(Dr. Iwona Jasiuk, advisor)
"A Multiscale Model Of Cancellous Bone"
Cancellous (trabecular) bone is a highly organized composite material in which various geometrical features appear on a wide range of length scales and work jointly to give bone its mechanical properties. Accurate mechanical models should include interaction between different length scales.
In this thesis we give a detailed description of cancellous bone microstructural features at each level based on both a literature survey and our experimental observations using the Scanning Electron Microscope (SEM) at magnifications ranging from 10X to 50,000X. We also review existing experimental data and mechanical models in order to determine the areas which have been extensively studied as opposed to those in which additional work would advance our understanding of bone. We select the optimal model for each scale to use it in our multiscale analysis.
Couple-stress theory, which has been employed to describe elastic properties
and characteristic lengths of foam materials, can be advantageously applied
to cancellous bone. We conduct finite element analysis of 2D regular periodic
composites, including porous materials, to evaluate couple-stress elastic
moduli and characteristic lengths. The results are applied to an idealized
trabecular geometry and included into a hierarchical model of cancellous