Explicit expressions for the estimation of the elastic constants of lamellar bone as a function of the volumetric mineral content using a multi-scale approach

Biomechanics and Modeling in Mechanobiology
Ana Vercher-MartínezF Javier Fuenmayor

Abstract

In this work, explicit expressions to estimate all the transversely isotropic elastic constants of lamellar bone as a function of the volumetric bone mineral density (BMD) are provided. The methodology presented is based on the direct homogenization procedure using the finite element method, the continuum approach based on the Hill bounds, the least-square method and the mean field technique. Firstly, a detailed description of the volumetric content of the different components of bone is provided. The parameters defined in this step are related to the volumetric BMD considering that bone mineralization process occurs at the smallest scale length of the bone tissue. Then, a thorough description provides the details of the numerical models and the assumptions adopted to estimate the elastic behaviour of the forward scale lengths. The results highlight the noticeable influence of the BMD on the elastic modulus of lamellar bone. Power law regressions fit the Young's moduli, shear stiffness moduli and Poisson ratios. In addition, the explicit expressions obtained are applied to the estimation of the elastic constants of cortical bone. At this scale length, a representative unit cell of cortical bone is analysed including the fibril ...Continue Reading

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Citations

Nov 25, 2018·Biomechanics and Modeling in Mechanobiology·Mohammad Maghsoudi-GanjehXiaowei Zeng

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