Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibres

Comninou, Maria; Yannas, I. V.

Affiliations

¹Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139. U.S.A.. and Fibers and Polymers Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A

²Department of Applied Mechanics and Engineering Science, University of Michigan, Ann Arbor

Abstract

Collagen fibers in connective tissues have a periodic, “crimped” shape. In this work, they are modelled as long, sinusoidal beams. Constitutive equations in uniaxial tension are obtained by geometric considerations for a single collagen fiber as well as for bundles of fibers embedded in a matrix. The effect of fiber orientation is briefly discussed.

Links

DOI: 10.1016/0021-9290(76)90084-1

PubMed: 939764

WoS: A1976BY24500001

History

Received: 1976-02-10

Cited Works (4)

Year	Entry
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Cited By (27)

Year	Entry
2003	Elliott DM, Robinson PS, Gimbel JA, Sarver JJ, Abboud JA, Iozzo RV, Soslowsky LJ. Effect of altered matrix proteins on quasilinear viscoelastic properties in transgenic mouse tail tendons. Ann Biomed Eng. May 2003;31(5):599-605.
2001	Weiss JA, Gardiner JC. Computational modeling of ligament mechanics. Crit Rev Biomed Eng. 2001;29(3):303-371.
1980	Kastelic J, Palley I, Baer E. A structural mechanical model for tendon crimping. J Biomech. 1980;13(10):887-893.
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.
1980	Dorlot J-M, Ait Ba Sidi M, Tremblay GM, Drouin G. Load elongation behavior of the canine anterior cruciate ligament. J Biomech Eng. August 1980;102(3):190-193.
1980	Lanir Y. A microstructure model for the rheology of mammalian tendon. J Biomech Eng. November 1980;102(4):332-339.
1985	Stouffer DC, Butler DL, Hosny D. The relationship between crimp pattern and mechanical response of human patellar tendon-bone units. J Biomech Eng. May 1985;107(2):158-165.
1992	Ault HK, Hoffman AH. A composite micromechanical model for connective tissues, I: theory. J Biomech Eng. February 1992;114(1):137-141.
1993	Woo SL-Y, Johnson GA, Smith BA. Mathematical modeling of ligaments and tendons. J Biomech Eng. November 1993;115(4B):468-473.
1997	Hurschler C, Loitz-Ramage B, Vanderby R Jr. A structurally based stress-stretch relationship for tendon and ligament. J Biomech Eng. November 1997;119(4):392-399.
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.
2016	Yoshida K. Characterizing the Structure-Function Relationships of the Mouse Cervix in Pregnancy: Towards the Development of a Hormone-Mediated Material Model for Cervical Remodeling [PhD thesis]. Columbia University; 2016.
2019	Groetsch A. Micro- and Nanomechanics of Mineralised Collagen Fibre Elasto-Plasticity [PhD thesis]. Ebinburgh, Scotland: Heriot-Watt University; November 2019.
2021	Notermans T. Computational Modeling of Mechanobiology in Intact and Healing Rat Achilles Tendon [PhD thesis]. Lund, Sweden: Lund University; June 18, 2021.
2016	Shiovitz DA. Scarless Tendon Healing in MRL/MpJ Mice Suggests Tissue-Driven Mechanisms of Regeneration [PhD thesis]. Icahn School of Medicine at Mount Sinai; 2016.
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.
1980	Wismans JSHM. A Three-Dimensional Mathematical Model of the Human Knee Joint [PhD thesis]. Eindhoven University of Technology; 1980.
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.
2005	Gimbel JA. The Role of Tension on Supraspinatus Tendon to Bone Healing in a Newly Developed Animal Model of Chronic Rotator Cuff Tears [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2005.
1994	Weiss JA. A Constitutive Model and Finite Element Representation for Transversely Isotropic Soft Tissues [PhD thesis]. Salt Lake City, UT: University of Utah; December 1994.
2002	Gardiner JC. Computational Modeling of Ligament Mechanics [PhD thesis]. University of Utah; May 2002.
1997	Hurschler C. Collagen Matrix in Normal and Healing Ligaments: Microstructural Behavior, Biological Adaptation, and a Structural Mechanical Model [PhD thesis]. University of Wisconsin – Madison; 1997.
1997	Rapoff AJ. Tensile Fatigue of Intervertebral Disc Annulus and a Probabilistic Rule of Mixtures for Elastic Moduli [PhD thesis]. University of Wisconsin – Madison; August 1997.