, Volume 53, Issue 3, pp 519–530 | Cite as

Viscoelastic modeling of articular cartilage under impact loading

  • R. SpringhettiEmail author
  • N. S. Selyutina
Recent Advances on the Mechanics of Materials


Recent unconstrained impact tests on articular cartilage indicate that under high strain rate the tissue behaves as a nonlinear viscoelastic material and hysteresis increases with impact velocity. As the dissipation of severe energies limits the potential damage in cartilage microstructure, the deep insight into the hysteretic properties of the tissue under impact loading represents a crucial issue. A quasilinear viscoelastic approach has been recently presented under simplified assumptions, in particular, the small strain hypothesis; the Kelvin–Voigt relaxation function was used besides. The current paper aims at extending this viscoelastic formulation into the framework of finite strain, in order to thoroughly investigate its accuracy to model impact loading on articular cartilage, taking into account the large deformation arising. Paralleling many hypotheses in the small strain approach, we describe the unconstrained impact test as uniaxial compression, assuming an average Cauchy stress in cartilage that obeys Fung’s model of viscoelasticity with Kelvin–Voigt relaxation function. The comparison between the experimental data available and the theoretical predictions on the basis of the current finite strain and the original small strain approaches shows a remarkable improvement in the descriptions of both stress–strain response and energy dissipation. Finally, the model formulated allows to single out some crucial physical aspects characterizing the behavior of articular cartilage under high strain-rates.


Articular cartilage Quasilinear viscoelasticity Impact Coefficient of restitution 



The authors acknowledge support from the FP7 IRSES Marie Curie Grant TAMER No. 610547. The authors would like to express their gratitude to professor Aspden for the data kindly supplied.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Civil, Environmental and Mechanical EngineeringUniversity of TrentoTrentoItaly
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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