Bone fragility fracture has been a major healthcare concern for a long time. Due to having hierarchical structure at different length scales, bone fragility fracture is directly related to structural hierarchy from macro scale to nano scale. In nano level mineral crystals and collagen fibrils construct mineral-collagen composite structure. Mineral crystals and collagen fibrils are aligned preferentially in primary loading directions to cope with external loading conditions. In situ behavior of mineral and collagen phases is vital which could affect bone nanomechanics and could alter tissue fragility. This thesis is a preliminary study of a long-term project of correlating ultrastructural behavior to bulk behavior of bone.
The first objective of this study was to develop 3D orientation distribution model of mineral crystals in bone based on experimental observations & using Bivariate Gaussian curve fitting technique. 3D orientation distribution of mineral crystals in bone was estimated in Cartesian coordinate system.
The second objective of this study was to estimate the in situ strain tensors of a set of mineral crystals that are aligned along longitudinal axis of bone under uniaxial compressive load. Using experimental data obtained from synchrotron X-ray scattering technique, a novel approach was implemented to obtain local strain tensor of mineral crystals. Obtained results indicate that subset of mineral crystals aligned in the loading direction is most likely deformed in a transversely isotropic manner. Also, existence of a significant amount of shear strain in transverse plane (x-y) suggests that interfacial sliding between mineral crystals and surrounding matrix likely to be occurred. In addition, shear components in longitudinal planes (y-z & z-x) are smaller compared to that in transverse plane(x-y).
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