8-chain model for PU
I have uniaxial compression data (nominal) from PU and I have been trying to use the 8-chain model (without amplified strain for now) to predict the deformation behaviour.
I have implemented the uniaxial, incompressible version of the model in Matlab in order to fit the material coefficients. When I try to fit true stress I do not get satisfying results. However, when I use nominal stress the fit is excellent. In my data, the slope of the nominal stress is increasing with increasing stretch (material gets stiffer and stiffer), whereas the slope of the true stress (calculated from nominal values) seems to level off or decrease slightly with increasing stretch. So what happens when I try to fit true stress, is the predicted slope increases and therefore diverges from the experimental data as stretch increases.
Another question I have, is how I know that my estimated coefficients make physically sense? Obviously, Matlab goes to what ever values it needs in order to get a fit. So I need upper and lower bounds. How do I define these?
Has anyone had similar problems with the 8-chain model?
The calibration problem with nominal vs. true stress sounds like a bug to me. You should get similar predictive qualities in the two cases. Are you sure you do it right?
One nice feature of the 8-chain model is that it is easy to interpret the material parameters. If both mu and kappa are positive then the model is stable and makes physical sense. I dont think there is a need to introduce any other bounds.
Im quite sure I do it right. At the moment Im using the uniaxial, incompressible version of the 8-chain model (the one in your PhD theses). For the inverse Langevin Im using a Pade approximation, though. I use Matlabs lsqcurvefit function with stretch and either true or nominal stress as input and mu and kappa as variables.
would it be possible to send you a sample data set (private msg)?