Modeling of human femoral bone idealized as functionally graded and laminated composite structure

Femur, the largest bone in the human skeletal system, provides critical mechanical support in bearing internal and external loads. It is a sophisticated natural composite with a complex hierarchical construction of multiple layers having varying material properties. This research work explores modeling approaches focusing on localized behavior of bone material under lateral loads. Small elements taken from crosssections of femur bone are considered for analysis. To simplify the analysis, it is assumed that the chosen elements can be idealized as plate structures. Two representative bone models are presented and their structural response under similar loading and boundary conditions is investigated. In the laminated composite approach, an idealized bone plate is modelled as a layered composite of discrete orthotropic and isotropic layers with a stepped variation in material properties along the thickness. In the functionally graded approach, an identical representative plate is modelled as a functionally graded structure with a gradual change in properties instead. Material properties of femoral bone used in this work were acquired from experimental data available in literature. A higher order shear deformation theory with seven degrees of freedom is then used to obtain deformation and stresses using analytical and finite element methods. Accuracy of the models are validated by benchmarking with 3-D elasticity solutions and published reference data in literature. Preliminary results show generally lower deformations in the functionally graded model with smooth and continuous stress profiles.