Mooney-Rivlin Model

Hello.

I study solid mechanics at a graduate school.

I tried to derive tangent modulus of the Mooney-Rivlin based Neo-Hookean material.

There might be no error in my derivation, but answer is wrong with referred right answer.

So, could you check my derivation?

I attached my derivation as a figure.

Thanks in advance.

I have a doubt regarding the Hyperelastic and Viscoelastic material modelling in ANSYS using Mooney-Rivlin material constants.

ANSYS theory manual says that for large deformation and large strains, the material modelling (i.e. constitutive behaviour) is same for hyperelastic and viscoelastic. Is it so?

Generally,  Mooney-Rivlin material constants are used to model Hyperelastic behaviour (rubber-like materials).

Why do some strain energy density (SED) function have 1 invariant (like neo-Hookean) while some others have both 1st and 2nd invariant like mooney-rivlin? is there a specific reason behind using 1st invariant in SED vs all invariants in the SED?

N