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MARIO DI PAOLA

Power-law hereditariness of hierarchical fractal bones

  • Authors: Deseri,L;Di Paola,M;Zingales,M;Pollaci,P
  • Publication year: 2013
  • Type: Articolo in rivista (Articolo in rivista)
  • OA Link: http://hdl.handle.net/10447/83757

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 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.