Trabecular bone as a hierarchical structure

Iwona Jasiuk, Mechanical Science and Engineering, UIUC

We study trabecular bone as a hierarchical material. We analyze bone at several different length scales: nanoscale (apatite crystal and collagen fibril level), sub-microscale (single lamella level), microscale (single trabecula level), and mesoscale (trabecular structure involving a random network of struts or plates). We model trabecular bone at each of these structural levels. Material properties are determined at each scale either analytically, using micromechanics theories, or numerically, using finite element and beam network approaches. Computational challenges include modeling of complex irregular, random structure at each level and accounting for the spatial heterogeneity of bone’s properties. Theoretical issues include separation of scales and dependence of properties on specimen size and boundary conditions. Elastic constants, calculated at each structural level, are compared with those measured experimentally. Results of this study should improve the understanding of bone remodeling and fracture processes. Finally, this study sets a framework for the analysis of other structural materials with hierarchical structures.