Hi. As far as my understanding, initlal Poisson ratio definition is fixed on deformation ratios which make sens in elasticity but not really on a non linear plastic (or else) deformation. If you model your plasticity with some kind of simple approach, then Poisson ratio would have a physical meaning from the modeling point of view (phenomenological approach). Does it make sens otherwise ? not sure.

I am sorry to say I don't really understand this question.  I expect it is because my mechanics is limited and my knowledge is only on testing and analysing results.   

Nevertheless, it seems to me that you could look at this from completely the opposite point of view.  For example:

The original problem was e1+e2+e3 0, i.e. constant volume is not obeyed in elasticity.  Poisson's ratio then is an empirical fudge factor to describe experimental observations that during elasticity the diameter of a bar (e2 and e3) was not observed to reduce as much as was expected from the change in length (e1).   

With regards to FEM; compatibility would be much easier to formulate if  e1+e2+e3 = 0 were always true.  The problem for early FEM codes was I suggest not plasticity but elasticity where e1+e2+e3 > 0.   The elastic Poisson's ratio then being the fudge needed to deal with the problem of compatibility when e1+e2+e3 > 0.  

The other problem for compatibility is of course Small Strains or Large Strains.  With small strains it is of course easier to maintain compatibility (irrespective of what Poisson's ratio is used).  I suggest for FEM it is not "plastic Poisson's ratio" that caused the problems to early 1970s codes but the need to maintain compatibility under large strains.  

Hence, 1970s FEM codes were first limited to small strains, then we engineers translated that to only applicable to elastic strains.  

I suggest it is a bit of lost in translation.  

P.S. I have made this up completely in the last 10 minutes and I would really like to know if I am talking complete BS .  Unfortunately I can't ask any of the people who developed BERSAFE as they have all retired.  If I could ask then they would tell all.  

Article The BERSAFE finite element system

"Plastic Poisson's Ratio" is defined in terms of the plastic lateral contraction of a tensile specimen stressed beyond the yield point, that is, in terms of plastic strains. For those who object to appropriation of what is usually considered as a term of elasticity, substitute "plastic contractile ratio". The plastic Poison ratio is used extensively in the mechanics of porous media. It has a value of 1/2 for fully dense metals and decreases toward 0 with increasing porosity. There are structures that may even have negative values of the contractile ratio. The question has to do with any special cases that would invalidate use of a Plastic Poisson's ratio? Load reversal, unproprtional loading, etc?