A non-linear viscoelastic constitutive equation for soft biological tissues, based upon a structural model

Decraemer, W. F.<sup>1</sup>; Maes, M. A.<sup>1</sup>; Vanhuyse, V. J.<sup>1</sup>; Vanpeperstrafte, P.<sup>1</sup>

Affiliations

¹Laboratory for Experimental Physics, Rijksuniversitair Centrum Antwerpen, Groenenborserlaan, 171, B-2020 Antwerpen, Belgium

Abstract

A viscoelastic model based on the material structure of soft biological tissue is proposed and a corresponding non-linear viscoelastic constitutive equation is derived. It is shown how the relaxation spectrum H(τ) may be derived using only the fundamental Fourierterm of the stress corresponding with harmonic strain oscillation.

The numerical determination of the parameters of the model, based upon a maximum likelihood method applied to a bivariate normal distribution, is shortly discussed.

Links

DOI: 10.1016/0021-9290(80)90056-1

PubMed: 7400184

WoS: A1980KE42000003

History

Received: 1978-12-13

Revised: 1979-10-31

Cited Works (2)

Year	Entry
1980	Decraemer WF, Maes MA, Vanhuyse VJ. An elastic stress-strain relation for soft biological tissues based on a structural model. J Biomech. 1980;13(6):463-468.
1972	Fung Y-CB. Stress-strain-history relations of soft tissues in simple elongation. In: Fung YC, Perrone N, Anliker M, eds. Biomechanics: Its Foundations and Objectives. Symposium on Biomechanics, its Foundations and Objectives; July 29-31, 1970. Englewood Cliff, NJ: Inc., Prentice-Hall International; 1972:181-208.

Cited By (22)

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2000	Woo SL-Y, Debski RE, Zeminski J, Abramowitch SD, Chan Saw SS, Fenwick JA. Injury and repair of ligaments and tendons. Annu Rev Biomed Eng. 2000;2:83-118.
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.
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.
1990	Monleón Pradas M, Diaz Calleja R. Nonlinear viscoelastic behaviour of the flexor tendon of the human hand. J Biomech. 1990;23(8):773-781.
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.
2017	Nie B, Panzer MB, Mane A, Mait AR, Donlon J-P, Forman JL, Kent RW. Determination of the in situ mechanical behavior of ankle ligaments. J Mech Behav Biomed Mater. January 2017;65:502-512.
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.
2005	Chancey VC. Strength of the Human Neck: Understanding the Contributions of the Ligamentous and Muscular Spine in Tension and Bending [PhD thesis]. Duke University; 2005.
1997	Pioletti DP. Viscoelastic Properties of Soft Tissues Application to Knee Ligaments and Tendons [PhD thesis]. Swiss Federal Institute of Technology Lausanne; 1997.
1990	Belkoff SM. A Microstructural Model of Skin: An Evaluation of Maturing Rat Dermis [PhD thesis]. East Lansing, MI: Michigan State University; April 1990.
2007	Lavagnino M. The Mechanotransduction Response of Tendon Cells to Tensile Loading [PhD thesis]. East Lansing, MI: Michigan State University; 2007.
2005	De Vita R. Structural Constitutive Models for Knee Ligaments [PhD thesis]. Pittsburgh, PA: University of Pittsburgh; 2005.
2007	Hao H. Identification of the Effects of Axonal Coupling to the Glial Matrix on Axonal Kinematics [PhD thesis]. Rutgers University; October 2007.
1997	Wren TAL. Structure-Function Relationships for Soft Skeletal Connective Tissues [PhD thesis]. Stanford University; June 1997.
1988	Lam T. The Mechanical Properties of the Maturing Medial Collateral Ligament [PhD thesis]. Calgary, AB: University of Calgary; March 1988.
1999	Kukreti U. Structure-Function Relationship in Connective Tissues: A Study of Rabbit Medial Collateral Ligaments [PhD thesis]. Baltimore County, University of Maryland; 1999.
2010	Shahmirzadi D. Experimental Characterization of Vascular Tissue Viscoelasticity With Emphasis on Elastin's Role [PhD thesis]. University of Maryland; 2010.
1998	Derwin KA. A Quantitative Investigation of Structure-Function Relationships in a Tendon Fascicle Model [PhD thesis]. University of Michigan; 1998.
1998	Bain AC. In Vivo Mechanical Thresholds for Morphological and Functional Axonal Injury [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1998.
2008	Lucas SR. A Microstructural Viscoelastic Ligament Failure Model [PhD thesis]. Charlottesville, VA: University of Virginia; January 2008.