Question about enforcing plane strain or plane stress conditions on 3D solid elements. 1

[justAnEngineer95]

Hi all,

I have a quick question regarding enforcing plane strain/plane stress conditions on 3D solid elements, e.g. hexahedrals or brick elements.

Lets say I only have a single layer of 3D solid elements in the z-direction.
There are no tractions applied in the z-direction.
The thickness of the elements is an arbitrary value. It may either be quite relatively large or not.

If I constrain movement of all nodes in the z-direction -> This creates a plane strain condition (check).

If all nodes are free to move in z-direction, and provided that I only have a single row of 3d elements, do I then achieve a plane stress condition regardless of thickness? Why and why not?

 

[FEA way]

Plane stress will be achieved sort of naturally as you said but you will have to apply some minimal constraints to avoid rigid body motions. Plane strain requires you to block translations in the normal direction so again your concept is correct. But I would advise you to carry out some simple tests first, verify all the stress and strain component outputs and do comparisons with actual 2D analyses.

 

[justAnEngineer95]

Thank you.
A follow up question. Would plane stress still be achieved naturally if I use quadratic brick elements or is it only the case for linear brick elements?

I can easily wrap my head around the plane strain, but for some reason, I can't do the same for the plane stress. Is the argument simply that the faces on z-direction are traction free?

 

[rb1957]

plane stress implies 3D strain, typically in thin sheet. Most readily visualised by what happens at a crack tip in thin sheet ... you can easily see the surface dish inwards in the plastic zone (ahead of the crack).

plane strain implies 3D stress, typically in thick sections where stress can develop in the thickness direction.

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