Interrelation of Creep and Relaxation: A Modeling Approach for Ligaments

[+] Author and Article Information
R. S. Lakes

Department of Engineering Physics and Biomedical Engineering Program, Rheloogy Research Center, University of Wisconsin, Madison, 147 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706-1687

R. Vanderby

Division of Orthopedic Surgery, Biomedical Engineering Program, University of Wisconsin, Madison, Madison, WI 53792-3228

J Biomech Eng 121(6), 612-615 (Dec 01, 1999) (4 pages) doi:10.1115/1.2800861 History: Received July 22, 1998; Revised May 25, 1999; Online October 30, 2007


Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R ≥ 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.

Copyright © 1999 by The American Society of Mechanical Engineers
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