Sander, O. and Klapproth, C. and Youett, J. and Kornhuber, R. and Deuflhard, P. (2013) Towards an efficient numerical simulation of complex 3D knee joint motion. Computing and Visualization in Science, 16 (3). pp. 119138. ISSN 14329360

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Official URL: http://dx.doi.org/10.1007/s0079101402276
Abstract
We present a timedependent 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 onedimensional nonlinear Cosserat rods. In order to capture the dynamical contact problems correctly, we solve the full PDEs of elasticity with strict contact inequalities. The spatiotemporal 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 contactstabilized Newmark method, while for the Cosserat rods we choose an energymomentum 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 nonsmooth Newton multigrid method.
Item Type:  Article 

Uncontrolled Keywords:  Biomechanics, Timedependent contact problem, Contactstabilized Newmark method, Domain decomposition, Energymomentum method, Geodesic finite elements, Knee model 
Subjects:  Mathematical and Computer Sciences > Mathematics > Numerical Analysis 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics 
ID Code:  1790 
Deposited By:  Ekaterina Engel 
Deposited On:  17 Feb 2016 09:36 
Last Modified:  03 Mar 2017 14:41 
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