Effect of osteonal microstructure on crack propagation: a computational study

Bone is a biological tissue with a highly hierarchical structure, playing a significant role in supporting body and protecting the organs. Ageing and degenerative bone diseases such as osteoporosis could cause a loss of bone mineral and change its micromorphology, leading to greater risk of fracture and limited functionalities. At micro-scale, cortical bone could be treated as natural composite material with four main constituents, namely, osteons, Haversian canals, cement lines and interstitial matrix. Changing the heterogeneous distributions of microstructural constituents alters local distributions of stresses and strains as well as propagation of cracks in case of fracture. Previous researches (Bernhard et al., 2013) on crack propagation in cortical bone focused on a relationship between the variation of micro-constituents and mechanical properties. However, a study of the effect of morphological variations originating from different population groups, including those affected by pathological conditions such as osteoporosis, on fracture resistance of cortical bone was not performed. Mechanical behaviour and crack-propagation characteristics for different population groups are still difficult to predict using experimental methods. Computational approaches including a cohesive-element (CE) method and an extended finite-element method (X-FEM) (Li, Abdel-Wahab, Demirci, & Silberschmidt, 2013a) are popular techniques for simulation of crack initiation/propagation thanks to their computational efficiency in modelling discontinuities and singularities in bone interior. However, the CE approach must define a single pre-path for crack propagation in the model while the standard XFEM-based technique used in commercial software cannot produce bifurcation and intersection of cracks and is limited to one crack per simulation domain, in contrast to real-life observations.

The aim of this PhD project is to investigate the effect of morphology and mechanical properties of microstructural constituents on crack propagation in various groups of cortical bone by development and implementation of the improved cohesive-element method and a special MATLAB program.

Numerical models of cortical-bone tissues with randomly distributed microstructural constituents were developed for four groups including young, senior, diseased (osteoporosis) and treated. They were based on the data collected for osteonal morphometric parameters from experimental images produced with a dedicated MATLAB program. Another MATLAB program was also developed to insert cohesive elements at the edges of solid elements, so that the model could generate multiple cracks instead of a single crack. This MATLAB program was also adapted to calculate the crack lengths in various microstructural constituents of the cortical bone models. The mesh-sensitivity test and validation for the developed models of the cortical bone were implemented to guarantee the reliability of the simulation tools. In order to analyse the effect of morphology of microstructural constituents of the cortical bone, two kinds of loading condition including (i) uniaxial tension without notch and (ii) compact tension with a single notch were employed to assess the crack growth in the cortical-bone models. Mechanical properties of three microstructural constituents were changed in the developed models, to analyse their effect on crack propagation in the cortical bone models.

The results of this study demonstrated the importance of the micromorphology of cortical bones on crack-propagation process and the higher strain-energy release rate of the osteons. Meanwhile, the crack propagation in the cement lines and uncracked ligament bridging were two significant phenomena enhancing toughness of the cortical bone during crack growth.