Scale transitions in bone elasticity from the nanometer level up to cortical and trabecular bone

摘要

Our goal, the prediction of the anisotropic elastic properties of bone on the basis of an appropriate description of its hierarchical organization, has been a research challenge for decades. However (cited from, p. 177), "so far", in 2001, "no one has developed a theory of bone structure that can satisfactorily explain its mechanical behavior on the basis of its internal structure and composition." This drawback seems to result from an insufficient nanostructural representation of the extracellular bone matrix or ultrastructure, defined at a characteristic length of 5 to 10 microns. We derived the morphology governing the ultrastructural elasticity from ultrasonic and chemical experiments, through energy considerations. Here we show how to integrate this morphology and the microporosity into a unified continuum micromechanics model, based on intrinsic stiffness values for bone mineral, collagen, non-mineral matter, and marrow, which are valid for all types of mineralized tissues in vertebrates. The volume fractions of the phases (mineral, collagen, microporosity), representing the composition of different tissues, serve as model input. Predicted elasticity tensors (output of the model) agree very well with experimental data.