Analysis of bone mechanical properties considering uncertainties in its constituents
Résumé
Bone is a natural composite with a hierarchical structure encompassing multiple length scales in which the material properties at each length scale affects the overall mechanical properties. At the nanoscale level, bone is composed of cross-linked collagen molecules, containing water and non-collagenous proteins in their gaps, coupled with hydroxyapatite-like nanocrystals reinforcements. Material properties at each scale are uncertain thus making deterministic approaches limited to predict accurately bone overall properties. To improve the accuracy of models to predict bone properties, there is a need to understand how uncertainties in the properties of the different constituents of bone affect its overall mechanical properties. The lack of a comprehensive model which accounts for such variability on the characterization of bone mechanical properties leads to the necessity of developing stochastic models to incorporate the uncertainties in the material properties of bones in different scales. For this study, the following research question was formulated: Can probabilistic techniques be used to effectively determine bone stiffness at the nanoscale? The specific aims developed to answer this question were: (1) make numerical predictions of bone stiffness at the nanoscale using micromechanics methods and (2) perform probabilistic analysis taking into account uncertainties in the volume fraction of bone constituents. The nanoscale is one of the building blocks of bone and properties gotten at this level are used as inputs for higher levels. Thus knowledge of how the stiffness of bone at this level behaves when subject to the variability of its constituents volume fractions, can be of high clinical and research interest.