Law, Man Fai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 84-86). / Text in English; abstract also in Chinese. / Law, Man Fai. / Contents --- p.i / Abstract --- p.iii / Acknowledgement --- p.iv / List of Figures --- p.v / List of Tables --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Spectral Representation of Composite Materials --- p.4 / Chapter 2.1 --- Spectral method --- p.6 / Chapter 2.2 --- General properties --- p.10 / Chapter 2.3 --- Duality --- p.12 / Chapter 2.4 --- Dilute limit --- p.13 / Chapter 2.5 --- Effective-medium approximation (EMA) --- p.15 / Chapter 2.6 --- Moment expansions --- p.16 / Chapter Chapter 3. --- Local Field Effect and Depolarization Factor --- p.19 / Chapter 3.1 --- Isotropic homogeneous media --- p.20 / Chapter 3.2 --- Linear anisotropic homogeneous media --- p.22 / Chapter 3.3 --- Inhomogeneous anisotropic media --- p.24 / Chapter Chapter 4. --- Simulation on Correlated Microstructures --- p.26 / Chapter 4.1 --- Solving the nonlinear impedance networks --- p.27 / Chapter 4.2 --- Models of correlated microstructure --- p.29 / Chapter 4.2.1 --- Two-site correlated microstruture --- p.29 / Chapter 4.2.2 --- Environment correlated microstructure --- p.38 / Chapter 4.3 --- Conclusions --- p.45 / Chapter Chapter 5. --- Simulation on Anisotropic Microstructure --- p.46 / Chapter 5.1 --- Solving anisotropic impedance networks --- p.50 / Chapter 5.2 --- Simulation and results --- p.50 / Chapter 5.2.1 --- Parallel response --- p.51 / Chapter 5.2.2 --- Perpendicular response --- p.57 / Chapter 5.2.3 --- Unpolarized response --- p.61 / Chapter 5.3 --- Conclusions --- p.65 / Chapter Chapter 6. --- Conclusions --- p.66 / Appendix A. Symbolic Simulation --- p.67 / Chapter A.1 --- Formalism --- p.67 / Chapter A.2 --- Scaling Properties --- p.69 / Chapter A.3 --- The simulation --- p.71 / Appendix B. Fluctuation of Local Field in Composite Materials --- p.74 / Chapter B.l --- Simulations and Results --- p.74 / Appendix C. Lattice Animals in Correlated Network --- p.82 / Bibliography --- p.84

Bone is a composite material consisting of hydroxyapatite crystals deposited in an oriented manner on a collagen backbone. The arrangement of the mineral and organic phases provides bone tissue with the appropriate strength, stiffness, and fracture resistance properties required to protect vital internal organs and maintain the shape of the body. A remarkable feature of bone is the ability to alter its properties and geometry in response to changes in the mechanical environment. However, in cases of metabolic bone diseases or aging, bone can no longer successfully adapt to its environment, increasing its fragility. To elucidate the mechanisms of bone microdamage, this research project developed a specimen-specific approach that integrated 3D imaging, histological damage labeling, image registration, and image-based finite element analysis to correlate microdamage events with microstructural stresses and strains under compressive loading conditions. By applying this novel method to different ages of bovine and human bone, we have shown that the local mechanical environment at microdamage initiation is altered with age. We have also shown that formation of microdamage is time-dependent and may have implications in age-related microdamage progression with cyclic and/or sustained static loading. The work presented in this dissertation is significant because it improved our understanding of trabecular bone microdamage initiation and unlocked exciting future research directions that may contribute to the development of therapies for fragility diseases such as osteoporosis.