Multi-scale Modeling of Cortical Bone
Bone is an important multifunctional biological tissue with remarkable mechanical properties: high strength and stiffness, high fracture toughness, and light weight. These superior properties are due, in part, to the hierarchical structure of bone ranging from molecular to macroscopic levels. However, it is not clearly understood how the microstructure and mechanical properties of various hierarchies at different length scales affect the overall behavior of bone. Such understanding is essential in orthopedics for designing implant materials and fabricating synthetic bone substitutes and also for assessing the effect of bone diseases and their medications on bone’s properties. It can, moreover, serve as a guide in design of advanced synthetic bio-inspired materials for a wide range of engineering applications.
In the present work, we model cortical bone as a composite material with hierarchical structure. Different continuum techniques, including micromechanics methods and composite laminate theories, are employed at different scales, spanning from nanostructural to mesostructural levels, to account for the microstructure of bone at the pertinent level. The results obtained at a lower scale serve as inputs for the higher level. The predictions for effective elastic constants of bone are in good agreement with the experimental data reported in literature.