Pressure in quad element

[BigBanana]

Hello,

I have a question about the pressure in 2D planestrain quad elements.

While visulizing the pressure in STKO post-processor, I found that the pressure for 2D planestrain quad elements equal to (sigma11+sigma22)/2. Why not 1/3*(sigma11+sigma22+sigma33)?

For 2D planestrain problem, strain in direction 33 (out-of-plane) is assumed to be zero but the stress in direction 33 (sigma33) is not necessarily zero. And even if sigma33 is zero, -1/3*(sigma11+sigma22+0) and -1/2*(sigma11+sigma22) will give two different confinement pressures.

Thanks,

[kesavapraba]

Hi,

While visulizing the pressure in STKO post-processor, I found that the pressure for 2D planestrain quad elements equal to (sigma11+sigma22)/2. Why not 1/3*(sigma11+sigma22+sigma33)?

Because, you are dealing with 2D stress state analysis by approximating the problem as plane strain. In case, sigma33 component is significant, then 3D stress state analysis should be carried out considering 1/3*(sigma11+sigma22+sigma33) for pressure.

For 2D planestrain problem, strain in direction 33 (out-of-plane) is assumed to be zero but the stress in direction 33 (sigma33) is not necessarily zero. And even if sigma33 is zero, -1/3*(sigma11+sigma22+0) and -1/2*(sigma11+sigma22) will give two different confinement pressures.

True, this is the assumption that essentially allows us to model the problem as 2D plane strain. Consider 3D stress analysis if the out-of-plane stress is significant.

[BigBanana]

Do you mean STKO uses different equations for pressure in 2D and 3D cases? i.e. (sigma11+sigma22)/2 for 2D and (sigma11+sigma22+sigma33)/3 for 3D?

For PlaneStrain 2D problem, the sigma33 is not zero and equals to Poisson’s ratio ν times (sigma11+sigma22). Are you completely ignore sigma33? And even if sigma33 is insiginificant (close to zero), then, why not using (sigma11+sigma22+0)/3 for 2D?

[kesavapraba]

Hi, I apologize for my earlier response. After consulting with the developers, it has been confirmed that there is an inconsistency in pressure calculations for 2D cases. The upcoming version of STKO will rectify this issue. For instance, it may involve addressing the inconsistency through a formula such as (sigma11 + sigma22 + 0) / 3 in the case of a plane stress problem or plane strain problem with negligible sigma33. Thank you.