John Doyle
Ansys Employee

I am not familiar with molded pulp product. The stress and strain values that you show are very small.  If the loading in your application is pure tension, and you are not trying to simulate failure, perhaps you could use the hyperelastic response function.  You might also be able to use a multlinear elastic option via MAPDL commands (TB,MELAS).  Refer to Section 4.6 of the MAPDL Material Reference guide.  If you understand what is driving the nonlinear behavior and you have the mathematical formulas that represent this, perhaps you could write your own UPF routine.  

Certainly, whichever path you chose.  You have to validate/calibrate the approach carefully.