A new model to simulate the elastic properties of mineralized collagen fibril

Abstract

Bone, because of its hierarchical composite structure, exhibits an excellent combination of stiffness and toughness, which is due substantially to the structural order and deformation at the smaller length scales. Here, we focus on the mineralized collagen fibril, consisting of hydroxyapatite plates with nanometric dimensions aligned within a protein matrix, and emphasize the relationship between the structure and elastic properties of a mineralized collagen fibril. We create two- and three-dimensional representative volume elements to represent the structure of the fibril and evaluate the importance of the parameters defining its structure and properties of the constituent mineral and collagen phase. Elastic stiffnesses are calculated by the finite element method and compared with experimental data obtained by synchrotron X-ray diffraction. The computational results match the experimental data well, and provide insight into the role of the phases and morphology on the elastic deformation characteristics. Also, the effects of water, imperfections in the mineral phase and mineral content outside the mineralized collagen fibril upon its elastic properties are discussed.

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.…”

“…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).…”

“…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). However, both tissue composition and hierarchical organisation must be taken into account to fully predict bone mechanical properties (Rho et al 1998;McNamara 2011).…”

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. They improved the shear lag Jaeger-Fratzl model [35] by incorporating more structural features of the MCF.…”

“…Some of these studies have focused on Mineralized Collagen Microfibrils (MCMs) scale [13][14][15][16][17]. Others have been interested on the second scale level Mineralized Collagen Fibrils (MCFs) [18][19][20][21]. There are also works dealing with lamella scale [11,22] and osteons scale [12].…”