Hello,
Could You help me understand when we can use plane strain?
For eg. if we want to simulate stretching of a sheet metal- which has very small thickness- we can use a plane stress (but of course, the results are some asumption, which is smallest when the thickness is going to 0).
In such a case plane strain could be also used (as I understand- it will give resuts closer to reallity) , or it will be a big mistake? (let’s forget for a moment about computing time )
How do you determine, which case is good to treat as plane stress, and which to treat as plane strain?
Where are the limits, above which the only good solution will be a fully 3d model? (I still think of just simple stretching of some element- no bending, no gravity, or other forces in Z direction, and still not worried about computing time)
The plane strain assumption is less commonly used. It can be applied to long parts like walls, dams or pipes. It’s a matter of experience and engineering judgment to determine whether a particular problem can be treated as plane stress/strain or not. You have to keep in mind that in plane stress models stress is zero in the out-of-plane direction while in plane strain models strain is zero in the out-of-plane direction. The book titled “Building Better Products with Finite Element Analysis” by V. Adams features a good description of these formulations.
“Practical Finite Element Analysis for Mechanical Engineers” by D. Madier is also very interesting (and fresh) but it mentions plane stress/strain only briefly.
It’s best to run all 3 kinds of analyses (3D, plane stress and plane strain) for some simple examples and compare the results to get a better understanding of these concepts.
Plane strain DO important to investigate when your structure has any stress concentration zones (cracks, cuts, holes, etc.). In the figure you can see stress distribution in a quarter of plate with hole in tension (all text is in Polish, excuse me). If you plot normal or effective stress distribution along such an stress riser (means along the yellow line in the figure) you will obtain a nail-shape plot shown at the left top corner of the figure. It shows that stress is lower at the fraction-free surface of a the plate (here we always have thin plane stress zone pointed by white arrows). In the middle of the body on the hole surface stress is higher and is nearly as high as in the plane strain conditions (corresponding zone is inside the green hole). Although a solid must be extremely thick (about 2,5 m for steel) for purely plain strain conditions, however, this example shows that plain strain result is always conservative in such a case. It gives you upper bond of the stress in a stress riser.
Plane strain is even more important for structural integrity assessment of your structure. Fracture toughness of most materials for the plane strain is usually much higher than for the plane strain. It means that in the plane strain domination zone some materials are more brittle than in the plane stress zone. Please read any good fracture mechanics textbook for more details.
From practice point of view, a coarse mesh 3D analysis + submodeling in the the stress concentration zones seams to be the safest method of analysis of complex structures.
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