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Updated: May 26, 2026

Investigating Stress-relaxation and Failure Responses in the Trachea
Published on: October 18, 2022
A comparison of cartilage stress-relaxation models in unconfined compression: QLV and stretched exponential in
Ronald K June1, David P Fyhrie
1Mechanical and Industrial Engineering Department, Montana State University, P.O. Box 73800, Bozeman, MT 59717-3800, USA. rjune@me.montana.edu
Abstract:
Cartilage exhibits nonlinear viscoelastic behaviour. Various models have been proposed to explain cartilage stress relaxation, but it is unclear whether explicit modelling of fluid flow in unconfined compression is needed. This study compared Fung's quasi-linear viscoelastic (QLV) model with a stretched-exponential model of cartilage stress relaxation and examined each of these models both alone and in combination with a fluid-flow model in unconfined compression. Cartilage explants were harvested from bovine calf patellofemoral joints and equilibrated in tissue culture for 5 days before stress-relaxation testing in unconfined compression at 5% nominal strain. The stretched exponential models fit as well as the QLV models. Furthermore, the average stretched exponential relaxation time determined by this model lies within the range of experimentally measured relaxation times for extracted proteoglycan aggregates, consistent with the hypothesis that the stretched exponential model represents polymeric mechanisms of cartilage viscoelasticity.
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