Elasto-plastic theory - ABAQUS

Hello,

I have started to study the plasticity theory few months ago. I'm trying to do one exercise in plane strain of one elasto-plastic material in ABAQUS and manually.

When the load is small, the material has just deformed elasticly and the total and elastic strain in z-direction (E33 and EE33) are zero (like say the theory of plane strain). 

But, when the load is increased and plastic deformation is observed, the total strain is zero (E33), but the elastic and inelastic strain have the same value with diferent signs. I know that total strain is the sum of elastic and plastic strais, but I guess that the elastic and inelastic strains should be zero too, doesn't should?

When I do the exercise manually, the load is applied as increments. So, first I calculated the elastic deformation and the stresses, so I can evaluate if there is or there isn't plastic deformation with the equation of yield surface. If, there is plastic deformation, I have to calculate again the exercise using the elasto-plastic stiffness matrix, so I have the plastic strain. But, in my counts the strain in z-direction is always zero.

 Anyone can help me? What book have this?

Thank  you!