Trabecular bone as a hierarchical material: Elasticity and fracture

We study trabecular bone as a hierarchical material. First, we characterize the trabecular bone's structure at the following structural levels: nanoscale (apatite crystals and collagen fibril level), sub-microscale (single lamella level), microscale (single trabecular pocket or single trabecula level), and mesoscale (porous trabecular network level) using scanning and transmission electron microscopy. We focus on bone's structure as well as crack patterns observed at these different structural levels. Then, we model the trabecular bone at each structural level as a linear elastic solid. Modeling techniques include analytical micromechanics theories and numerical simulations involving finite element, spring network, and beam network approaches. We compare our theoretical results at each scale with our experimental measurements and observations. This study sets a framework for the analysis of other biological materials with hierarchical structures.