true vs nominal stress

Hi,

 I have cyclic uniaxial compression data of a PU.  When I look at nominal stress vs nominal strain then the relation is clearly nonlinear (increasing stiffnes with increasing  strain).  When I convert to true stress vs true strain I still have a nonlinear relation, however, not as strong and the stiffness decreases with increasing strain.
When I look at true stress vs stretch, however, the relation seems to be almost (I'm only talking about the first loading cycle) linear. Nominal stress vs stretch is still nonlinear.