Anisotropic Validation of Hexahedral Meshes for Composite Materials in Biomechanics

We use a concrete simulation scenario to study the effect of hexahedral mesh size and mesh quality on the accuracy of the solution of a finite element analysis (FEA). Our test cases stem from biomedical research. We investigate a composite two-material model of a piece of bone from the human mandible on which we simulate a bite. In particular, we are interested whether material properties (soft vs. hard and isotropic vs. anisotropic) have a significant impact on the accuracy which can be achieved for the different kind of meshes. We constructed hexahedral meshes of varying size, with an increasing number of elements in the neighborhood of the external force of our load case. For the hexahedral mesh generation, we used the iterative cycle elimination method of the first author together with squared condition number based optimized smoothing. In this paper, we focus on the deformation as the postprocessing variable. In our experiments, it seems that the solution of the FEA converges relatively fast with an increasing number of elements. Our methodology to investigate the influence of the mesh quality on several post-processing variables is a systematic variation of the mesh quality by means of a controlled perturbation of an optimized mesh with a fixed mesh topology. The influence of mesh quality on the analysis results turns out to be relatively small. Even the mesh of poorest quality is within a range of not more than four Dr. Matthias Müller-Hannemann, Rheinische Friedrich-WilhelmsUniversität Bonn, Forschungsinstitut für Diskrete Mathematik, Lennéstr. 2, 53113 Bonn, Germany, [email protected]; www.math.tuberlin.de/ ̃mhannema. Dr. Cornelia Kober, Freie Universität Berlin, Institut für Mathematik II, WE2, Arnimallee 2-6, 14195 Berlin, Germany, [email protected]. yyPD Dr. Dr. Robert Sader, PD Dr. Dr. Hans-Florian Zeilhofer, Klinik und Poliklinik für Mund-Kiefer-Gesichtschirurgie der Technischen Universität München, Ismaninger Str. 22, 81675 München, Germany. percent from the results of our best quality mesh. Concerning the analysis of a possible interdependence between numerical behavior and material law, we observed that the fully anisotropic (and so the most realistic) case shows also the best numerical behavior.