期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2019.0294
关键词
nonlinear hereditariness; quasi-linear viscoelasticity; single-integral; tendons and ligaments
资金
- MIUR [DOT1320558]
- ARO Numerical Analysis [W911NF-17-1-0084]
- ONR Applied and Computational Analysis [N00014-18-1-2528]
- NSF Mechanics of Materials and Structures [1635407]
- ARO MURI Program [W911NF-19-1-0245]
In this paper the authors introduce a nonlinear model of fractional-order hereditariness used to capture experimental data obtained on human tendons of the knee. Creep and relaxation data on fibrous tissues have been obtained and fitted with logarithmic relations that correspond to power-laws with nonlinear dependence of the coefficients. The use of a proper nonlinear transform allows one to use Boltzmann superposition in the transformed variables yielding a fractional-order model for the nonlinear material hereditariness. The fundamental relations among the nonlinear creep and relaxation functions have been established, and the results from the equivalence relations have been contrasted with measures obtained from the experimental data. Numerical experiments introducing polynomial and harmonic stress and strain histories have been reported to assess the provided equivalence relations. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
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