Mixed finite element modelling of cartilaginous tissues

  • Authors:

  • E. F. Kaasschieter;A. J. H. Frijns;J. M. Huyghe

  • Affiliations:

  • Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
  • Year:
  • 2003

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Abstract

Swelling and shrinking of cartilaginous tissues is modelled by a four-component mixture theory. This theory results in a set of coupled non-linear partial differential equations for the electrochemical potentials and the displacement. For the sake of local mass conservation these equations are discretised in space by a mixed finite element method. Integration in time by backward Euler leads to a non-linear system of algebraic equations. A subtle solution strategy for this system is proposed and tested for one-dimensional situations.