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In this work, a procedure is proposed to estimate the critical energy release rate G c of the so-called cement line in cortical bone tissue. Due to the difficulty of direct experimental estimations, relevant elastic and toughness material properties at bone microscale have been inferred by correlating experimental tests and finite element simulations. In particular, three-point

Cortical bone can be considered as a heterogeneous composite at microscopic scale, composed of osteons that act as reinforcement fibres embedded in interstitial matrix. Cement lines constitute the interface between osteons and matrix, and they often behave as the weakest links along which microcracks tend to propagate. However, current simulations of crack growth using XFEM combined with usual orientation criteria as implemented in commercial codes do not capture this behaviour: they predict crack paths that do not follow the cement lines surrounding osteons. The reason is that the orientation criterion used in the implementation of XFEM does not take into account the heterogeneity of the material, leading to simulations that differ from experimental results. In this work, a crack orientation criterion for heterogeneous materials based on interface damage prediction in composites is proposed and a phantom node approach has been implemented to model crack propagation. The method has been validated by means of linear elastic fracture mechanics (LEFM) problems obtaining accurate results. The procedure is applied to different problems including several osteons with simplified 2 geometry and an experimental test reported in the literature leading to satisfactory predictions of crack paths.

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Eighty used and 20 new silicone, polyurethane and polyvinylchloride central venous catheters were tested to establish the Young's modulus and the bending stiffness of the catheters and their introducers. The catheters were subjected to longitudinal traction forces and their lengthening measured. Young's modulus and the geometric moment of inertia were then calculated. It is shown that polyurethane catheters show least variation in their elastic characteristics, and that silicone catheters offer least resistance to bending and do not change their elastic properties after use. All catheters were equally unlikely to cause thrombus production if this is related to excessive bending stiffness.

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In this work, explicit expressions to estimate all the transversely isotropic elastic constants of lamellar bone as a function of the volumetric bone mineral density (BMD) are provided. The methodology presented is based on the direct homogenization procedure using the finite element method, the continuum approach based on the Hill bounds, the least-square method and the mean field technique. Firstly, a detailed description of the volumetric content of the different components of bone is provided. The parameters defined in this step are related to the volumetric BMD considering that bone mineralization process occurs at the smallest scale length of the bone tissue. Then, a thorough description provides the details of the numerical models and the assumptions adopted to estimate the elastic behaviour of the forward scale lengths. The results highlight the noticeable influence of the BMD on the elastic modulus of lamellar bone. Power law regressions fit the Young's moduli, shear stiffness moduli and Poisson ratios. In addition, the explicit expressions obtained are applied to the estimation of the elastic constants of cortical bone. At this scale length, a representative unit cell of cortical bone is analysed including the fibril orientation pattern given by Wagermaier et al. (Biointerphases 1:1-5, 2006) and the BMD distributions observed by Granke et al. (PLoS One 8:e58043, 2012) for the osteon. Results confirm that fibril orientation arrangement governs the anisotropic behaviour of cortical bone instead of the BMD distribution. The novel explicit expressions obtained in this work can be used for improving the accuracy of bone fracture risk assessment.