Towards an efficient numerical simulation of complex 3D knee joint motion

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

  • Oliver Sander - , Free University of Berlin (Author)
  • Corinna Klapproth - , Zuse Institute Berlin (Author)
  • Jonathan Youett - , Free University of Berlin (Author)
  • Ralf Kornhuber - , Free University of Berlin (Author)
  • Peter Deuflhard - , Free University of Berlin, Zuse Institute Berlin (Author)

Abstract

We present a time-dependent finite element model of the human knee joint of full 3D geometric complexity together with advanced numerical algorithms needed for its simulation. The model comprises bones, cartilage and the major ligaments, while patella and menisci are still missing. Bones are modeled by linear elastic materials, cartilage by linear viscoelastic materials, and ligaments by one-dimensional nonlinear Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity with strict contact inequalities. The spatio-temporal discretization follows a time layers approach (first time, then space discretization). For the time discretization of the elastic and viscoelastic parts we use a new contact-stabilized Newmark method, while for the Cosserat rods we choose an energy-momentum method. For the space discretization, we use linear finite elements for the elastic and viscoelastic parts and novel geodesic finite elements for the Cosserat rods. The coupled system is solved by a Dirichlet–Neumann method. The large algebraic systems of the bone–cartilage contact problems are solved efficiently by the truncated non-smooth Newton multigrid method.

Details

Original languageEnglish
Pages (from-to)119-138
Number of pages20
JournalComputing and visualization in science
Volume16
Issue number3
Publication statusPublished - 2014
Peer-reviewedYes
Externally publishedYes

External IDs

Scopus 84925538039
ORCID /0000-0003-1093-6374/work/142250574