Proper way to define plasticity?

[curlyq]

I am trying to figure out the proper way to define plasticity in my model. I am using a hyperelastic material model that essentially looks like a bell curve. (data taken from stress-strain plot from tensile testing I completed). I have my plasticity portion defined as everything to the right of max stress (input a table of values of yield stress v. plastic strain, where the plastic strain starts at 0 since that is the initiation of plasticity). How do I define my elastic portion? I have attempted 1) using the full bell curve for the elastic portion - essentially doubling-up then the definition on the plastic portion, and 2) also only defining elastic up until where plastic starts. I'm really confused because the two different methods give extremely different results.

The model is an axisymmetric model, displacement placed on the left pushing to the right. For #1, the simulation completed, and the deformed plot is on the top. For #2, the simulation only made it just about 50% complete, and the deformed plot is below.

So, what is the accurate way to defined plasticity? Leave the full elastic portion in, or segment it? #2 the max displacement and deformed shape is similar to when no plasticity was defined at all. #1 appears quite different, and it seems a bit skeptical that I was able to get almost twice the deformation. Overall with this simulation, I really actually do not want to be extremely far into the "plastic" or "damage" region - that implies tissue damage - something I am attempting to avoid.

If anyone has any insight into this issue I would appreciate the knowledge.