Tetrahedral versus hexahedral finite elements in numerical modelling of the proximal femur.

The objective of this study was to evaluate and compare tetrahedral and hexahedral finite element meshes of simplified and realistic proximal intact femur geometries. Theoretical expressions of stresses and strains were derived for the simplified model of the femur. For the analysis of the realistic geometry of the proximal femur, a CAD model of the third generation composite femur (Pacific Research Labs, Vashion Island, WA) was used and simulations were performed with Hyperworks (Altair Engineering, Inc., Troy, MI) finite element analysis software. Convergence tests with hexahedral (8- and 20-node brick-elements) and tetrahedral (4- and 10-node tetrahedrons) elements were analysed by comparing the periosteal von Mises stresses and principal strains at a selected point of the femur. The numerical periosteal strains were also compared with experimental ones to determine the accuracy of the finite elements. Overall, we concluded, for the simplified femur, that tetrahedral linear element allowed results more closely to theoretical ones, but hexahedral quadratic elements seem to be more stable and less influenced to the degree of refinement (NDOF) of the mesh. It was not possible to correlate these findings with those observed for the realistic proximal femur simulations where no significant differences were seen using refined meshes, with more than NDOF=20,000 for hexahedral elements.

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