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

Abstract

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.