The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions. The traction derivation involves time and space dependent natural boundary conditions, and requires special numerical treatment. This paper (Part II) describes how we obtain an efficient nonlinear finite element procedure to solve for the biphasic response of the individual contacting layers. In particular, alternate linearization of the nonlinear weak form, as well as both velocity-pressure, , and displacement-pressure, , mixed formulations are considered. We conclude that the approach, with linearization of both the material law and the deformation gradients, performs best for the problem at hand. The nonlinear biphasic contact solution will be demonstrated for the motion of the glenohumeral joint of the human shoulder joint.
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December 2006
Technical Papers
A Penetration-Based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact. Part II: Finite Element Simulations
Kerem Ün,
Kerem Ün
Department of Biomedical Engineering and Scientific Computation Research Center,
Rensselaer Polytechnic Institute
, Troy, NY 12180-3590
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Robert L. Spilker
Robert L. Spilker
Department of Biomedical Engineering and Scientific Computation Research Center,
e-mail: spilker@rpi.edu
Rensselaer Polytechnic Institute
, Troy, NY 12180-3590
Search for other works by this author on:
Kerem Ün
Department of Biomedical Engineering and Scientific Computation Research Center,
Rensselaer Polytechnic Institute
, Troy, NY 12180-3590
Robert L. Spilker
Department of Biomedical Engineering and Scientific Computation Research Center,
Rensselaer Polytechnic Institute
, Troy, NY 12180-3590e-mail: spilker@rpi.edu
J Biomech Eng. Dec 2006, 128(6): 934-942 (9 pages)
Published Online: May 10, 2006
Article history
Received:
November 17, 2005
Revised:
May 10, 2006
Citation
Ün, K., and Spilker, R. L. (May 10, 2006). "A Penetration-Based Finite Element Method for Hyperelastic 3D Biphasic Tissues in Contact. Part II: Finite Element Simulations." ASME. J Biomech Eng. December 2006; 128(6): 934–942. https://doi.org/10.1115/1.2354203
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