What constitutive model to use for very stiff rubber

In our particular application, our rubber material will only see compression (essentially uniaxial compression).

The strain rates will range from .5s^-1 to 5s^-1. Both the loading and unloading behavior are important. The strain value will never exceed 25%.

Years ago, someone performed what were essentially drop tests on the material. With that data available to me, I had planned to use the Arruda-Boyce model to fit the drop test data. I am using LS-DYNA, where the Arruda-Boyce model is built-in, and incorporates viscoelasticity via a Maxwell model.

Only recently were quasi-static (monotonic) baseline tests performed [attached]. I was surprised to see that this material softens in compression (perhaps it would eventually roll-over, but we only care about strains up to 25%).
Is this common with very stiff rubbers?
Am I correct that the Arruda-Boyce model cannot capture this behavior?

I may use a metal constitutive model instead, or a MAT_181 in DYNA, which I believe is based on the Ogden model, but modified to be able to grab stresses and strains from any tabulated [uniaxial] stress-strain curve. Or I may go with something else entirely, I am open to suggestions.

thanks,

edit: the attached is force vs. time, but it was a displacement controlled compression test on a small (few inches) cube specimen that went to about 25% strain

I am not quite sure I understand what you mean by softens in compression. Are you saying that the stress magnitude is not monotonically increasing? Or perhaps that the tangent stiffness is not monotonically increasing?

-Jorgen