Multiscale modeling of elastic properties of cortical bone

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

“…This represents a simplification of the actual nanostructural arrangement which has been reported to also contain water (Weiner and Wagner 1998) and non-collagenous proteins (NCPs) (Olszta et al 2007). While some analytical approaches have considered these phases in their models (Hamed et al 2010;Martínez-Reina et al 2011), other finite element investigations (Ghanbari and Naghdabadi 2009;Yuan et al 2011) assume a mineral-collagen morphology, similar to that presented here. Therefore it seems reasonable to assume that the effects of these nanoscale constituents, i.e.…”

“…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).…”

“…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. Mori-Tanaka) at each analysis level to predict the effective properties of bone.…”

“…While previous step-by-step analytical approaches have been used to analyse bone on three or more different length scales (Hamed et al 2010;Martínez-Reina et al 2011), to date, multiscale finite element investigations have been limited to predicting mechanical behaviour between two independent length scales, i.e. they predict tissue properties based on mineral content or variation in tissue organisation, but cannot account for both simultaneously (Ghanbari and Naghdabadi 2009;De Micheli and Witzel 2011;Reisinger et al 2011;Yuan et al 2011).…”