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Power‐law hereditariness of hierarchical fractal bones
Author(s) -
Deseri Luca,
Paola Mario Di,
Zingales Massimiliano,
Pollaci Pietro
Publication year - 2013
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2572
Subject(s) - fractal , fractal dimension , power law , fractal derivative , exponent , creep , superposition principle , fractional calculus , mathematics , mathematical analysis , law , physics , fractal analysis , thermodynamics , linguistics , statistics , philosophy , political science
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.