6533b83afe1ef96bd12a7103
RESEARCH PRODUCT
Fractional-order nonlinear hereditariness of tendons and ligaments of the human knee
Luca DeseriKaushik DayalEmanuela BolognaM. Di PaolaMassimiliano Zingalessubject
LogarithmQuasi-linear viscoelasticityGeneral MathematicsGeneral Physics and AstronomyHarmonic (mathematics)02 engineering and technology01 natural sciences010305 fluids & plasmasTendonsSuperposition principle0203 mechanical engineeringtendons and ligaments0103 physical sciencesHumansEquivalence relationnonlinear hereditarinessKneesingle-integralMechanical PhenomenaMathematicsPolynomial (hyperelastic model)LigamentsMathematical analysisGeneral EngineeringRelaxation (iterative method)Biomechanical PhenomenaFractional calculusNonlinear system020303 mechanical engineering & transportsNonlinear Dynamicsdescription
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’.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-05-12 | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |