A Finite Element Analysis of Mid-Shaft Femoral Tolerance under Combined Axial-Bending Loading

Bone fractures occur frequently at mid-shaft femoral site during frontal and offset automotive crashes. Because these injuries are expensive, it is crucial to understand the injury mechanisms if this injury is to be prevented. The experimental investigation of femoral shaft tolerance under loading corresponding to real world accidents requires a challenging test setup that allows applying external loads in controlled conditions, mimics the boundary conditions of the femur, and measures the loads at the mid-shaft cross-section of the femur. In addition, the variability of mechanical and structural properties of the specimens complicates the determination of the injury tolerance of the femur under different loading conditions. A numerical alternative is presented in the current study. First, a subject specific finite element model of a femur is developed based on medical images. Then, the parameters of two material models frequently used to approximate the cortical bone properties are identified using the Successive Response Surface Methodology in the ranges reported in the literature. The objective function is defined based on the impact force data recorded during a three-point bending test and its corresponding numerical simulations. The polynomial meta-models implemented in LS-Opt converge at close values of the material parameters suggesting good performance of the heuristic design search in the current identification problem. The femoral tolerance at mid-shaft location is determined using a virtual test setup that applies combined axial –sagittal bending loading through an axial preload along the knee-hip line and a transversal impact load at the mid-shaft site along anterior-posterior or posterior-anterior directions. The femoral tolerance curves calculated based on external loads show sensitivity with respect to the impact direction of transversal load due to the initial curvature of the femur, but insignificant dependence on the material mode, or the failure criteria used for femoral cortical bone. In addition to suggesting a numerical approach that uses finite element simulations and optimization techniques to determine the injury tolerance of long bones, the results highlight the predominant role of the bending loading in a combined loading of the femur.