HI EVERYONE

I am trying to fit my tensile test data in axial and circumferential direction to an anisotropic hyperelastic model (holzapfel 2006 energy function), I have taken derivatives of the energy function with respect to the stretch in each of the directions to derive the lagrangian stress (engineering stress) in each direction. but fitting the data of two tensile tests in two directions to one function is awkward in practice. Does anybody have any experience with this?

My other question is when giving the test data to abaqus we should give the nominal (Eng.) stress and strain, but with the new builtin holzapfel hyperelastic model im wondering how this works as the constants in papers by holzapfel are based on Cauchy stress.????!!