Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone

William J. Parnell, M. B. Vu, Q. Grimal, S. Naili

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We compare theoretical predictions of the effective elastic moduli of cortical bone at both the meso- and macroscales. We consider the efficacy of three alternative approaches: The method of asymptotic homogenization, theMori-Tanaka scheme and theHashin-Rosen bounds. The methods concur for specific engineering moduli such as the axialYoung'smodulus but can vary for others. In a past study, the effect of porosity alone on mesoscopic properties of cortical bone was considered, taking the matrix to be isotropic. Here, we consider the additional influence of the transverse isotropy of thematrix.We make the point that micromechanical approaches can be used in two alternative ways to predict either the macroscopic (size of cortical bone sample) or mesoscopic (in between micro- and macroscales) effective moduli, depending upon the choice of representative volume element size. It is widely accepted that the mesoscale behaviour is an important aspect of the mechanical behaviour of bone butmodels incorporating its effect have started to appear only relatively recently. Before this onlymacroscopic behaviourwas addressed. Comparisons are drawn with experimental data and simulations from the literature for macroscale predictions with particularly good agreement in the case of dry bone. Finally, we show how predictions of the effective mesoscopic elastic moduli can be made which retain dependence on the well-known porosity gradient across the thickness of cortical bone. © Springer-Verlag 2011.
    Original languageEnglish
    Pages (from-to)883-901
    Number of pages18
    JournalBiomechanics and modeling in mechanobiology
    Volume11
    Issue number6
    DOIs
    Publication statusPublished - Jul 2012

    Keywords

    • Asymptotic homogenization and micromechanics
    • Cortical bone
    • Macroscale
    • Mesoscale
    • Porosity
    • Transverse isotropy

    Fingerprint

    Dive into the research topics of 'Analytical methods to determine the effective mesoscopic and macroscopic elastic properties of cortical bone'. Together they form a unique fingerprint.

    Cite this