S33 stresses in plane strain

[lupex]

Hi guys,
I am running pure shear experiments with 2d plane strain elements. My mesh is made up of only 1 element. I know that in plane strain E33 is zero and S33 is not.
What is the role of S33 in plane strain? What is its physical significance?
For example in pure shear experiments S33 is non-zero but in simple shear experiments is always 0.
Why S33 is non-zero in pure shear and zero in simple shear?
The same questions for E33 in plane stress elements?
Thanks,
lupex

 

[gwolf2]

In a plane strain problem the applied loads/stresses in the 1 and 2 directions cause strains in the 11 and 22 directions. Because of Poisson's ratio any positive strain in the 11 or 22 directions causes the material to shrink in the 33 direction.

If you constrain the material in such a way that it is held more or less rigidly in the 33 direction (or is adjacent to other material elements trying to do the same thing acting against it) then E33 is zero. This develops stresses as if the E33 strain was allowed to happen but was then pushed back to it's original plane by another load. Example - concrete dam where 33 direction is across the gorge.

If you allow the material to contract in the 33 direction then there will be no stress S33 because nothing is resisting the contraction. You now have a situation where the strains E11, E22, and E33 are non-zero and the stresses S11 and S22 are non-zero but the out of plane stress S33 is Zero - this is called Plane stress. Example - aeroplane 1mm thick wing panel.

Basically it's all about out of plain constraints. Now map these concepts onto your test specimens.

gwolf.

 

[lupex]

Thanks gwolf
Did you ever look at what is the effect of prior pure shear on subsequent simple shear? Did you or anyone noticed if residual stresses and/or residual strain energy is propagated from pure shear to simple shear therefore making the simple shear deformation more energy expensive? All this at constant strain rate.
Cheers

 

[gwolf2]

That's another question, please post it on a materials or geotech forum.