Homogenization with incompressible material

[autrera]

Hi!

I've been working on a homogenization problem with embedded trusses. While I was doing some initial tests on the micro-material (just with solid elements), I found some strange behavior when I used an incompressible material in the RVE model.

I started with a simple uniaxial stretch in a single hex macro model, where the RVE mesh is formed by 8 hex elements. The homogenization works as expected (same stress in all the hex elements, and same results in two different gauss points RVE's).

Then, when I changed the mesh to a Tet mesh (still a box, same material in the RVE model and same macroscopic condition), I started noticing an issue during the solution. The results on different RVE's are extremely different, where some of them even have compressive stresses. The homogenized response doesn't fit the material behavior anymore. I also tested this with an unstructured hex mesh, getting the same issue.

I figured that this difference between RVE results is quite higher when there is a higher enforcement of incompressibility on the RVE material, tested with both elastic (near 0.5 Poisson) or uncoupled neo hookean materials. This happens even at not so high bulk modulus, so I can't reliably enforce incompressibility in the macroscopic model. This doesn't happen to the regular hex RVE model tough. I can easily enforce incompressibility without noticing any change in the results.

I can tell that the automatic boundary condition is working properly (no bc_set is used, but FEBio correctly detects the boundary nodes in both cases), and the imposed displacement is the same across different RVE's. From my debugging, I suspect that the RVE model is not iterating properly when the macroscopic deformation gradient is updated, but I am not sure of this. The yy and zz stresses are quite high for the tet RVE's, so I suspect that the RVE's stresses aren't in equilibrium.

I am attaching two simple cases that demonstrate the issue. They have the same macroscopic conditions and materials (the incompressibility condition is quite hard, but it is for testing purposes), but different RVE models.

I'm going to keep looking for the issue.
I hope you can give me any insight to test of any comments. I would be happy to help.

Best,
Andres

[maas]

Hi Andres,

I'm afraid I cannot reproduce this on my end. I seem to get consistent output for the macroTET and both microTET models. I'm not sure why you are getting such different results. One possibility is that there is some kind of race condition that is affecting the results. I haven't been able to confirm this, but try running the model on a single processor. (by setting the environment variable OMP_NUM_THREADS to 1). If you find the results to be consistent with a single processor, but not with multiple processors, then there might be a race conditions. Let me know what you find.

Best,

Steve