Elastic properties of nanocomposite structure of bone

A three-scale finite element investigation into the effects of tissue mineralisation and lamellar organisation in human cortical and trabecular bone

“…The resulting effective properties are again expressed in terms of the MVF, as shown in Figure 3(c). Here, it is apparent that a high aspect ratio leads to an increased longitudinal modulus, as seen by the 75×25×3nm model, which is in agreement with the analytical model presented by Ji and Gao (2006). By resolving local stress and strain field within each unit cell analysed, it may be seen that the reason for this increase in modulus is that the larger mineral crystals facilitate a more effective stress transfer through the length of the crystal, allowing them to bear a much higher load, as shown by the longitudinal stress distributions in Figure 4.…”

“…A distinct advantage of this current study over previous analytical (Porter 2004;Ji and Gao 2006;Hamed et al 2010;Martínez-Reina et al 2011) andnumerical (Predoi-Racila andCrolet 2008) models is that we have developed a framework that can be incorporated with the finite element method to predict tissue and whole bone behaviour…”

“…More recently, various analytical (Porter 2004;Ji and Gao 2006;Hamed et al 2010;Martínez-Reina et al 2011) and computational (Ghanbari and Naghdabadi 2009;De Micheli and Witzel 2011;Yuan et al 2011) models have been proposed in order to fully predict macroscopic behaviour based on the nanostructural constituents. Analytical approaches have included an energy-sharing model by Porter (2004) and a tension-shear chain model by Ji and Gao (2006). Multilevel step-by-step homogenisation schemes have been proposed by both Hamed et al (2010) and Martínez-Reina et al (2011), who used classical continuum micromechanics homogenisation schemes (e.g.…”

“…Also, a comprehensive numerical homogenisation model has been developed, which predicts the mechanical behaviour of cortical bone as a function of a multitude of compositional and architectural parameters (Racila and Crolet 2007;Predoi-Racila and Crolet 2008). These analytical and numerical models have established microstructureproperty relationships for bone tissue, such as the effect of porosity (Racila and Crolet 2007; Predoi- Racila and Crolet 2008;Martínez-Reina et al 2011), mineral content (Porter 2004;Racila and Crolet 2007;Predoi-Racila and Crolet 2008;Martínez-Reina et al 2011) and mineral aspect ratio (Ji and Gao 2006) Reisinger et al (2011), for dictating the mechanical behaviour of bone.…”

A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method

“…Ji and Gao [37] used the same model geometry coupled with analytical formulation and a FEM analysis to obtain the transversely isotropic elastic constants of the MCF as a function of mineral aspect ratio. Yuan et al [18] used a FEM analysis to predict the elastic properties of a MCF both in 2D and 3D and validated their computational results with experimental data obtained by synchrotron X-ray diffraction.…”