An Improved Method to Analyze the Stress Relaxation of Ligaments Following a Finite Ramp Time Based on the Quasi-Linear Viscoelastic Theory

[+] Author and Article Information
Steven D. Abramowitch, Savio L.-Y. Woo

Musculoskeletal Research Center, Department of Orthopaedic Surgery, Department of Bioengineering, University of Pittsburgh, E1641 Biomedical Science Tower, 210 Lothrop Street, P.O. BOX 71199, Pittsburgh, PA 15213 Phone: 412-648-2000 FAX: 412-648-2001e-mail: ddecenzo@pitt.edu

J Biomech Eng 126(1), 92-97 (Mar 09, 2004) (6 pages) doi:10.1115/1.1645528 History: Received April 02, 2003; Revised October 02, 2003; Online March 09, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Fung, Y. C., 1972, “Stress Strain History Relations of Soft Tissues in Simple Elongation,” in Biomechanics: Its Foundations and Objectives, eds., Y. C. Fung, N. Perrone, and M. Anliker, PrenticeHall, Englewood Cliffs, NJ, pp. 181–207.
Carew,  E. O., Talman,  E. A., Boughner,  D. R., and Vesely,  I., 1999, “Quasi-Linear Viscoelastic Theory Applied to Internal Shearing of Porcine Aortic Valve Leaflets,” J. Biomech. Eng., 121(4), pp. 386–392.
Huang,  C. Y., Mow,  V. C., and Ateshian,  G. A., 2001, “The Role of Flow-Independent Viscoelasticity in the Biphasic Tensile and Compressive Responses of Articular Cartilage,” J. Biomech. Eng., 123(5), pp. 410–417.
Huyghe,  J. M., van Campen,  D. H., Arts,  T., and Heethaar,  R. M., 1991, “The Constitutive Behavior of Passive Heart Muscle Tissue: A Quasi-Linear Viscoelastic Formulation,” J. Biomech., 24(9), pp. 841–849.
Iatridis,  J. C., Setton,  L. A., Weidenbaum,  M., and Mow,  V. C., 1997, “The Viscoelastic Behavior of the Non-Degenerate Human Lumbar Nucleus Pulposus in Shear,” J. Biomech., 30(10), pp. 1005–1013.
Kim,  S. M., McCulloch,  T. M., and Rim,  K., 1999, “Comparison of Viscoelastic Properties of the Pharyngeal Tissue: Human and Canine,” Dysphagia, 14(1), pp. 8–16.
Myers,  B. S., McElhaney,  J. H., and Doherty,  B. J., 1991, “The Viscoelastic Responses of the Human Cervical Spine in Torsion: Experimental Limitations of Quasi-Linear Theory, and a Method for Reducing These Effects,” J. Biomech., 24(9), pp. 811–817.
Provenzano,  P., Lakes,  R., Keenan,  T., and Vanderby,  R., 2001, “Nonlinear Ligament Viscoelasticity,” Ann. Biomed. Eng., 29(10), pp. 908–914.
Puso,  M. A., and Weiss,  J. A., 1998, “Finite Element Implementation of Anisotropic Quasi-Linear Viscoelasticity Using a Discrete Spectrum Approximation,” J. Biomech. Eng., 120(1), pp. 62–70.
Rousseau,  E. P., Sauren,  A. A., van Hout,  M. C., and van Steenhoven,  A. A., 1983, “Elastic and Viscoelastic Material Behavior of Fresh and Glutaraldehyde-Treated Porcine Aortic Valve Tissue,” J. Biomech., 16(5), pp. 339–348.
Sauren,  A. A., van Hout,  M. C., van Steenhoven,  A. A., Veldpaus,  F. E., and Janssen,  J. D., 1983, “The Mechanical Properties of Porcine Aortic Valve Tissues,” J. Biomech., 16(5), pp. 327–337.
Woo,  S. L.-Y., Simon,  B. R., Kuei,  S. C., and Akeson,  W. H., 1980, “Quasi-Linear Viscoelastic Properties of Normal Articular Cartilage,” J. Biomech. Eng., 102(2), pp. 85–90.
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(3), pp. 413–419.
Funk,  J. R., Hall,  G. W., Crandall,  J. R., and Pilkey,  W. D., 2000, “Linear and Quasi-Linear Viscoelastic Characterization of Ankle Ligaments,” J. Biomech. Eng., 122(1), pp. 15–22.
Toms,  S. R., Dakin,  G. J., Lemons,  J. E., and Eberhardt,  A. W., 2002, “Quasi-Linear Viscoelastic Behavior of the Human Periodontal Ligament,” J. Biomech., 35(10), pp. 1411–1415.
Thomopoulos,  S., Williams,  G. R., and Soslowsky,  L. J., 2003, “Tendon to Bone Healing: Differences in Biomechanical, Structural, and Compositional Properties Due to a Range of Activity Levels,” J. Biomech. Eng., 125(1), pp. 106–113.
Elliott,  D. M., Robinson,  P. S., Gimbel,  J. A., Sarver,  J. J., Abboud,  J. A. , 2003, “Effect of Altered Matrix Proteins on Quasilinear Viscoelastic Properties in Transgenic Mouse Tail Tendons,” Ann. Biomed. Eng., 31(5), pp. 599–605.
Woo,  S. L.-Y., Gomez,  M. A., and Akeson,  W. H., 1981, “The Time and History-Dependent Viscoelastic Properties of the Canine Medical Collateral Ligament,” J. Biomech. Eng., 103(4), pp. 293–298.
Kwan,  M. K., Lin,  T. H., and Woo,  S. L.-Y., 1993, “On the Viscoelastic Properties of the Anteromedial Bundle of the Anterior Cruciate Ligament,” J. Biomech., 26(4–5), pp. 447–452.
Johnson,  G. A., Tramaglini,  D. M., Levine,  R. E., Ohno,  K., Choi,  N. Y., and Woo,  S. L.-Y., 1994, “Tensile and Viscoelastic Properties of Human Patellar Tendon,” J. Orthop. Res., 12(6), pp. 796–803.
Lin, H. C., Kwan, M. K., and Woo, S. L.-Y., 1987, “On the Stress Relaxation Properties of Anterior Cruciate Ligament (ACL),” Proceedings, ASME Adv Bioeng., pp. 5–6.
Nigul,  I., and Nigul,  U., 1987, “On Algorithms of Evaluation of Fung’s Relaxation Function Parameters,” J. Biomech., 20(4), pp. 343–352.
Abramowitch,  S. D., Yagi,  M., Tsuda,  E., and Woo,  S. L.-Y., 2003, “The Healing Medial Collateral Ligament Following a Combined Anterior Cruciate and Medial Collateral Ligament Injury—A Biomechanical Study in a Goat Model,” J. Orthop. Res., 21(6), pp. 1124–1130.
Scheffler,  S. U., Clineff,  T. D., Papageorgiou,  C. D., Debski,  R. E., Benjamin,  C., and Woo,  S. L.-Y., 2001, “Structure and Function of the Healing Medial Collateral Ligament in a Goat Model,” Ann. Biomed. Eng., 29(2), pp. 173–180.
Lee,  T. Q., and Woo,  S. L.-Y., 1988, “A New Method for Determining Cross-Sectional Shape and Area of Soft Tissues,” J. Biomech. Eng., 110(2), pp. 110–114.
Woo,  S. L.-Y., Gomez,  M. A., Seguchi,  Y., Endo,  C. M., and Akeson,  W. H., 1983, “Measurement of Mechanical Properties of Ligament Substance From a Bone-Ligament-Bone Preparation,” J. Orthop. Res., 1(1), pp. 22–29.
Woo,  S. L.-Y., Orlando,  C. A., Camp,  J. F., and Akeson,  W. H., 1986, “Effects of Postmortem Storage by Freezing on Ligament Tensile Behavior,” J. Biomech., 19(5), pp. 399–404.
Woo,  S. L.-Y., Danto,  M. I., Ohland,  K. J., Lee,  T. Q., and Newton,  P. O., 1990, “The use of a Laser Micrometer System to Determine the Cross-Sectional Shape and Area of Ligaments: A Comparative Study With Two Existing Methods,” J. Biomech. Eng., 112(4), pp. 426–431.
Woo,  S. L.-Y., 1982, “Mechanical Properties of Tendons and Ligaments. I. Quasi-Static and Nonlinear Viscoelastic Properties,” Biorheology, 19(3), pp. 385–396.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, “Chapter 15: Modeling of Data,” in Numerical Recipies in C: The Art of Scientific Computing, Cambridge University Press, New York, NY, pp. 681–688.
Woo,  S. L.-Y., Peterson,  R. H., Ohland,  K. J., Sites,  T. J., and Danto,  M. I., 1990, “The Effects of Strain Rate on the Properties of the Medial Collateral Ligament in Skeletally Immature and Mature Rabbits: A Biomechanical and Histological Study,” J. Orthop. Res., 8(5), pp. 712–721.
Yin,  F. C., Chew,  P. H., and Zeger,  S. L., 1986, “An Approach to Quantification of Biaxial Tissue Stress-Strain Data,” J. Biomech., 19(1), pp. 27–37.
Dortmans,  L. J., Sauren,  A. A., and Rousseau,  E. P., 1984, “Parameter Estimation Using the Quasi-Linear Viscoelastic Model Proposed by Fung,” J. Biomech. Eng., 106(3), pp. 198–203.
Sauren,  A. A., and Rousseau,  E. P., 1983, “A Concise Sensitivity Analysis of the Quasi-Linear Viscoelastic Model Proposed by Fung,” J. Biomech. Eng., 105(1), pp. 92–95.
Lyon, R. M., Lin, H. C., Kwan, M. K., Hollis, J. M., Akeson, W. H., and Woo, S. L.-Y., 1988, “Stress Relaxation of the Anterior Cruciate Ligament (ACL) and the Patellar Tendon,” Proceedings, 34th Annual Meeting, Orthopaedic Research Society, Atlanta, GA, p. 81.


Grahic Jump Location
A typical residual plot demonstrating systematic deviations of the model and experimental data
Grahic Jump Location
A typical random error plot with distribution 0±0.00874 (mean±SD)
Grahic Jump Location
A typical curve fit using the strain history approach to experimental data (γ=0.15%/s during ramping)
Grahic Jump Location
The reduced relaxation function as determined using the instantaneous assumption approach and the strain history approach
Grahic Jump Location
Prediction of the peak stresses of a cyclic loading history based on the constants obtained from the stress relaxation experiment using the strain history approach for individual specimens (a) best prediction; (b) worst prediction




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In