## Difference between Plane Stress & Plane Strain in 2D FEM formulation??

## Difference between Plane Stress & Plane Strain in 2D FEM formulation??

(OP)

Hi guys,

I am writing my own MATLAB code for 2D linear quadrilateral finite elements. The code is complete and when I compare the values of nodal displacement I get from a problem with the values from the same problem in ABAQUS, they are the exact same for Plane Stress problems but different for Plane Strain problems!

As far as I can see the only difference in the formulation is the material stiffness matrix which I have inputted correctly and tested by hand for plane strain. Is there anywhere else I could be going wrong? The type of element I use for plane stress in abaqus is CPS4 and for plane strain CPE4. Does ABAQUS formulte plane strain in a different manner?

Any help would be greatly appreciated.

Mark.

I am writing my own MATLAB code for 2D linear quadrilateral finite elements. The code is complete and when I compare the values of nodal displacement I get from a problem with the values from the same problem in ABAQUS, they are the exact same for Plane Stress problems but different for Plane Strain problems!

As far as I can see the only difference in the formulation is the material stiffness matrix which I have inputted correctly and tested by hand for plane strain. Is there anywhere else I could be going wrong? The type of element I use for plane stress in abaqus is CPS4 and for plane strain CPE4. Does ABAQUS formulte plane strain in a different manner?

Any help would be greatly appreciated.

Mark.

## RE: Difference between Plane Stress & Plane Strain in 2D FEM formulation??

Careful with plane strain elements in FEA as they're prone to "locking" or acting excessively stiff.

## RE: Difference between Plane Stress & Plane Strain in 2D FEM formulation??

The examples I tried have been similar to say a 1x1 block with a thickness of 20. I am only comparing the results from my FEA code and ABAQUS results so shouldnt the over-stiffening affect both results?

## RE: Difference between Plane Stress & Plane Strain in 2D FEM formulation??

Did you solve your problem?. I got a similar one: I want to turn a plane strain code into plane stress. It seems that in some plane strain formulations, four stress components (Sxx,Syy,Szz,Sxy) are included while in others, Szz is not.

In the plane strain code refered, the C matrix looks like: C=(E/((1+v)(1-2v)))[1-v, v, v, 0; v, 1-v, v, 0; v, v, 1-v, 0; 0,0,0,(1-2v)/2]

while the results compare very well with those of Ansys for a thick wall cylinder.

Regards,

Rogelio