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Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cnm Power-law hereditariness of hierarchical fractal bones

By L. Deseri, M. Di Paola, M. Zingales and P. Pollaci

Abstract

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 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 c ○ 2013 John Wiley & Sons, Ltd

Topics: Received... KEY WORDS, Bone Hereditariness, Fractional Calculus, Hierachic Structure, Mechanical Fractance, Power-Law
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.8269
Provided by: CiteSeerX
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