Power-law hereditariness of hierarchical fractal bones

Authors

  • Luca Deseri,

    1. Center for Nonlinear Analysis and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, U.S.A.
    2. Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Universitá degli Studi di Trento, 38123 Trento, Italy
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  • Mario Di Paola,

    1. Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale e dei Materiali (DICAM), Universitá degli Studi di Palermo, 90100 Palermo, Italy
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  • Massimiliano Zingales,

    Corresponding author
    1. Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale e dei Materiali (DICAM), Universitá degli Studi di Palermo, 90100 Palermo, Italy
    2. (BM) 2-Lab, Mediterranean Center of Human Health and Advanced Biotechnologies, Universitá degli Studi di Palermo, 90100 Palermo, Italy
    • Correspondence to: Massimiliano Zingales, Journals Production Department, John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, U.K.

      E-mail: massimiliano.zingales@unipa.it

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  • Pietro Pollaci

    1. Dipartimento di Ingegneria Civile, Ambientale e Meccanica, Universitá degli Studi di Trento, 38123 Trento, Italy
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SUMMARY

In this paper, the authors introduce a hierarchic fractal model to describe bone hereditariness. Indeed, experimental data of stress relaxation or creep functions obtained by compressive/tensile tests have been proved to be fit by power law with real exponent 0 ⩽ β ⩽1. The rheological behavior of the material has therefore been obtained, using the Boltzmann–Volterra superposition principle, in terms of real order integrals and derivatives (fractional-order calculus). It is shown that the power laws describing creep/relaxation of bone tissue may be obtained by introducing a fractal description of bone cross-section, and the Hausdorff dimension of the fractal geometry is then related to the exponent of the power law. Copyright © 2013 John Wiley & Sons, Ltd.

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