Singular Perturbation Analysis of the Nonlinear, Flow-Dependent Compressive Stress Relaxation Behavior of Articular Cartilage

[+] Author and Article Information
M. H. Holmes

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, N.Y. 12180

W. M. Lai, V. C. Mow

Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, N.Y. 12180

J Biomech Eng 107(3), 206-218 (Aug 01, 1985) (13 pages) doi:10.1115/1.3138545 History: Received September 01, 1984; Revised April 01, 1985; Online June 15, 2009


The dominant mechanism giving rise to the viscoelastic response of articular cartilage during compression is the nonlinear diffusive interaction of the fluid and solid phases of the tissue as they flow relative to one another. The present study is concerned with the role of this interaction under uniaxial stress relaxation in compression. The model is a biphasic mixture of fluid and solid which incorporates the strain-dependent permeability found earlier from permeation experiments. When a ramp-displacement is imposed on the articular surface, simple, but accurate, asymptotic approximations are derived for the deformation and stress fields in the tissue for slow and moderately fast rates of compression. They are shown to agree very well with experiment and they provide a simple means for determining the material parameters. Moreover, they lead to important insights into the role of the flow-dependent viscoelastic nature of articular cartilage and other hydrated biological tissues.

Copyright © 1985 by ASME
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