Micro Fracture in Human Haversian Cortical Bone Under Compression

As the population is aging, pathologies such as osteoporosis modify the bone microstructure that can be more prone to fracture. It appears critical to understand the mechanism behind the growth of cracks in such biological systems. In this thesis, the primary focus is on compressive loading. During a micro compression test, the stress field on the surface of a millimetric specimen of human Haversian cortical bone is numerically reconstructed as micro fractures appear in order to measure local Stress Intensity Factors (SIF). At each step of the compression test, the surface displacement field of the bone specimen is measured by Digital Image Correlation (DIC) using a cross-correlation gradient descent formulation with domain partition of the multiple phases. Between successive light microscopy observations, two approaches are investigated: either a Direct method between the initial and considered images or a Gradual method between pairs of consecutive images which is finally preferred. The cortical bone microstructure is modeled by a Finite Element Method (FEM) where frictional contact along the crack edges is enforced by penalty and cohesive forces near the crack tips represent bridging of the collagen fibres. A local damage criterion is applied to calibrate the response of the numerical model to the experiment. The displacement boundary conditions are imposed by DIC measurements. The solution is obtained by a two-level Newton-Raphson algorithm. The local Stress Intensity Factors are calculated by the Interaction integral.