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Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage -1.16 %, tension damage 0.69 %, compression fracture -2.91 % and tension fracture 1.98 %. Ultimate strength and post-ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile-brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post-ultimate strength softening.

Cortical bone is a heterogeneous material with a complex hierarchical microstructure. In this work, unit cell finite element models were developed to investigate the effect of microstructural morphology on the macroscopic properties of cortical bone. The effect of lacunar and vascular porosities, percentage of osteonal bone and orientation of the Haversian system on the macroscopic elastic moduli and Poisson's ratios was investigated. The results presented provide relationships for applying more locally accurate material properties to larger scale and whole bone models of varying porosity. Analysis of the effect of the orientation of the Haversian system showed that its effects should not be neglected in larger scale models. This study also provides insight into how microstructural features effect local distributions and cause a strain magnification effect. Limitations in applying the unit cell methodology approach to bone are also discussed.

The purpose of this work was to investigate differences which may exist in the crack resistance of the microstructural bone tissues, i.e., osteonal, interstitial and trabecular bone. Indentations, using varying loads were used to initiate cracks of the same size scale as those which exist habitually in bone. The crack lengths and corresponding toughness values are presented for each of the tissues. Specimens were prepared using standard nanoindentation preparation techniques. Young's modulus and hardness were measured using a Berkovich tip, while cracks were produced using a cube-corner tip. Crack lengths were subsequently measured using scanning electron microscopy. Cracks produced at the same loads were significantly longer in trabecular bone than in interstitial and osteonal cortical bone. Similarly, within individual subjects, cracks produced in interstitial bone were longer than those produced in osteonal bone. These results provide significant experimental evidence that bone microstructural tissues exhibit differing resistance to crack growth and may help explain the incidence of more microcracks in interstitial than osteonal bone. The ability of the technique to distinguish differences between individual bone tissues is promising in an area where the focus has switched to the microscale, and in particular, to measures bone quality.

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