A biphasic visco-hyperelastic damage model for articular cartilage: application to micromechanical modelling of the osteoarthritis-induced degradation behaviour

  • Dongxu Liu
  • Songyun MaEmail author
  • Marcus Stoffel
  • Bernd Markert
Original Paper


Osteoarthritis-induced microstructural and compositional changes of articular cartilage affect its load-bearing capacity and the damage resistance. The aim of the present study is to analyse effects of the osteoarthritis-induced microstructural degradation on the damage behaviour of articular cartilages. A poro-visco-hyperelastic damage model is proposed within the theoretical framework of continuum mechanics to describe the deformation and damage behaviour of collagen fibrils and highly hydrated proteoglycan matrix in articular cartilages. An integral-type nonlocal algorithm is employed to overcome the mesh dependence of simulation results involving strain localization. 3D computational models for a normal cartilage and two osteoarthritic cartilages with different degeneration levels are developed to study the degradation of the damage resistance of articular cartilages. In addition, the present simulations take into account the alterations of collagen fibril networks as well as compositional changes of cartilage constituents at different osteoarthritic stages. The material parameters of the constitutive model are identified by comparing the computational results to unconfined compression tests. The simulation results of spherical indentation tests show that damage in the articular cartilage with high-stage osteoarthritis is much more significant than that in the normal cartilage under identical loadings. The proposed computational methods can be used for studying the relationship between the damage behaviour and the complex morphology of the collagen fibril networks in biomaterials.


Articular cartilage Osteoarthritis Damage behaviour Porous media Poro-visco-hyperelastic Nonlocal modelling 



The first author would like to acknowledge the research funding from China Scholarship Council (201606890022).

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 2019

Authors and Affiliations

  • Dongxu Liu
    • 1
  • Songyun Ma
    • 1
    Email author
  • Marcus Stoffel
    • 1
  • Bernd Markert
    • 1
  1. 1.Institute of General MechanicsRWTH Aachen UniversityAachenGermany

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