期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
卷 29, 期 12, 页码 1338-1360出版社
WILEY
DOI: 10.1002/cnm.2572
关键词
bone hereditariness; fractional calculus; hierarchic structure; mechanical fractance; power law
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 <= ss <= 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 (c) 2013 John Wiley & Sons, Ltd.
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