Biomechanics and Modeling in Mechanobiology

, Volume 17, Issue 6, pp 1875–1883 | Cite as

An elasto-viscoplastic model to describe the ratcheting behavior of articular cartilage

  • Yilin ZhuEmail author
Original Paper


In the present work, a constitutive model for articular cartilage is proposed in finite elasto-viscoplasticity. For simplification, articular cartilage is supposed to be a typical composite composed of a soft basis and a fiber assembly. The stress tensor and free energy function are hence accordingly divided into two components. The high nonlinear stress-strain response is assumed to be mainly related to the fiber assembly and described by an exponential-type hypoelastic relation. Ratcheting is considered according to the viscoplasticity, the evolution rule of which is deduced from the dissipative inequality by the co-directionality hypotheses. Then, the capability of the proposed model is validated by comparing its predictions with related experimental observations. Results show that the ratcheting behavior and stress-strain hysteresis loops are reasonably captured by the proposed model.


Articular cartilage Constitutive model Logarithmic stress rate Ratcheting 



This study was funded by the National Natural Science Foundation of China (11702036) and Chengdu University New Faculty Start-up Funding (2081915038).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Architectural and Civil EngineeringChengdu UniversityChengduPeople’s Republic of China
  2. 2.School of Electromechanical Automobile EngineeringYantai UniversityYantaiPeople’s Republic of China

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