estimation of function parameters for best curve fitting

Hi,

my aim is to create a stress strain curve which best fit the curve I got through experimental data. The stress strain curve I need to define depends on the following parameters: mu1, mu2, alpha1, alpha2 since it comes from the nonlinear Ogden 2nd order model represented in the attached picture (below) where sigma1 is the stress, N is the order of the model (2 in my case), mup and alpha are the Ogden parameters I need to find for best fit, and lambda is the stretch (a datum that I have).Basically by varying the values of those parameters different curves are generated, but I want to find out the one which best match the experimental data derived curve.

I wrote this function using symbolic paramters in this way:

syms mu1 mu2 alpha1 alpha2;

f(mu1,mu2,alpha1,alpha2)=(mu1*(lambda.^alpha1- (1./(lambda.^(alpha1/2)))))+ (mu2*(lambda.^alpha2-(1./(lambda.^(alpha2/2)))));

g=matlabFunction(f).

Once defined the function I need to create an algorithm for best fitting of the curve coming from experimental data which is plot(strain, stress) by finding out the values of mu1,mu2,alpha1,alpha2 to get the best matching. How can I do this?

I though about using lsqcurvefit but it takes as input stress and strain and error arise. Would you be so kind to suggest me a way to achieve a solution?

Thanks!

[Sonal Gahlawat]

Hi, I am trying to do the same thing. Did you get any advice?

[Ameer Hamza]

@Sonal, see the fittype() and fit() function from curve fitting toolbox.