Nonlinear viscoelastic characterization of bovine trabecular bone

Krishnagoud Manda*, Robert J. Wallace, Shuqiao Xie, Francesc Levrero-Florencio, Pankaj Pankaj

*Corresponding author for this work

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    The time-independent elastic properties of trabecular bone have been extensively investigated, and several stiffness–density relations have been proposed. Although it is recognized that trabecular bone exhibits time-dependent mechanical behaviour, a property of viscoelastic materials, the characterization of this behaviour has received limited attention. The objective of the present study was to investigate the time-dependent behaviour of bovine trabecular bone through a series of compressive creep–recovery experiments and to identify its nonlinear constitutive viscoelastic material parameters. Uniaxial compressive creep and recovery experiments at multiple loads were performed on cylindrical bovine trabecular bone samples ((Formula presented.)). Creep response was found to be significant and always comprised of recoverable and irrecoverable strains, even at low stress/strain levels. This response was also found to vary nonlinearly with applied stress. A systematic methodology was developed to separate recoverable (nonlinear viscoelastic) and irrecoverable (permanent) strains from the total experimental strain response. We found that Schapery’s nonlinear viscoelastic constitutive model describes the viscoelastic response of the trabecular bone, and parameters associated with this model were estimated from the multiple load creep–recovery (MLCR) experiments. Nonlinear viscoelastic recovery compliance was found to have a decreasing and then increasing trend with increasing stress level, indicating possible stiffening and softening behaviour of trabecular bone due to creep. The obtained parameters from MLCR tests, expressed as second-order polynomial functions of stress, showed a similar trend for all the samples, and also demonstrate stiffening–softening behaviour with increasing stress.

    Original languageEnglish
    Pages (from-to)173-189
    Number of pages17
    JournalBiomechanics and Modeling in Mechanobiology
    Issue number1
    Early online date20 Jul 2016
    Publication statusPublished - Feb 2017


    • Creep
    • Nonlinear viscoelasticity
    • Recoverable and irrecoverable strains
    • Recovery
    • Schapery model
    • Trabecular bone
    • RCUK
    • EPSRC
    • EP/K036939/1


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