Theory-driven design of mechanical experiments for elasticity determination at multiple length scales : application to bone and bone biomaterials

Abstract

Bone is a natural material, which undergoes constant remodeling processes. It exhibits a complex hierarchical morphology with elementary components (in particular hydroxyapatite, collagen, and water with non-collagenous organics) governing its mechanical behavior, through building up hierarchically organized structures. Consequently, mechanical properties of bone are dependent on length scale and anatomical position. In this context, the present thesis is concerned with development of physically sound and reliable experiments for the determination of the elasticity of bone and of bone biomaterials, at multiple length scales. In the first chapter an experimental set-up for elasticity measurement of polymerceramic biomaterials at the millimeter scale is developed. In more detail, the Young's modulus is derived, for thermodynamical reasons, from unloading paths of stress-strain characteristics obtained from uniaxial compressive tests. This strategy for elasticity determination is then successfully validated through ultrasonic experiments, and further supported by a campaign of nanoindentation tests, together with micromechanical analysis of the investigated composite. In the second chapter the aforementioned strategy for Young's modulus measurement undergoes another validation check. This time, high resolution Computed Tomography images, with a pixel size of several micrometers, together with a micromechanical model of the polymer-ceramic composite, are utilized to develop Finite Element models. The latter deliver then values for Young-s modulus, which are consistent with those obtained from unloading experiments. In the third chapter, the aforementioned experimental strategy for elasticity determination is applied to several-millimeter-sized cortical bone samples, to be then again successfully validated through an ultrasound-based multistep micromechanical model. In the fourth chapter, a sophisticated sample preparation routine is presented. It enables carving of ideally prismatic micrometer-sized bovine cortical bone samples, which are attached to a virtually rigid and perfectly flat substrate. These samples are then subjected to the same experimental routine and evaluation procedure, as had been applied to the macroscopic samples previously. The results obtained from physically sound experiments, which have ensured homogeneous stress distribution within the samples, reveal not only more than double strength values as comparing to macroscopic bone, but also indicate that cortical bone at the extracellular level behaves elastoplastically. Moreover, obtained values for Young-s modulus are consistent with an extensively validated micromechanical model. In the fifth chapter, a micromechanics-enhanced ultrasonic study of different natural and synthetic coatings for bioglass scaffolds, reveals superiority in terms of stiffness improvement of polycaprolactone and collagen.