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Umat for plane stress

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I have created successfully a UMAT code for J2 elasto-plasticity with isotropic hardening

for 3D solid elements.At this point I would like to support also plane stress shell elements.

What changes in the code are suggested?

The already implemented code, takes as input the strain tensor at time tn and the strain

increment tensor and updates the stress at time tn+1 and calculates the material Jacobian

and achieve quadratic convergence. The stress and strain tensors are manipulated as 6x1

vectors and the material Jacobian as a 6x6 tensor. I know that in case of plane stress the

vectors should be 3x1 and 3x3 respectively. What else should i take into consideration?

The strain tensor as used by the umat contains olny the values of ε = [ε11, ε22, ε21]

in case of CPS4R elements. What about the ε33? This should not be zero as it is calculated

from the incompressibility condition and from the plane stress constraint where

σ33 is zero. Is ε33 used by ABAQUS at all, or should I keep it only as state variable?

What about the material jacobian in plane stress? Is it calculated as in the 3D case?

Any thoughts or suggestions would be highly appreciated.