Polymer Dynamics as a Mechanistic Model for the Flow-Independent Viscoelasticity of Cartilage

[+] Author and Article Information
D. P. Fyhrie

Bone and Joint Center, Department of Orthopaedic Surgery, Henry Ford Health System, Detroit, MI 48202

J. R. Barone

USDA/ARS/ANRI/EQL, Bldg. 012, Rm. 1-3, BARC-West, 10300 Baltimore Ave., Beltsville, MD 20705

J Biomech Eng 125(5), 578-584 (Oct 09, 2003) (7 pages) doi:10.1115/1.1610019 History: Received February 05, 2002; Revised May 12, 2003; Online October 09, 2003
Copyright © 2003 by ASME
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Fit of the polymer reptation relaxation function to the stress data of 4 for 201 data points (20.1 s of data, τd=99.06 s,σ0=0.0747 MPa). The data were equally well fit for periods of 2 to 20 s, but were increasingly poorly fit for longer times.
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Discrete relaxation spectrum of the reptation relaxation function with τd=1 s and p<203. The complete relaxation spectrum has an infinite number of small components that converge to (0,0).
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(a) Strain history for data from Huang, et al. and DiSilvestro, et al.; (b) possible stress responses: dashed line is nonsteady state, solid line reaches steady state (note: neither is an equilibrium state); (c) strain rate history for data from Huang, et al. and DiSilvestro, et al.
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Normalized average errors for different amounts of data fit by the polymer reptation relaxation function. One set of cartilage stress relaxation data showed existence of a best-fit time at approximately 0.5 s (minimal average error) and the other had a plateau of accuracy between approximately 2 and 20 s. The results for the latter data set do not rule out the possibility of an unresolved minimum for t<1 s. On the figure, the small numbers next to the curves are representative numbers of data points that were fit. Results from less than 21 data points are not appropriate for testing the usefulness of the fitted model.
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Fit of the polymer reptation relaxation function to the stress relaxation data of 7 for the best-fit time (50 data points, τd=11.02 s,σ0=0.6178 MPa). The reptation function was increasingly poor at representing the data as the fitted time was increased or decreased.
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A two-dimensional sketch of a polymer molecule (solid) of length L in a network of obstacles that create a confining tube (dotted lines)




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