is highly linear, eg. like the Young's modulus would constantly change. There is no clear Young's modulus, so use of Bulk modulus better if possible.

Hyperelastic models usually mirror the given polynomial function to the origin, so not appropriate for more than one load cycle as the tension and compression data will be the same.
(If anybody knows a software which can do both, please let me know).

Poisson ratio should be 0.5 for Hyperelasticity, but this will cause an awful lot of trouble at large deformation -> hourglassing.
By the way your soft Neoprene is not incompressible. Is it closed cell or open cell Neoprene?

Besides hyperelasticity, viscoelasticity can also give you adequate results depending the properties you have. There is also a good hope in advanced foam honeycomb models.

There are some dirty tricks you can do sometimes with the Poisson's ratio (solver dependent) setting it to rather low (1.5-0.2-0.25) without introducing major errors in the result. This will help the calculation to converge if with using 0.49999999 it fails. Use carefully!

Piecewise linear representation can cause over 15% error if the resolution of the approach is not fine enough. I ran some tests earlier and there were 5-10% error in a 10 segment quadratic approach approaching the experimental curve first from the top, then from the bottom. Take special care on the maths used when creating your input curve. Generally you approach from the bottom, as the FE tend to stiffen your structure.

Explicit codes are generally better for large soft-rubber models.

I tried Mooney-Rivlin, lots of problems with hourglassing, and the Mooney curve unfortunately first softening then stiffening. Soft Neoprene usually does the opposite.

You mentioned that linear curves were obtained from the test. Either your test equipment's load cell is not sensitive enough or the sample was slipping out from the grips. Check it! Its worth to use lightweight air-activated grips if you have one for such a soft material.

Good luck
GSC

 

[Bhat165]

Hello GSC,

Thanks so much for information. I would like to know what level of strain you were experiencing with your neoprene? The reason why I am asking you this is: for small range of strains (less than 1%, say) the curve behaves linearly. True rubber always shows nonlinear curve at higher strain levels (thats why we use nonlinear geometric effect in analysis). Max anticipated strain level in my problem is not more than 1000 micro strain. When I am using a test data, I am certainly using a larger range of strains. In that small range, you are initially in the straight portion of the curve. But that does not help you to use it as elastc material, because, then you have to give Poisson ratio close to 0.5 and causing trouble. When you use Hyperelastic model, it automaically takes care of that problem, but it assumes you have large displacement. So I believe I am having problem in both ways. I would appreciate your comment on this.

Thanks.

Sudip

 

[jgough]

There seems to be a lot of information and mis-information in this thread. My remarks are:

(1) I have used Marc and Abaqus for modelling rubber. Both softwares have their own advantages and disadvantages but generally give good results.

(2) Poisson's ratio is not a particularly useful concept for rubber as it arises out of small-strain linear elasticity theory. People have attempted to define &quot;large-strain&quot; or &quot;non-linear&quot; Poisson's ratio, but it is not necessary and better to use finite-strain elasticity theory which is what is implemented in the hyperelastic models in Marc and Abaqus. The shear modulus (Young's modulus/3 at small strains) is a useful concept as it appears in the basic rubber elasticity model, arising from the statistical theory (neo-Hookean model). For an excellent readable introduction to finite-strain elasticity see Treloar &quot;The Physics of Rubber Elasticity&quot;(1975)3rd Edition, Claredon Press, Oxford

(3)I think Sudip would be best advised to use a Neo-Hookean hyperelastic model as it is simple and robust. As he is only interested in fairly small strains its inability to model non-linear features well is not a problem. In this case his uniaxial tension test should suffice to provide a value for C10. Theoretically it shouldn't matter what deformation mode he uses (as long as his material is isotropic, which it should be) although it is sensible to fit the constant at a strain appropriate to the application. However, since his application involves rubber constrained between two much stiffer materials, the assumption of incompressibility (correctly defined as no change in volume on deforming), which is usually very sensible for solid (ie not foam) rubbers, isn't really appropriate and he should use a bulk modulus (=2/D in Abaqus) of about 2000MPa for solid rubbers, thus making his hyperelastic model slightly compressible.

(4) Another organisation offering characterisation tests and FEA of rubber components is Rubber Consultants (rubbercon@tarrc.co.uk).

(5) Look out for a new British Standard BSI 903-5 &quot;Guide on the application of rubber testing to finite element analysis.&quot; It is currently at the draft stage (though may still be available for purchase) but hopefully will be published soon.

(6) No-one has mentioned the main drawbacks of the hyperelastic approach to modelling rubber, which are that it is not perfectly elastic and exhibits softening on repeated stressing (Mullins and Payne effect), and has some hysteresis and permanent deformation (set). The consequences of this for carrying out the characterisation tests is fully discussed in the BSI Guide cited above. Modelling them in FEA is still a research topic.

(7) Finally, maybe Sudip could have got the information he sought without doing FEA at all: there is a simple, approximate equation for the compression modulus of a block of rubber bonded between two rigid plates, E=3*G(1+2*S^2), where G is the shear modulus and S is the Shape Factor: S=(area of one loaded face / force free area). This equation is based on small-strain elasticity and ignores compressibility but still gives a reasonable answer. See &quot;Engineering design with natural rubber&quot; published by TARRC (

http://www.tarrc.co.uk)

for further details of simple design formulae for rubber.

 

[EnglishMuffin]

jgough :

I have what I think is an earlier edition of that guide -&quot;Engineering Design with Natural Rubber&quot; by P.B. Lindley, published by the Malayan Rubber Fund Board. I have used it on a number of occasions and it always &quot;puts me in the ball-park&quot;. But you can see where a lot of confusion about poissons ratio arises in treating rubber as a simple hookean elastic material because in my edition it states that for filled rubbers, Eo = 4*G, which is clearly inconsistent with a poissons ratio of .5 in classical elasticity. Also, I think it should be mentioned that in your formula, 3*G should be replaced with 4*G (or more logically the Eo value, as in the text I have) if one happens to be dealing with a filled rubber up around 60 - 65 durometer. For the case of very thin laterally contrained layers, very little shear takes place and you are then really dealing with a bulk modulus situation, which is taken care of in the formula by large S values - my edition has a graph showing this effect, where the compression modulus of the rubber block reaches a (finite) limiting value for very large values of S. So in my opinion this formula does NOT ignore compressibility as you state - it converges to pure uniaxial compression for very large S values.

 

[EnglishMuffin]

jgough :
Sorry - I take that back - I meant my last sentence to read &quot;So in my opinion the formula should not ignore compressibility - it should converge to pure uniaxial strain for very large S values&quot;.
You quite correctly state that the formula ignores compressibility.

 

[GSC]

Re: Bhat165

I was working with Neoprene on biomechanical applications. We experienced pretty large deformations up to 150%. With respect to your last comments now I see why did you mention measuring linear stress-strain curve at the beginning of the thread.

-If you say that the S-S curve in the deformation domain of your analysis can be treated as linear and the strains are really as small as you mentioned then the choice should be the best fitting hyperelasticity theory (as others already recommended) to stay on the safe side with incompressibility. (Mooney-Rivlin, Neo-Hookean, etc....)
-According to my best knowledge if you switch on the large deformation option in your solver it will not affect the results at small deformation.
-Ignore my comments on setting poisson's ratio low, the trick can be used only at extremely large deformations.
-Setting linear or piecewise linear elastic properties with poisson ratio > 0.495 could give fairly good results at small deformations only. You can compare it with the results using hyperelastic.

However, I am afraid you will have to consider some additional influence of creep, relaxation, and hysteresis in a layered material loaded by a car-tyre unless you are investigating only the effect of very short term loading...

GSC