Parameter optimization problem (using fminsearch)

Hello everyone,

I am performing parameters optimization for soft biological tissue. I am trying to optimize parameters by comparing experimental data to numerical coding (stress-stretch diagrams).

The material law is given with the code mainDER.m (not written by myself).

Berechne_fehler.m is the code that calculates the error between the numerical and experimental data. Specimen.dat is the data file that has the experimental data points necessary for the calculations (uploaded here in .txt format).

Running_script is the code I am using to find the optimized parameters. I have been using the minimization function fminsearch (fminsearchbnd).

I need to model three cycles (as can be seen in image 1.png). I fit two sets of parameters. First I fit k1,k2 and kappa (also known as material parameters, lower bound set to 0) to the primary loading path and then I fit rm, rf, mm, mf (as shown in the codes uploaded). I have tried to fit the data for each cycle separately and I get wildly differing values for the parameters (specifically applicable to k1, k2 and kappa), which I think is plausible given the behaviour of the curves. When trying to fit all three cycles at once, the best results I get are the ones seen in the image I have uploaded. I don't know the range of these values, and hence tried out with many many different combinations of starting values, and chose the ones that gave the least value for the minimized function.

I tried also using lsqnonlin, however besides the fact that it runs very very slowly, and doesn't converge, or rather gives back the same value until it reaches the maximum number of function evaluations (which after a while of waiting for results, I gave a smaller value so I can check the parameters), and I don't get much different values than with fminsearch.

My supervisor is pushing me to get good results, but I have simply run out of ideas of how to get them. Does anyone have an idea of something I could try out, or point out any mistakes that I am making in my current approach?

Thanks a lot.