convergence and fibre orientation

[maas]

Hi Spencer,

Please post PreView related issues in the PreView User's forum.

To answer your question, there is no easy way to figure out the local node numbering, but you can look at the fiber orientation by checking the "show material fibers" on the Display tab. You might have to hide some elements to inspect the interior fibers. Hope this helps.

Cheers,

Steve.

[cesarleonelflores83]

Hi Vittoria,

I believe the problem is that your bulk modulus (k) is too small. If I set it in both cases to 100MPa I can apply much larger loads. (~ x1000). Also, keep in mind that using negative values for C2 may in some cases lead to instabilities. It is for this reason that you'll notice that in the second paper I reference above they've used C2=0 in all their analyses.

Another thing I want to point out is that you apply the same force on all top nodes. It may sound strange, but this will not generate a uniform force at the top as you might expect. The reason for this odd behavior lies in the details of the FE method. One way of understanding it is that nodes that are attached to more elements will appear stiffer and move less. You'll see what I mean once you start applying larger forces. In the next release of FEBio we'll have a way around this: You can attach the nodes to a rigid body and apply the force on the rigid body. Let me know if you have any other questions.

Cheers,

Steve.

Hi Steve,

I was wondering if you could elaborate on the bulk modulus parameter in the transversely isotropic Mooney-Rivlin material. I find that if it's set too low the material tends to expand in an unrealistic way in tension and that if it's too high febio has a tough time converging for large bending strains. You recommend k = 100 MPa as does Weiss in "Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading" without justification. Shouldn't biologic tissue have a bulk modulus similar to water's, on the order of 1 GPa? I imagine setting the bulk modulus this high would create even more convergence problems with large strains.

Let me know what you think.

Thanks,

Cesar Flores

[maas]

Hi Cesar,

The transversely isotropic Mooney-Rivlin material in FEBio is implemented as a (nearly)-incompressible material. For such materials, FEBio uses a different formulation (a so called three-field formulation) instead of the usual FE formulation for compressible materials. The reason for this is that true incompressibility is numerically very problematic to enforce and several different schemes have been designed to deal with the problem. In FEBio, the three-field formulation enforces incompressibility by splitting the isochoric behavior from the volumetric behavior. The volumetric response is then treated as a penalty term that enforces the incompressibility constraint. The bulk modulus serves as a scale factor that determines how tight the constraint needs to be enforced.

The bottom line is that for all incompressible materials in FEBio, the bulk modulus is not really a true physical parameter (after all, for truly incompressible materials the bulk modulus is infinite) but simply a control parameter that allows the user to choose how well to enforce the incompressibility constraint. It has been our experience that a bulk-to-shear ratio of 1000 gives good results. Making the bulk modulus even higher may result in numerical instability of the stiffness matrix and therefore causing problematic convergence. Setting the bulk modulus too low may also result in unphysical results since the incompressibility constraint is not at all satisfied. When you notice the expansion you mentioned, that is a clear indication that the bulk modulus is set too low. This would be equivalent to choosing a negative Poisson's ratio, which theoretically is still okay, but undoubtetly not what you had intended. I hope this helps. Let me know if you have any further questions.

Cheers,

Steve.