On 02/15/2013 09:18 PM, David N. Mashburn wrote:
Hello sfepy developers and users!
I am modelling a simple linear elastic sheet under isotropic stress with an elliptical hole in the center (and I have it working under sfepy, great little platform!).
It is obvious the model should initially yield more easily in the direction of the short axis of the ellipse. What is not so obvious to me is what should happen in the limit as stress goes to infinity. Part of me wants to believe that the hole should eventually become a circular, but the results of the simulation show that the ellipse eventually switches its aspect ratio with what was the the short axis becoming the long axis and vice-versa.
My question is whether: A: The finite element result is the product of a small-displacement/non-moving mesh artifact (and if so, if there is a way to get the correct behavior using sfepy...)
From the picture I would say the deformation is well outside of the validity of the linear elasticity theory. You could try using a hyperelastic formulation such as the one described in . Caveat: I have never tested those terms in 2D, so if you find that something does not work, let us know, please.
OR B: My intuition about the physical behavior of this ideal system is incorrect and the ellipse really wouldn't round out into a circle under increasingly large stress (aka, the FE model is still physical/correct with large displacements).
I cannot help you with this one - my physical intuition fails me all the time :)
This might be obvious to people who have done more finite element modeling than I have, but thanks anyway! I'm attaching a picture to make it easier to see at a glance (quarter-ellipse with x and y symmetry boundary conditions and equal tractions applied at the top and right boundaries).
I would a) try to google the problem - I am sure there are analytical expressions for stress concentration in a plate with a circular hole, so there might be something for your case too. Then b) use the large deformation formulation.