I found an Abaqus Verification Manual problem that contained and compared a UHYPER user-subroutine to a UHYPER_STRETCH user-subroutine.  The R2025x version of the Material Calibration App only supports the UHYPER version (based on invariants), but in our developments for R2026x we have already added the UHYPER_STRETCH version (based on stretches).  In the UHYPER version it calculates a response for a Neo-Hookean material model.  In the UHYPER_STRETCH version it calculates the response for an Ogden, N=1 material model with alpha1 set = 2.0

Uniaxial Tension: 

In uniaxial tension, the material is stretched in one direction (say, the x-direction) and the other two directions are free to contract. 

For an incompressible Neo-Hookean material under uniaxial tension, the nominal stress component in the direction of stretching (S₁) is given by: 

S₁ = 2C10*(λ - λ⁻²)

For an incompressible Ogden, N=1 material under uniaxial tension, the nominal stress component in the direction of stretching (S₁) is given by: 

S₁ = mu1*(λ - λ⁻²)

So, if the Ogden, N=1 model has mu1 = 2*C10 and alpha1 set = 2.0, then the Ogden response should be the same as the Neo-Hookean response.   

In the video below I have used the current public cloud version of 3DExperience, R2025x HF 3.19.  There is no calibration performed. We are just comparing the response of a Neo-Hookean model to that of a Ogden, N=1 model.  We do this using "Response Only" data for a uniaxial deformation to a nominal strain of 1.0 (stretch=2).  And we use the "Material Calibration Case" feature for making the comparison.  We will set C10=80 MPa, mu1 = 160 MPa, alpha1 =2 and D1=0.001

Notes on the UHYPER user-subroutine: There is an Abaqus Verification Manual problem named UHYPER_STRETCH.  From that problem I have used the file uhyper_uhyper_stretch.for    That Fortran source file actually contains two user-subroutines. I compiled it like this:

Abq2025hf3 make -lib uhyper_uhyper_stretch.for -uniquelibs

The make facility will create two .dll files:

uhyper_usub.dll       (I used this one in the video above)

uhyper_stretch_usub.dll    (I will use this one later in R2026x)

Zip file:  The zip file contains the Fortran source file and the two .dll files.