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Element formulation and stability

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Joined: 2 years ago

Hi All,

I am trying, for pedagogical purposes, to implement my own hybrid element.

At the moment I am just after a 8-node, linear brick, with constant pressure: something like C3D8H in Abaqus, I believe. I ended up with an element which seems to be working, apart from one test.

I get a one-element cube. I fix all DOFs of one vertex.

Two (say, vertical) faces are forced to slide on their original plane. On the other (vertical) two, the same pressure is applied via nodal forces.

Top and bottom face are stress-free. I even constrain the top face to remain on its original plane.

To cut a long story-short, a biaxial stress test.

I use a Neo-Hookean material model, could not get more robust.

Yet, once I get around a pressure roughly 5 times higher than the material constant, somewhere past stretch = 2, it stops converging, as it gets into a "wedge" type shape (the edge opposite the constrained vertex, shared by the two pressurised faces,  moves out and the pressurised faces are not perpendicular any more.). 

I was pretty sure I made some mistake somewhere, but I managed to get hold of a computer with ANSYS software and I tried the same test, and still it would not converge. Tried all the elements one could, tightened Newton-Raphson convergences to the bone. I noticed from ANSYS's converged substeps that shear strains develop well before the loss of convergence.

I am not aware of any physical instability that could affect a Neo-Hookean block in a biaxial stress state.

Is any of you?

If not, what else. Has anybody tried anything similar in ABAQUS or MARC?

It must certainly possibly to load biaxially a single element up to 500-600%! Yet I cannot get there in ANSYS, let alone my patched up element. I am losing the plot. 

I could provide the ANSYS input file.