In this work, we present two strategies for the numerical modeling of microcracks and damage within an osteon. A numerical model of a single osteon under compressive diametral load is developed, including lamellae organized concentrically around the haversian canal and the presence of lacunae. Elastic properties have been estimated from micromechanical models that consider the mineralized collagen fibrils reinforced with hydroxyapatite crystals and the dominating orientation of the fibrils in each lamella. Microcracks are simulated through the node release technique, enabling propagation along the lamellae interfaces by application of failure criteria initially conceived for composite materials, in particular the Brewer and Lagacé criterion for delamination. A second approach is also presented, which is based on the progressive degradation of the stiffness at the element level as the damage increases. Both strategies are discussed, showing a good agreement with experimental evidence reported by other authors. It is concluded that interlaminar shear stresses are the main cause of failure of an osteon under compressive diametral load.

Fuenmayor Fernández, FJ. (2014). Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models. Biomechanics and Modeling in Mechanobiology. 13(2):1-21. doi:10.1007/s10237-013-0507-y.

ElsevierVercher Martínez, A.; Giner Maravilla, E.; Arango Villegas, C.; Fuenmayor Fernández, FJ. (2015). Influence of the mineral staggering on the elastic properties of the mineralized collagen fibril in lamellar bone. AbstractIn this work, a three-dimensional finite element model of the staggered distribution of the mineral within the mineralized collagen fibril has been developed to characterize the lamellar bone elastic behaviour at the sub-micro length scale. Minerals have been assumed to be embedded in a collagen matrix, and different degrees of mineralization have been considered allowing the growth of platelet-shaped minerals both in the axial and the transverse directions of the fibril, through the variation of the lateral space between platelets. We provide numerical values and trends for all the elastic constants of the mineralized collagen fibril as a function of the volume fraction of mineral. In our results, we verify the high influence of the mineral overlapping on the mechanical response of the fibril and we highlight that the lateral distance between crystals is relevant to the mechanical behaviour of the fibril and not only the mineral overlapping in the axial direction.

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

ElsevierGiner Maravilla, E.; Vercher Martínez, A.; Marco, M.; Arango Villegas, C. (2015). Estimation of the reinforcement factor xi for calculating the transverse stiffness E2 with the Halpin-Tsai equations using the finite element method. AbstractIn this work, an estimation of the reinforcement factor ξ of the Halpin-Tsai equations used to calculate the transverse stiffness E 2 is provided. An improved estimation of the value ξ = 2 originally proposed by Halpin andTsai is given through a set of finite element analyses that consider randomly distributed unidirectional fibers for different volume fractions. The analysis overcomes the original hypothesis of a square array distribution of fibers in the transverse plane. It is concluded that a value of ξ = 1.5 is a better estimation for the usual volume fractions found in practice for a unidirectional lamina of fiber reinforced composites.