Experimental and numerical analysis of deformation and fracture of cortical bone tissue

Bones are the principal structural components of a skeleton; they provide the body with unique roles, such as its shape maintenance, protection of internal organs and transmission of muscle forces among body segments. Their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain loads until a certain limit, beyond which it fails. Usually, the reasons for bone fracture are traumatic falls, sports injuries, and engagement in transport or industrial accidents. The stresses imposed on a bone in such activities can be far higher than those produced during normal daily activities and lead to fracture. Understanding deformation and fracture behaviours of bone is necessary for prevention and diagnosis of traumas. Even though, in principle, studying bone’s deformation and fracture behaviour is of immense benefit, it is not possible to engage volunteers in in-vivo investigations. Therefore, by developing adequate numerical models to predict and describe its deformation and fracture behaviours, a detailed study of reasons for, and ways to prevent or treat bone fracture could be implemented. Those models cannot be formulated without a set of experimental material data. To date, a full set of bone’s material data is not implemented in the material data-base of commercial finiteelement (FE) software. Additionally, no complete set of data for the same bone can be found in the literature. Hence, a set of cortical bone’s material data was experimentally measured, and then introduced into the finite-element software. A programme of experiments was conducted to characterise mechanical properties of the cortical bone tissue and to gain a basic understanding of the spatial variability of those properties and their link to the underlying microstructure. So, several types of experiments were performed in order to quantify mechanical properties of the studied bone tissue at macro- and microscales under quasi-static and dynamic loading regimes for different cortex positions called anterior, posterior, medial and lateral. Those experiments included: (1) uniaxial tension and creep tests to obtain its elastic, plastic and viscoelastic properties; (2) nanoindentation tests to characterise its microstructural elastic-plastic properties; (3) Izod tests to investigate its fracture properties under impact bending loading; (4) tensile-impact tests to characterise its impact strength and fracture force when exposed to a longitudinal loading regime. All the experiments were performed for different cortex positions and different directions (along the bone axis and perpendicular to it) when possible. Based on the results of those experiments, a number of finite-element models were developed in order to analyse its deformation and fracture using the extended finiteelement method (X-FEM) at different length scales and under various loading conditions. Those models included: (1) two-dimensional (2D) FE models to simulate its fracture and deformation at microscale level under quasi-static tensile loading. Additionally, the effect of the underlying microstructure on crack propagation paths was investigated; (2) 2D and three-dimensional (3D) FE models to simulate its fracture and deformation at macroscale level for the Izod impact test setup. In addition, the applicability of different constitutive material models was examined; (3) 3D FE models to simulate its fracture and deformation at macroscale level for tensile-impact loading conditions. The developed models provided high-quality results, and most importantly, they adequately reflected the experimental data. The main outcome of this thesis is a comprehensive experimental analysis and numerical simulations of the deformation and fracture of the cortical bone tissue at different length scales in response to quasi-static and dynamic loading. Recommendations on further research developments are also suggested.