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TECHNICAL BRIEFS

The Effect of Overshooting the Target Strain on Estimating Viscoelastic Properties From Stress Relaxation Experiments

[+] Author and Article Information
Jonathan A. Gimbel, Joseph J. Sarver, Louis J. Soslowsky

McKay Orthopaedic Research Laboratory, University of Pennsylvania, Philadelphia, PA 19104-6081 e-mail: soslowsk@mail.med.upenn.edu

J Biomech Eng 126(6), 844-848 (Feb 04, 2005) (5 pages) doi:10.1115/1.1824132 History: Received November 07, 2003; Revised July 01, 2004; Online February 04, 2005
Copyright © 2004 by ASME
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References

Fung, Y. C., 1972, “Stress–Strain-History Relations of Soft Tissues in Simple Elongation,” in Biomechanics: Its Foundations and Objectives, edited by Y. C. Fung, N. Perrone, and M. Anliker, Prentice-Hall, San Diego, pp. 181–208.
Woo,  S. L., Johnson,  G. A., and Smith,  B. A., 1993, “Mathematical Modeling of Ligaments and Tendons,” J. Biomech. Eng., 115, pp. 468–473.
Kwan,  M. K., Lin,  T. H., and Woo,  S. L., 1993, “On the Viscoelastic Properties of the Anteromedial Bundle of the Anterior Cruciate Ligament,” J. Biomech., 26, pp. 447–452.
Nigul,  I., and Nigul,  U., 1987, “On Algorithms of Evaluation of Fung’s Relaxation Function Parameters,” J. Biomech., 20, pp. 343–352.
Thomopoulos,  S., Williams,  G. R., Gimbel,  J. A., Favata,  M., and Soslowsky,  L. J., 2003, “Variation of Biomechanical, Structural, and Compositional Properties Along the Tendon to Bone Insertion Site,” J. Orthop. Res., 21, pp. 413–419.
Gimbel,  J. A., Van Kleunen,  J. P., Mehta,  S., Perry,  S. M., Williams,  G. R., and Soslowsky,  L. J., 2004, “Supraspinatus Tendon Organizational and Mechanical Properties in a Chronic Rotator Cuff Tear Animal Model,” J. Biomech., 37(5), pp. 739–749.
Abramowitch,  S. D., and Woo,  S. L.-Y., 2004, “A Improved Method to Analyze the Stress Relaxation of Ligaments Following a Finite Ramp Time Based on the Quasi-Linear Viscoelastic Theory,” J. Biomech. Eng., 126(1), pp. 92–97.
Doehring,  T. C., Carew,  E. O.and Vesely,  I., 2004, “The Effect of Strain Rate on the Viscoelastic Response of Aortic Value Tissue: A Direct-Fit Approach,” Ann. Biomed. Eng., 32, pp. 223–232.
Turner, S., 1973, “Creep in Glassy Polymers,” in The Physics of Glassy Polymers, edited by R. H. Howard, Wiley, New York.
Lakes, R. S., 1999, Viscoelastic Solids, CRC Press, Boca Raton.

Figures

Grahic Jump Location
Example of a stress response for tendon measured from a stress relaxation experiment containing overshoot. Please note that the shape of the curve is similar to the simulated experiment (Fig. 3).
Grahic Jump Location
Study design for simulated stress relaxation experiment that was first performed to quantify the effect of overshoot on the estimated QLV parameters. Strain histories (a) with a small finite ramp time (∼0.06 s) and different amounts of overshoot, and a set of input QLV parameters (b) were used to determine the stress response (d) according to the constitutive equation proposed by Fung (c). The strain history was then assumed to have a finite ramp time but no overshoot (e), and a curve-fitting algorithm (f) was then used to estimate the QLV parameters (g).
Grahic Jump Location
Example of the simulated strain histories for overshoot amounts of 0% and 10% of the intended strain. The overshoots were varied from 0% to 10% in 1% increments. An overshoot of 7.5% was also added to correspond to the experimental data.
Grahic Jump Location
Example of the stress response determined for overshoot amounts of 0% and 10% of the intended strain. This was obtained using the QLV constitutive equation by numerically convolving the reduced relaxation function with the simulated strain histories.
Grahic Jump Location
Study design for actual stress relaxation experiment. Experimental data from tendon were used to determine if the errors associated with overshoot could be reduced by using a direct fit. The stress response (a) of tendon subjected to a ramp and hold with a small finite ramp time (∼0.06 seconds) was measured using an Instron materials testing machine. The strain history was then assumed to have a finite ramp, but no overshoot (b) as in the simulated experiment. A curve fit (c) was then used to estimate the QLV parameters (d). Additionally, nothing was assumed about the strain history (e) and a curve fit (f) was used to estimate a second set of QLV parameters (g).
Grahic Jump Location
Example of a strain history from an actual stress relaxation experiment. The overshoot magnitude averaged 7.5% of the intended strain for the experimental data.

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