(Dr. Iwona Jasiuk, advisor)
"Hierarchical Modeling of the Mechanical Behavior of Human Trabecular Bone"
Human trabecular bone is a hierarchical composite material. The four different length scales are distinguished: nanoscale (under 1 micron, describes the crystal/fiber level), submicroscale (1-10 microns, describes single lamella level), microscale (10-500 microns, single trabecula level), and mesoscale (1mm- 10cm, random network of trabecular plates or struts).
This research models trabecular bone on the mesoscale level. Two 3D FE models were created: an idealized periodic model and a model from digitized micro-CT human tibia samples. Because the sample sizes are smaller than the Representative Volume Element (RVE), apparent properties were analyzed. An RVE represents a statistically homogeneous sample that is large enough to describe the overall mechanical behavior and is independent of boundary conditions, while apparent properties are those obtained using regions smaller than the RVE.
The idealized periodic model was used to establish apparent elastic property bounds which were obtained by displacement and traction boundary conditions. These bounds were compared with the apparent moduli obtained from periodic boundary conditions. A study on the effects of bone volume fraction, window size, and boundary conditions on mechanical behavior was conducted. Reduction of modulus due to nonlinear effects was also examined.
The micro-CT model incorporated the actual geometry of human trabecular bone on the meso-level by utilizing computer aided tomography digitized imaging. The calculated results were compared with experimental results obtained from uniaxial compression testing of the actual digitized sample.