• Specifications
• MeshConvergence

Target Outcome

This specification defines the test parameters and the results obtained from a mesh convergence test run on a single region at different densities (Most relevant test at the bottom of this page).

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. Models were generated in Meshlab with Poisson reconstruction with an octree depth of 7, and a solver divide of 7 (small isolated component was removed). Iso parameterization was run with default settings, except convergence precision which was set to 5. These models were generated at 5 different mesh surface densities by varying the iso parameterization remeshing sample rate, with values in the table below. These 5 different mesh surface densities produced 5 different volume densities. GMSH was utilized for tetrahedral meshing due to more consistent node counts and a significant speedup in runtime relative to meshing with Salome. Runtimes were between 2 to 5 times faster with GMSH. Febio test parameters were as follows:

Results

Results for pure penalty method (same models, test parameters changed to pure penalty with no augmented lagrangian method):

Results still suggest that mesh density has an effect on contact within Febio, at least with the current geometries and contact definitions. Penetration of the probe into the flesh surface decreased with increasing mesh density, and although turning on the augmented Lagrangian method for the last time step did further reduce probe penetration(contact gap) by a factor of ~10 for all trials, the augmented Lagrangian method also increased runtime in all but the highest density trial. Both tests converged at the same density. The highest density mesh required the high performance computing cluster in order to run.

Low density meshes can have their material properties calibrated to compensate for the differences resulting from mesh density (e.g. scale C₁ for the tissue to increase or decrease reaction force to match experimental data), given that the mesh density needed for convergence is computationally intensive. Febio developers have suggested that 10 node tetrahedrons might perform better, due to the locking of 4 node tetrahedral elements. Results for the 2nd-Order 10 node tetrahedrals are below. These simulations utilized penalty method at a value of 100, and the same simulation parameters as above other than dtmin, which was increased to 1e-2 to keep the time step from getting too small. Results for the 10 node tets converged at a similar node count to the 4 node tets:

Reran quad models with material parameters from calibrated lumped model paper (c1 = .01, k = 10). Optimal number of iterations increased to 100 because this was seen to improve model run time. Models run on a single cpu for consistency. Results unaffected by material parameters as compared to last test: