Discretization error when using finite element models: analysis and evaluation of an underestimated problem

Mesh convergence tests are often insufficiently performed in finite element analyses. There are many parameters which may have an effect on the mesh convergence behavior. The aim of this study was to identify the influence of different parameters on the mesh convergence behavior. For this purpose we used a simplified axis-symmetrical model of a single pedicle screw flank with surrounding bone to simulate a pull-out test. In parameter studies, the flank radii and the contact conditions at the bone-screw interface were varied. These parameter studies were carried out using an implicit and explicit solver. Thereby, the convergence criteria and the number of the substeps for the implicit nonlinear iteration process as well as the velocity and the material density for the explicit approach were considered. The mesh convergence behavior was influenced by varying the flank radii and the contact conditions. The implicit calculations led to a reaction force, which converged rapidly to a certain value with increasing mesh density, whereas the maximum von-Mises stress showed substantial convergence problems. The number of substeps and the convergence criteria of the iteration process strongly influenced the implicit solutions. In contrast, the maximum von-Mises stresses resulting from explicit calculations converged to a certain value after only a few refinement steps. Different pull-out velocities substantially affected the mesh convergence behavior, while the material density showed only a negligible influence. The results indicated the need to perform an appropriate mesh convergence test when using finite element methods. We were able to show that different parameters strongly influence the mesh convergence behavior and we demonstrated that convergence tests do not always lead to a satisfactory or acceptable solution.