A case study in hexahedral mesh generation: Simulation of the human mandible

We provide a case study for the generation of pure hexahedral meshes for th e numerical simulation of physiological stress scenarios of the human mandi ble. Due to its complex and very detailed free-form, geometry, the mandible model is very demanding. This test case is used as a running example to de monstrate the applicability of a combinatorial approach for the generation of hexahedral meshes by means of successive dual cycle eliminations, which has been proposed by the second author in previous work. We report on the p rogress and recent advances of the cycle elimination scheme. The given inpu t data, a surface triangulation obtained from computed tomography data, req uires a substantial mesh reduction and a suitable conversion into a quadril ateral surface mesh as a first step, for which we use mesh clustering and b -matching techniques. Several strategies for improved cycle elimination ord ers are proposed. They lead to a significant reduction in the mesh size and a better structural quality. Based on the resulting combinatorial meshes, gradient-based optimized smoothing with the condition number of the Jacobia n matrix as objective together with mesh untangling techniques yielded embe ddings of a satisfactory quality. To test our hexahedral meshes for the man dible model within an FEM simulation we used the scenario of a bite on a 'h ard nut.' Our simulation results are in good agreement with observations fr om biomechanical experiments.