A constitutive equation for the canine anterior cruciate ligament

Bingham, D. N.<sup>1,2</sup>; DeHoff, P. H.<sup>3,4</sup>

Affiliations

¹Division of Interdisciplinary Studies, Clemson University, Clemson, S.C. 29631

²Present address: Mechanical Engineering Department, Union College, Schenectady, N.Y. 12308

³Mechanical Engineering Department, Bucknell University, Lewisburg, Pa. 17837

⁴Present address: ESM Department, University of North Carolina at Charlotte, UNCC Station, Charlotte, N.C. 28228

Abstract

A simplified constitutive equation is proposed to characterize the nonlinear viscoelastic behavior of the canine anterior cruciate ligament. The theory contains a single relaxation function which was measured experimentally by a series of uniaxial relaxation tests. To test the applicability of the theory, the experimentally determined function was used to attempt to predict the results of a special log-ramp test, as well as a constant strain-rate test. It was found that the simplified equation predicted stress results which were somewhat higher than experiment throughout much of the strain range tested.

Links

DOI: 10.1115/1.3426217

WoS: A1979GL81900002

History

Received: 1978-07-25

Cited Works (10)

Year	Entry
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1973	Wang C-J, Walker PS, Wolf B. The effects of flexion and rotation on the length patterns of the ligaments of the knee. J Biomech. November 1973;6(6):587-596.
1972	Haut RC, Little RW. A constitutive equation for collagen fibers. J Biomech. September 1972;5(5):423-430.
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1967	Fung YCB. Elasticity of soft tissues in simple elongation. Am J Physiol. December 1967;213(6):1532-1544.

Cited By (10)

Year	Entry
2002	Provenzano PP, Lakes RS, Corr DT, Vanderby R. Application of nonlinear viscoelastic models to describe ligament behavior. Biomech Model Mechanobiol. June 2002;1(1):45-57.
1982	Woo SL-Y. Mechanical properties of tendons and ligaments, I: quasi-static and nonlinear viscoelastic properties. Biorheology. 1982;19(3):385-396.
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
1983	Lanir Y. Constitutive equations for fibrous connective tissues. J Biomech. 1983;16(1):1-12.
1993	Kwan MK, Lin TH-C, Woo SL-Y. On the viscoelastic properties of the anteromedial bundle of the anterior cruciate ligament. J Biomech. April–May 1993;26(4-5):447-452.
1981	Woo SL-Y, Gomez MA, Akeson WH. The time and history-dependent viscoelastic properties of the canine medical collateral ligament. J Biomech Eng. November 1981;103(4):293-298.
1993	Woo SL-Y, Johnson GA, Smith BA. Mathematical modeling of ligaments and tendons. J Biomech Eng. November 1993;115(4B):468-473.
1996	Johnson GA, Livesay GA, Woo SL-Y, Rajagopal KR. A single integral finite strain viscoelastic model of ligaments and tendons. J Biomech Eng. May 1996;118(2):221-226.
2005	Weiss JA, Gardiner JC, Ellis BJ, Lujan TJ, Phatak NS. Three-dimensional finite element modeling of ligaments: technical aspects. Med Eng Phys. December 2005;27(10):845-861.
1997	Richards M. Strain Environment Effects on New Bone Formation and Precursor Tissue Differentiation During Distraction [PhD thesis]. University of Michigan; 1997.