Target Outcome
This specification documents and compares the results of different element type and integration rules in Febio during uncalibrated indentation simulations.
Protocols
Required Infrastructure
FEBio is a nonlinear implicit FE framework designed specifically for analysis in biomechanics and biophysics (Custom open source license; free for research use, licensing for commercial use is available, see http://www.febio.org).
Input
Fully specific lumped model for specimen 008's upper leg, for details on the modeling steps refer to our specifications on Fully Specific Modeling. GMSH was utilized for linear and 10-node quadratic tetrahedral meshing. Febio test parameters were as follows:
Model |
Febio Version |
Contact Formulation |
Contact Penalty |
Auto Penalty |
Augmented Lagrangian Method |
Boundary Conditions |
CMULTIS008_UL |
2.8.3 |
sliding-elastic (non-symmetric) |
100 |
On |
Off |
Y-axis: -15 mm displacement |
Results
3 different integration formulations are available within Febio for 4 node tetrahedral elements: Gauss1, Gauss4, and UT4 (a nodally integrated tetrahedron, see the following for details: http://www.sci.utah.edu/publications/SCITechReports/UUSCI-2011-007.pdf ). Section 3.5.1 of the 2.8 Febio user manual briefly describes the UT4 rule as well. Only a difference in runtime was observed in model behavior when switching between Gauss1 and Gauss4 integration, with Gauss1 completing quicker than Gauss 4 (590 vs 737 seconds).
Behavior between Gauss1 integration and UT4 integration/2nd order tets was very different, with the UT4/2nd order tets having much more concentrated displacements and lower reaction forces. Setting "Iso_Stab" to 1 in the UT4 integration resulted in a model that did not converge, so 0 was used with an alpha value of .05. Results summarized below:
Tet Type |
Integration Rule |
Face Count |
Node Count |
Probe Reaction Force (N) |
Max Contact Gap (mm) |
Max Contact Pressure (MPa) |
Runtime (s) |
Tet4 |
Gaussian, 1 Point |
32164 |
45168 |
86.692 |
.26658 |
.20977 |
591 |
Tet4 |
UT4 |
32164 |
45168 |
24.105 |
.04952 |
.03616 |
30620 |
Tet10 |
Gaussian, 4 Point |
8146 |
44968 |
20.804 |
.08057 |
.02147 |
2405 |
Reaction forces and displacement differed drastically between the two models, suggesting that the Gauss1 tetrahedral elements are experiencing locking. Febio developers have discouraged the usage of linear tets. (see my discussion on the Febio forums). Also see the following paper, figure 6 is especially relevant: https://mrl.sci.utah.edu/papers/maas_jbm_2016.pdf ). The discrepancy between the reaction forces observed in linear and quadratic elements in our mesh convergence tests suggest that our Gauss1 linear tet models are experiencing significant artificial stiffness due to element locking. Although the UT4 element performs closer to the 2nd order elements, the runtime and some convergence issues mean they are probably not a practical choice and Febio developers also seem to discourage their usage. Different integration rules for the triangular surface elements, as well as the tet10 elements could still be explored.
Comparing the wrapping of the tissue around the probe between the tet4, Gauss1 and the tet10, Gauss4: 
