This is an artefact of the fitting, magnified when some of the powers {αp| p} in the Ogden model are negative; in such case, a small but positive shear modulus can artificially appear as negative. You may use a constrained fitting procedure, requiring the shear modulus to be positive (if you know, or can independently measure, the value of the shear modulus, you can constrain the fit exactly to reproduce this value).

Behnam Farid thanks for adding an answer. I figured that since the data is for compression test, then the stress is negative. in this regard, I will get a non-negative shear modulus when fitting data with Ogden model.

Mahdieh Babaiasl : My pleasure. Good to know that you have resolved the problem. Indeed the {λi | i=1,2,3}, with λi ≥ 0, in the Ogden model for the strain energy correspond to stretches (in fact the shear modulus in this model is obtained from the second partial derivative of the strain energy with respect to λ1 and λ2, after eliminating λ3 on the basis of the equality λ1 λ2 λ3 =1, at λ1 = λ2 = 1). Do you have any independent measurement of the shear modulus for comparison with what follows from the Ogden model after fitting to strain data?

Behnam Farid Dr. Farid, thanks for your valuable comments. Yes, I have measured Young's modulus and Poisson's ratio therefore I can calculate the shear modulus from G = E/2(1+nu), where E is Young's mod, and nu is poisson's ratio.

Mahdieh Babaiasl : My pleasure, and thank you for your prompt response. You have not mentioned whether your measured μ is in good agreement with the μ deduced from the Ogden model after fitting to stretch data.

Behnam Farid Dr. Farid, yes it is indeed so close to the calculated one and I got a fit with R^2 ~ 0.99. I will use these data to validate my developed mechanics-based model for depth of cut of water-jet in soft tissue.

Mahdieh Babaiasl : Thank you for the information.