Biomechanics and Modeling in Mechanobiology

, Volume 12, Issue 4, pp 685–703 | Cite as

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

  • Nicola Kelly
  • Noel M. Harrison
  • Pat McDonnell
  • J. Patrick McGarryEmail author
Original Paper


Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.


Trabecular bone Pressure-dependent yielding Hydrostatic compression Confined compression microCT finite element analysis Vertebral subsidence Crushable foam 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Nicola Kelly
    • 1
    • 2
  • Noel M. Harrison
    • 1
    • 2
  • Pat McDonnell
    • 1
    • 2
  • J. Patrick McGarry
    • 1
    • 2
    Email author
  1. 1.Department of Mechanical and Biomedical EngineeringNational University of IrelandGalwayIreland
  2. 2.National Centre for Biomedical Engineering ScienceNational University of IrelandGalwayIreland

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