hyperelastic models - simple shear + ogden

[sarthak]

Hi:

I have two questions and hoping someone might be able to help:
(1)
I have experimental data from shear experiments and able to fit N=1 Ogden parameters to my model. Now when I compare my analytical stress value, with the evaluate Ogden material parameters, the I get very different values if I run a simulation in ABAQUS with the same Ogden coefficients. The simulation is that of simple shear and I have derived a corresponding analytical expression which is consistent with what ABAQUS has in its theory manual.

(2)
I have experimental data from shear and compression tests for the same material. The shear data is over large strains (60%) with stresses (400 Pa). But my compression data is over small strains (~5%) and large stresses (1 MPa). The only model that fits this experimental data is a Mooney-Rivlin model, but the model is very sensitive to parameters changes. Ogden or Arruda-Boyce model though stable, seems to ignore the compression data while fitting. Does anyone have any suggestions on what model I could use or how proceed?

Many thanks,
Sarthak

[Jorgen]

(1) That should not happen. A closed-form solution should give the same result as an ABAQUS simulation. I suspect that there is problem with your analysis somewhere :(

(2) How do you do the fitting? Have you tried to fit the data yourself? I have not seen your data, but my guess is that you should be able to get a reasonable good fit with all the different hyperelastic models that you mention. Another comment: where the shear and compression tests performed using similar conditions? Many materials are strain-rate dependent...

- Jorgen

[sarthak]

Hi Jorgen:

Thanks for replying.

(1) The cauchy stress for a simple shear problem is:
sigma11 = -p + (2*mu*Lambda1^(alpha))/alpha
sigma22 = -p + (2*mu*Lambda2^(alpha))/alpha
where sigma33 = 0 ==> p = (2*mu*lambda3^(alpha))/mu
and, sigma12 = (sigma11 - sigma22)/K

where mu and alpha and the ogden coefficients as defined in the strain energy function by ABAQUS and K is the shear strain.
Lambda3 = 1 and Lambda1 = 1/Lambda2. The above solution is consistent with ABAQUS. The only problem might be the way Lambda1 relates to the shear strain (via the invariants)...which I think should be
Lambda1 = 1/2*(K + sqrt(K^2 + 4)). So I don't know where my mistake is?

(2)
I tried fitting using derived analytical expressions in Matlab. The Money-Rivlin parameters fit the experimental data well but I am not able to run a simulation with ABAQUS. And in ABAQUS, Ogden and Arruda-Boyce models ignore the stress data. The compression test was done at strain rates of 0.001 1/s and the shear test at 0.01 1/s. The sample was soft gel and if you would be willing to look at the data, I could you a sample of the shear and compression data?
Thanks for your help
Sarthak

[Jorgen]

I would be willing to analyze your data if you: (1) can specify what type of gel it is, and (2) allow me to publish the data in the experimental data section (http://www.polymerfem.com/modules.php?name=Materials_Models) of this web site. That way other people can benefit :)

- Jorgen

[sarthak]

Sure. I am will the share the data. The gel is called Sylgard 527 and simulates brain tissue. How do I send a set of Compression and Shear Stress/Strain Data.

Sarthak

[Jorgen]

I received the your data. The data seems strange, however.

A quick calculation shows that the compressive Young's modulus is about 6 MPa, and the shear modulus about 1 kPa. Hence the Young's modulus is about 6000 times higher than the shear modulus. That is strange :!:

Are you sure your data is correct? Can you explain this big difference?

- Jorgen

[sarthak]

thanks for replying. i cannot explain the large difference between the shear and compressive young's modulus. in another independent experiment the bulk modulus of sylgard 527 was found to 1.9 GPa, which tells me that is almost incompressible.

i don't think i have made a mistake. so is there no way to fit this data?

thanks,
sarthak

[Jorgen]

There is something about the data that is very strange :o

Can you explain in more detail how the tests were done and how the samples were prepared.

- Jorgen