Application of the u-p Finite Element Method to the Study of Articular Cartilage

[+] Author and Article Information
Jennifer S. Wayne, Savio L.-Y. Woo, Michael K. Kwan

Orthopaedic Bioengineering Laboratory, San Diego Veterans Affairs Medical Center & University of California, San Diego, La Jolla, CA 92093; Musculoskeletal Research Laboratories, Department of Orthopaedic Surgery, University of Pittsburgh, Pittsburgh, PA 15261

J Biomech Eng 113(4), 397-403 (Nov 01, 1991) (7 pages) doi:10.1115/1.2895418 History: Received November 02, 1989; Revised April 22, 1991; Online March 17, 2008


The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (u) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.

Copyright © 1991 by The American Society of Mechanical Engineers
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