This dissertation aims to explore the structure-property relations of bone as a nanocomposite material with hierarchical structure at different length scales. The studied mechanical properties of bone include elastic moduli and ultimate strength.

In the first part of the current study, multiscale modeling approaches are proposed to predict the elastic stiffness constants of bone. The structure and properties of cortical and trabecular bones are analyzed separately at different length scales:​ nanoscale (mineralized collagen fibril level), sub-microscale (single lamella level), microscale (single osteon and interstitial lamella level in cortical bone and single trabecula level in trabecular bone), and mesoscale (cortical bone level and trabecular bone level). Different micromechanics methods, laminated composite materials theories, cellular solids approaches, and finite element methods are employed at each scale to account for the microstructure of bone at that scale. The predicted results for the elastic properties of bone at a lower scale serve as the inputs for a higher scale. Finally, the modeling results are verified by the experimental data available in the literature.

Next, the developed multiscale models of bone are finetuned by analyzing the elastic behavior of treated (demineralized and deproteinized) cortical and trabecular bones. This study helps to better understand the effect of bone’s main constituents, namely protein and mineral phases, on bone’s overall mechanical behavior and to shed light on the interaction between these two phases. The predicted theoretical results for the elastic moduli of demineralized and deproteinized cortical and trabecular bones are verified by the corresponding results obtained by compression testing of bone samples.

The second part of this dissertation focuses on the study of damage and failure in bone. To that end, first, the dominant deformation and damage mechanisms of bone are identified at each level of hierarchy, and, next, appropriate models are proposed to capture those mechanisms. The modeling is performed in a bottom-up fashion starting at the sub-nanoscale (collagen micro-fibril level) and moving the scales up to the nanoscale (mineralized collagen fibril level), submicroscale (single lamella level), and finally microscale (lamellar structures level). Finite element and cohesive finite element methods are employed to model the damage mechanisms of bone and predict its strength at the above-mentioned length scales. The predicted modeling results are compared with other theoretical and experimental data available in the literature.