Multiscale Explanation of Elasticity and Strength of Bone and Bone Replacement Materials Made of Hydroxyapatite, Glass-ceramics, or Titanium: a Continuum Micromechanics Approach

Bone is a hierarchically organized material, characterized by an astonishing variability and diversity. Bone replacement or biomaterials are critical components in artificial organs, and they are also used as scaffolds in tissue engineering. The aim of this thesis is the prediction of the strength of bone and bone replacement materials, from their composition and microstructure, by means of multiscale models. The theoretical developments are supported by comprehensive experiments on cortical bone and on biomaterials made of hydroxyapatite, glass-ceramic, and titanium. Chapter A investigates different morphological concepts (spheres vs. needles) for homogenization of linear elastic properties of porous polycrystals, as can be found in the mineral phase of bone. Chapter B proposes a first attempt to model the strength properties of hydroxyapatite biomaterials, based on a micromechanical description of the elasticity and brittle failure of interfaces between isotropic, spherical crystals. In order to avoid optimization procedures for back-analysis of interface properties (as used in Chapter B), we developed an alternative approach (Chapter C) where we considered the non-spherical shape of the hydroxyapatite crystals. Using needles implies a 1D stress state in the bulk phase related to the needle direction, and this stress can be regarded as relevant for the stresses at the interface between crystals. Chapter D presents an experimentally supported micromechanical explanation of cortical bone strength, based on a new vision on bone material failure: mutual ductile sliding of hydroxyapatite mineral crystals along layered water films is followed by rupture of collagen crosslinks. The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their porosities, and the elastic and strength properties of hydroxyapatite and (molecular) collagen. Experimental investigations and modeling of two other classes of biomaterials accompany the theoretical developments: In Chapter E, porous titanium samples are tested acoustically and mechanically, and the corresponding mechanical properties, stiffness and strength, are predicted by a poro-micromechanical model. Chapter F presents a micromechanical description of bioresorbable porous glass ceramic scaffolds. Again, a material model predicting relationships between porosity and elastic/strength properties is developed and validated.