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This paper presents a two-dimensional (2D) finite element model of the mineralized collagen fibril. The model was developed to investigate the relationship between fibril elasticity and degree of mineralization, the latter is measured by volume fraction of minerals. Mineralized fibrils were modeled as two-phase composite materials with mineral platelet inclusions embedded in the collagen matrix. Fibril elasticity moduli were determined by finite element analyses. It was found that the fibril elastic modulus increases slowly with the volume fraction of minerals up to a volume fraction of 39.2%. Beyond this point, the elastic modulus increases rapidly with volume fraction. This rapid increase is probably attributed to the sharp gain in von Mises strain within the fibril resulting from a decrease in axial spacing between hydroxyapatite crystals. These results provide insights into the mechanical properties of bone at the nano-mesoscale. The results from the finite element modelling are compared with predictions from theoretical models such as the Mori-Tanaka Scheme, the Self-consistent scheme, and the Voigt-Reuss bounds. Whereas there are considerable differences between theoretical predictions and finite element results, similar trends can still be observed, indicating that finite element modelling is a promising approach to understand the effects of bone chemical composition on its mechanical behaviour.

A Finite Element Study of the Relationship Between Bone Fibril Elasticity and Degree of Mineralization