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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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).
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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.
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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.
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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).
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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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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).



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