I am trying to use finite element modeling of indentation experiments to extract hyperelastic material parameters. I am having a dilemma, when the tissue has residual strain, the model couldnt achieve the high nonlinear relationship between displacement vs reaction force as measured in the experiments.

I have tried several strain energy potential, such as Mooney-rivlin, and exponential type (W=C1[exp(C2(I1-3)]). If residual strain is zero, the displacement vs. reaction force can be very nonlinear (concave shape), however when the residual strain is high (stretch ratio>=1.2), the displacement vs. reaction force relation is either straight or convex.

I am not sure how could I model this nonlinearity with residual strain:confused:. Does anyone have any clue?