hello
fminsearch can be quite sensitive to IC, so even a slightly sub optimal IC value can lead to lack of performance / robustness. There coud be other, more robust optimizers to try (if you have the Optimisation Tbx)
otherwise I could get reasonnable results for both data files , after doing some modifications , the most important maybe is to take only the unique values from your experimental data and interpolate both y data sets on a common x axis
I put back all your files in attachment - hope it helps !
summary of my results
file = sample_anastasia.xls
R^2 for the longitudinal direction is: 0.9993
R^2 for the circumferential direction is: 0.9996
file = 130L-130C.xls
R^2 for the longitudinal direction is: 0.9876
R^2 for the circumferential direction is: 0.9962
main code modification :
%% keep only unique (and sort) data
[stretch_exp_l_unic,ia,ic] = unique(stretch_exp_l);
stress_exp_l_unic = stress_exp_l(ia);
[stretch_exp_c_unic,ia,ic] = unique(stretch_exp_c);
stress_exp_c_unic = stress_exp_c(ia);
% create common x axis
m = max(min(stretch_exp_l_unic),min(stretch_exp_c_unic));
n = min(max(stretch_exp_l_unic),max(stretch_exp_c_unic));
stretch = linspace(m,n,100)';
% interpolation
stress_exp_l = interp1(stretch_exp_l_unic,stress_exp_l_unic,stretch);
stress_exp_c = interp1(stretch_exp_c_unic,stress_exp_c_unic,stretch);
% overwrite stretch_exp_l and stretch_exp_c
stretch_exp_l = stretch;
stretch_exp_c = stretch;
this avoids the zig zags as you showed in your post
next I opted for slightly different IC (obtained from a first run of fminsearch) and also increased MaxIter to 1E4
another simple mod I made in the Objective_Func function is to replace the for loop by a simpler vectorized code :
% SS=0;
% for i = 1: length(lamda1)
% SS = SS +((stress_exp_1(i)-stress_mod_1(i))^2 + (stress_exp_2(i)-stress_mod_2(i))^2);
% end
% obj = SS;
% one line code :
obj=sum((stress_exp_1(:)-stress_mod_1(:)).^2 + (stress_exp_2(:)-stress_mod_2(:)).^2);
