Question about curve fitting indentation data with large residual strain

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 couldn't achieve the
high nonlinear relationship between displacement vs reaction force as
measured in the experiments.

I have tried several strain energy potentials,

1) W=A/B*{exp[B(I1-3)]-1}
2) W=C10(I1-3)+C01(I2-3) 

3) W=C10(I1-3)+C20(I1-3)^2+C30(I1-3)^3

4) Arruda-Boyce type model

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 couldn't be as nonlinear as measured in experiments.
I am not sure how could I model this large nonlinearity with residual strain. Does anyone have any clue?