Multiscale poroelastic modeling of bone

Total Hip Arthroplasty is nowadays one of the most performed orthopedic surgery and is representing a major health and economic issue. Bone is a complex material showing a hierarchical and porous structure, but also a natural ability to remodel itself thanks to specific cells, which are sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed within this thesis in order to simulate the bone response under external mechanical solicitations. The developed model relies on the homogenization technique for periodic structures based on an asymptotic expansion. It simulates cortical bone as a homogeneous structure. The first application of the developed model is the case of the loading of a finite volume of bone, allowing for the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions (impermeable walls and atmospheric pressure), the analysis of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. To validate the developed model, both a numerical and an experimental validation are realized. The numerical validation consists in the variation of parameters such as material properties or boundary conditions to estimate the accuracy of the model tendencies. Regarding the experimental validation, a cubic trabecular bone sample, extracted from a human hip and put under a compressive load, has been used. Increasing the load applied on the top of the bone specimen, the displacement is extracted, allowing to computation of the equivalent strain-stress curve. The equivalent stiffness of the bone specimen calculated numerically is then compared with the one from the experiments. A good agreement between the curves attests the validity of the developed numerical model, accounting for both the solid matrix and fluid contributions.