Mooney Rivlin

[Muzialis]

Hello,

I am a design engineer only recently involved with rubber peculiarities, and I have a few questions: first of all, I have read fitting the results of an uniaxial stress strain test with a Mooney Rivlin type equation can be a faulty method, as results from biaxial tests including shear should be considered. On the other hand if I try the best fit on a whole range of tests the uniaxial results fit is of a poorer quality. Does it mean one should consider mainly the strain states of interest for their application?
Secondly, I am modelling a device whose main feature is rubber compression: what choices do I have as far a constitutive equation is concerned? Strains are below 1%, but it seems modelling rubber as imcompressible leads to results higher by an order of magnitude.
Can you advice on a good book for a general overview of materials models, especially the Mooney Rivlin one ?

Thank you very much

Marco

[Grant]

The answer to your first question is yes, but with strains less than 1%, I wonder whether there is a need to go with a nonlinear model at all. I would try plain old linear elasticity first and only consider MR if you can't get good correlation to test data.

If your geometry is highly confined (like a thin layer of rubber in between two metal plates), the bulk modulus (i.e. the compressibility) of the rubber will strongly affect your results. With a linear elastic model, rubber usually has a Poisson's ratio of 0.49-0.4999. Incompressible is exactly 0.5. Your FEM solver may or may not let you use exactly 0.5.

A good starting point for compressibility is to take the elastic modulus and back out a value of Poisson's ratio that gives you a rubber bulk modulus close to that of water. That should get you within an order of magnitude anyway.

You also have to be careful of rate effects. Make sure your material and component testing is done at a rate close to the rate you expect in the application. If you have a well-defined loading rate in your application, you can probably get away with testing at that rate and use an elastic material model. If not, you might have to go to viscoelasticity.

Good luck!

[Muzialis]

Grant,

thank you for your answer.
At the moment I am using linear elasticity with very good results, but I am not sure the approach is formally correct and I have a few problems:
with the testing fixture I have easy access to it is difficult to measure the modulus in the neighbourhood of zero.
Your advice about water bulk modulus is precious (your personal experience?, please let me know more), but which value for the modulus should I use? (by the way, I cannot use 0.5 for the Poisson coefficient not because of my FEM solver but because I get division by zero error message,as you know, plane strain stress strain relation has a term 1 - 2 ni).
Would you expect a stress strain curve to be C1 around zero strain or as I am being told the modulus in compression changes abruptly?
And last dilemma, would you expect the modulus in compression in the radial direction (for a cylinder let's say) to be anyhow dependant on the strain in the axial direction?

Thank you very much

Marco

[Grant]

Using the bulk modulus of water is something that has worked for me in the past. It's just a way to get an initial guess for Poisson's ratio that is close enough to the real value that you can iterate quickly to the real value.

For a typical elastomer, even a foam, I would expect the stress-strain curve as well as its slope to be continuous across zero load, at least to an engineering approximation. There are materials that don't obey this, but they generally involve some kind of unusual or damaged microstructure. If your loads are high enough that you get different tensile and compressive moduli, then you'll probably need to use a nonlinear model.