Large indentation of elastic material with rigid body

[LionelG]

Hello,

I am modeling the indentation of a cell (modeled here as a parallepipedic neo-hookean elastic solid) by a spherical rigid indenter. I wish to compress the cell all the way to the bottom.

In the user documentation, it recommends in this case taking the augmented Lagrangian method, with a penalty factor worth E*A/V (E is Young's modulus, A is an element area and V is an element volume), the single pass method, and to have a coarser mesh for the rigid indentor than for the soft cell.

However, I am surprised to see that my model converges best when using the penalty factor method, with a higher penalty factor than recommended (between 10-100 times higher), the double pass method, and to have a finer mesh for the rigid indentor (this part is actually what surprises me most). Does someone have an explanation for this? Is this because I am setting some parameters incorrectly?
(nb: by better convergence, I mean that the computations converge for higher indentations, and that the reaction force on the rigid body rigid.Fz is very close to the reaction force computed using the Cauchy tensor and surface normals inside the cell)

Also, as I refine all meshes while keeping mesh size ratios intact, I often do not obtain a better convergence. How can we explain that, and is there some changes I should make to observe this expected behavior? Would it help to do quarter symmetry?

Many thanks for your help,
Lionel

[ateshian]

Hi Lionel,

When the rigid surface is curved, it is okay to use a finer mesh to get a more accurate representation of the geometry. When using a single-pass analysis and choosing the deformable surface as the slave surface, the contact pressure is evaluated at integration points on that surface, which is why it is recommended to have a finer mesh there. However, there is no major harm in refining the mesh on both surfaces other than increased computational time.

If augmented Lagrangian is turned off, the only way to prevent significant overlap of the contacting surfaces is to increase the penalty factor. If that does not cause element inversion, then there is no harm in using that approach. Augmented Lagrangian becomes helpful when you notice significant overlap between contact surfaces and increasing the penalty factor becomes problematic due to element inversion.

In the problem you attached, the analysis progresses well for most time steps, but as the indenter reaches the bottom of the deformable layer it become apparent that significant overlap is occurring (you can see it by using a plane cut in PostView). Turning on augmented Lagrangian and tightening the tolerance will improve things a bit. However, ultimately you need to refine the mesh through the layer thickness to get better results.

Best,

Gerard

[LionelG]

Hello Gerard,

Thank you very much for your detailed answer. After some trial and error, I have now been able to refine mesh while maintaining convergence for most time steps (convergence until ~70% compression for mesh on the order of 0.01) (in case that is helpful to future users, the best combination turned out to be turning off augmented lagrangian, and compensating with a large penalty factor and two-pass analysis).

I had two follow up questions:
- I wish to compute contact surface area. Is there an efficient way to do this in febio?
- is there in general an element type that is best suited for compression problems (I currently have tetrahedras)?

Thanks again for your help,
Lionel

[ateshian]

Hi Lionel,

- I wish to compute contact surface area. Is there an efficient way to do this in febio?

No, as of now, there is no efficient way to extract the contact surface area. If you would like that feature added, please submit a request on the FEBio bug report/feature request page.

- is there in general an element type that is best suited for compression problems (I currently have tetrahedras)?

Linear hex (hex8) elements are the best choice for contact analyses.

Best,
Gerard

[LionelG]

Thank you very much for all your support, Gerard!