A finite element model for direction-dependent mechanical response to nanoindentation of cortical bone allowing for anisotropic post-yield behavior of the tissue.

A finite element model was developed for numerical simulations of nanoindentation tests on cortical bone. The model allows for anisotropic elastic and post-yield behavior of the tissue. The material model for the post-yield behavior was obtained through a suitable linear transformation of the stress tensor components to define the properties of the real anisotropic material in terms of a fictitious isotropic solid. A tension-compression yield stress mismatch and a direction-dependent yield stress are allowed for. The constitutive parameters are determined on the basis of literature experimental data. Indentation experiments along the axial (the longitudinal direction of long bones) and transverse directions have been simulated with the purpose to calculate the indentation moduli and the tissue hardness in both the indentation directions. The results have shown that the transverse to axial mismatch of indentation moduli was correctly simulated regardless of the constitutive parameters used to describe the post-yield behavior. The axial to transverse hardness mismatch observed in experimental studies (see, for example, Rho et al. [1999, "Elastic Properties of Microstructural Components of Human Bone Tissue as Measured by Nanoindentation," J. Biomed. Mater. Res., 45, pp. 48-54] for results on human tibial cortical bone) can be correctly simulated through an anisotropic yield constitutive model. Furthermore, previous experimental results have shown that cortical bone tissue subject to nanoindentation does not exhibit piling-up. The numerical model presented in this paper shows that the probe tip-tissue friction and the post-yield deformation modes play a relevant role in this respect; in particular, a small dilatation angle, ruling the volumetric inelastic strain, is required to approach the experimental findings.

Continuum damage model for bioresorbable magnesium alloy devices - Application to coronary stents.

The main drawback of a conventional stenting procedure is the high risk of restenosis. The idea of a stent that "disappears" after having fulfilled its mission is very intriguing and fascinating, since it can be expected that the stent mass decreases in time to allow the gradual transmission of the mechanical load to the surrounding tissues owing to controlled dissolution by corrosion. Magnesium and its alloys are appealing materials for designing biodegradable stents. The objective of this work is to develop, in a finite element framework, a model of magnesium degradation that is able to predict the corrosion rate, thus providing a valuable tool for the design of bioresorbable stents. Continuum damage mechanics is suitable for modeling several damage mechanisms, including different types of corrosion. In this study, the damage is assumed to be the superposition of stress corrosion and uniform microgalvanic corrosion processes. The former describes the stress-mediated localization of the corrosion attack through a stress-dependent evolution law, while the latter affects the free surface of the material exposed to an aggressive environment. Comparisons with experimental tests show that the developed model can reproduce the behavior of different magnesium alloys subjected to static corrosion tests. The study shows that parameter identification for a correct calibration of the model response on the results of uniform and stress corrosion experimental tests is reachable. Moreover, three-dimensional stenting procedures accounting for interaction with the arterial vessel are simulated, and it is shown how the proposed modeling approach gives the possibility of accounting for the combined effects of an aggressive environment and mechanical loading.

Differences in the crack resistance of interstitial, osteonal and trabecular bone tissue.

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.