A constitutive equation for collagen fibers

Haut, Roger C.; Little, Robert W.

Year	Entry
2007	Cowin SC, Doty SB. Kinematics and mechanics of large deformations. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:507-557.
2007	Cowin SC, Doty SB. Tendon and ligament. In: Tissue Mechanics. Boca Raton, FL: Springer; 2007:559-594.
1990	Viidik A. Structure and function of normal and healing tendons and ligaments. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:3-38.
1990	Mow VC, Hou JS, Owens JM, Ratcliffe A. Biphasic and quasilinear viscoelastic theories for hydrated soft tissues. In: Mow VC, Ratcliffe A, Woo SL-Y, eds. Biomechanics of Diarthrodial Joints. Vol 1. New York, NY: Springer-Verlag; 1990:215-260.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
2005	Limbert G, Middleton J. An anisotropic viscous hyperelastic constitutive model of the posterior cruciate ligament suitable for high loading rate situations: theoretical framework and material identification. In: Gilchrist MD, ed. IUTAM Symposium on Impact Biomechanics: From Fundamental Insights to Applications. Dordrecht, The Netherlands: Springer; 2005:477-483. Solid Mechanics and Its Applications; vol 124.
1996	Bilston LE, Thibault LE. The mechanical properties of the human cervical spinal cord in vitro. Ann Biomed Eng. January–February 1996;24(1):67-74.
2001	Provenzano P, Lakes R, Keenan T, Vanderby R Jr. Nonlinear ligament viscoelasticity. Ann Biomed Eng. October 2001;29(10):908-914.
2011	Shen ZL, Kahn H, Ballarini R, Eppell SJ. Viscoelastic properties of isolated collagen fibrils. Biophys J. June 22, 2011;100(12):3008-3015.
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.
1974	Bargren JH, Bassett CAL, Gjelsvik A. Mechanical properties of hydrated cortical bone. J Biomech. May 1974;7(3):239-245.
1974	Lakes RS, Katz JL. Interrelationships among the viscoelastic functions for anisotropic solids: application to calcified tissues and related systems. J Biomech. May 1974;7(3):259-270.
1974	Jenkins RB, Little RW. A constitutive equation for parallel-fibered elastic tissue. J Biomech. September 1974;7(5):397-402.
1976	Kulak RF, Belytschko TB, Schultz AB, Galante JO. Nonlinear behavior of the human intervertebral disc under axial load. J Biomech. 1976;9(6):377-386.
1976	Comninou M, Yannas IV. Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibres. J Biomech. 1976;9(7):427-433.
1978	Dehoff P. On the nonlinear viscoelastic behavior of soft biological tissues. J Biomech. 1978;11(1-2):35-40.
1983	Lanir Y. Constitutive equations for fibrous connective tissues. J Biomech. 1983;16(1):1-12.
1983	Sauren AAHJ, van Hout MC, van Steenhoven AA, Veldpaus FE, Janssen JD. The mechanical properties of porcine aortic valve tissues. J Biomech. 1983;16(5):327-337.
1984	Butler DL, Grood ES, Noyes FR, Zernicke RF, Brackett K. Effects of structure and strain measurement technique on the material properties of young human tendons and fascia. J Biomech. 1984;17(8):579-596.
1986	Shirazi-Adl A, Ahmed AM, Shrivastava S. A finite element study of a lumbar motion segment subjected to pure sagittal plane moments. J Biomech. 1986;19(4):331-350.
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.
1998	Pioletti DP., Rakotomanana LR, Benvenuti J-F, Leyvraz P-F. Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. J Biomech. August 1998;31(8):753-757.
1999	Liao H, Belkof SM. A failure model for ligaments. J Biomech. 1999;32(2):183-188.
2004	Wilson W, van Donkelaar CC, van Rietbergen B, Ito K, Huiskes R. Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J Biomech. March 2004;37(3):357-366.
1979	Bingham DN, DeHoff PH. A constitutive equation for the canine anterior cruciate ligament. J Biomech Eng. February 1979;101(1):15-22.
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.
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.
1983	Sauren AAHJ, Rousseau EPM. A concise sensitivity analysis of the quasi-linear viscoelastic model proposed by Fung. J Biomech Eng. February 1983;105(1):92-95.
1983	Haut RC. Age-dependent influence of strain rate on the tensile failure of rat-tail tendon. J Biomech Eng. August 1983;105(3):296-299.
1984	Dortmans LJMG, Sauren AAHJ, Rousseau EPM. Parameter estimation using the quasi-linear viscoelastic model proposed by Fung. J Biomech Eng. August 1984;106(3):198-203.
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.
1987	Ueno K, Liu YK. A three-dimenstional nonlinear finite element model of lumbar intervertebral joint in torsion. J Biomech Eng. August 1987;109(3):200-209.
1988	Shrive NG, Lam TC, Damson E, Frank CB. A new method of measuring the cross-sectional area of connective tissue structures. J Biomech Eng. May 1988;110(2):104-109.
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.
1999	Soulhat J, Buschmann MD, Shirazi-Adl A. A fibril-network-reinforced biphasic model of cartilage in unconfined compression. J Biomech Eng. June 1999;121(3):340-347.
2002	Roeder BA, Kokini K, Sturgis JE, Robinson JP, Voytik-Harbin SL. Tensile mechanical properties of three-dimensional type I collagen extracellular matrices with varied microstructure. J Biomech Eng. April 2002;124(2):214-222.
1997	Thornton GM, Oliynyk A, Frank CB, Shrive NG. Ligament creep cannot be predicted from stress relaxation at low stress: a biomechanical study of the rabbit medial collateral ligament. J Orthop Res. 1997;15(5):652-656.
1984	Shirazi-Adl SA, Shrivastava SC, Ahmed A. Stress analysis of the lumbar disc-body unit in compression: a three-dimensional nonlinear finite element study. Spine. March 1984;9(2):120-134.
1986	Shirazi-Adl A, Ahmed AM, Shrivastava SC. Mechanical response of a lumbar motion segment in axial torque alone and combined with compression. Spine. November 1986;11(9):914-927.
1995	Sharma M, Langrana NA, Rodriguez J. Role of ligaments and facets in lumbar spinal stability. Spine. April 15, 1995;20(8):887-900.
1995	Esteki A. Dynamic Model of the Hand With Application in Functional Neuromuscular Stimulation [PhD thesis]. Cleveland, OH: Case Western Reserve University; August 1995.
2010	Shen ZL. Tensile Mechanical Properties of Isolated Collagen Fibrils Obtained by Microelectromechanical Systems Technology [PhD thesis]. Cleveland, OH: Case Western Reserve University; August 2010.
1997	Pioletti DP. Viscoelastic Properties of Soft Tissues Application to Knee Ligaments and Tendons [PhD thesis]. Swiss Federal Institute of Technology Lausanne; 1997.
2017	Christou A. Modelling Spinal Injury Due to High-Rate Axial Loading [PhD thesis]. Imperial College London; June 2017.
2022	Draper D. Validation of Human Body Model Lumbar Spine Performance for Use in New Seating Positions [PhD thesis]. Ludwig Maximilian University of Munich; 2022.
1986	Pintar FA. The Biomechanics of Spinal Elements [PhD thesis]. Marquette University; December 1986.
1973	Jenkins RB. A Constitutive Equation for Parallel-Fibered Elastic Tissue [PhD thesis]. East Lansing, MI: Michigan State University; 1973.
1976	Butler DL. A Constitutive Equation for Mammalian Skeletal Muscle Tissue in the Passive and Fully Stimulated States [PhD thesis]. East Lansing, MI: Michigan State University; 1976.
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.
1997	Soulhat J. Développement et analyse d'un modèle poroélastique et composite du cartilage [Master's thesis]. École polytechnique de Montréal; June 1997.
2008	Shirazi Aghjari R. Computational Biomechanics of the Human Knee Joint: Role of Collagen Fibrils Networks [PhD thesis]. École polytechnique de Montréal; December 2008.
1998	Carey JPR. The Compressive Characteristics of the Glenoid Labrum [Master's thesis]. Queen's University; January 1998.
2008	Natoli RM. Impact Loading and Functional Tissue Engineering of Articular Cartilage [PhD thesis]. Houston, TX: Rice University; October 2008.
2011	Responte DJ. Novel Exogenous Agents for Improving Articular Cartilage Tissue Engineering [PhD thesis]. Houston, TX: Rice University; October 2011.
1992	Schutte LM. Using Musculoskeletal Models to Explore Strategies for Improving Performance in Electrical Stimulation-Induced Leg Cycle Ergometry [PhD thesis]. Stanford University; 1992.
1980	Wismans JSHM. A Three-Dimensional Mathematical Model of the Human Knee Joint [PhD thesis]. Eindhoven University of Technology; 1980.
1988	Lam T. The Mechanical Properties of the Maturing Medial Collateral Ligament [PhD thesis]. Calgary, AB: University of Calgary; March 1988.
1988	Kim YE. An Analytical Investigation of Ligamentous Lumbar Spine Mechanics University of Iowa; May 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.
1997	Richards M. Strain Environment Effects on New Bone Formation and Precursor Tissue Differentiation During Distraction [PhD thesis]. University of Michigan; 1997.
1998	Derwin KA. A Quantitative Investigation of Structure-Function Relationships in a Tendon Fascicle Model [PhD thesis]. University of Michigan; 1998.
2012	Chiravarambath SS. Finite Element Modeling of Articular Cartilage At Different Length Scales [PhD thesis]. University of Minnesota; April 2012.
1994	Bilston LE. The Biomechanics of the Spinal Cord During Traumatic Spinal Cord Injury [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1994.
1999	Ledoux WR II. A Biomechanical Model of the Human Foot With Emphasis on the Plantar Soft Tissue [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1999.
2009	Lake SP. Anisotropic, Inhomogeneous and Nonlinear Structure-Function of Human Supraspinatus Tendon [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2009.
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	Lee JB. Development of a Finite Element Model of the Human Abdomen [PhD thesis]. Detroit, MI: Wayne State University; 2002.
2003	Provenzano PP. Damage and Disuse in Collagenous Extracellular Matrices: Biological Responses and Mechanical Consequences [PhD thesis]. University of Wisconsin – Madison; 2003.

Year	Entry
1967	Abrahams M. Mechanical behaviour of tendon in vitro: a preliminary report. Med Biol Eng. September 1967;5(5):433-443.
1936	Cronkite AE. The tensile strength of human tendons. Anat Rec. January 1936;64(2):173-186.
1959	Rigby BJ, Hirai N, Spikes JD, Eyring H. The mechanical properties of rat tail tendon. J Gen Physiol. November 1959;43(2):265-283.
1969	Haut RC, Little RW. Rheological properties of canine anterior cruciate ligaments. J Biomech. 1969;2(3):289-298.