Nonlinear model for viscoelastic behavior of achilles tendon

Journal of Biomechanical Engineering

Volumn 132, Issue 11, 2010, Pages

  Kahn, Cyril J F ^a   Wang, Xiong ^a,b   Rahouadj, Rachid ^a  

^a NANCY UNIVERSITÉ   (France)

^b Biopôle de l Université de Lorraine   (France)

Author keywords

Achilles tendon; Loading cycles; Mechanical properties; Relaxation; Relaxed stress; Tendon

Indexed keywords

ACHILLES TENDONS; COLLAGEN FIBER; ELEMENT VOLUME; EXPERIMENTAL DATA; LOADING CYCLES; MACROSCOPIC BEHAVIORS; MECHANICAL FORMULATION; NEW MODEL; NEW ZEALAND RABBITS; NON-LINEAR MODEL; PROTEOGLYCANS; RELAXATION; RELAXED STRESS; STRAIN LEVELS; THERMODYNAMIC EVOLUTION; VISCOELASTIC BEHAVIORS;

COLLAGEN; LOADING; MECHANICAL PROPERTIES; STRESS ANALYSIS; TENDONS; UNLOADING;

MECHANISMS;

COLLAGEN FIBER; COLLAGEN TYPE 1; COLLAGEN TYPE 3; PROTEOGLYCAN; WATER; COLLAGEN;

ACHILLES TENDON; ANIMAL EXPERIMENT; ARTICLE; BIOMECHANICS; CONTROLLED STUDY; MECHANICAL STRESS; MUSCLE RELAXATION; NONHUMAN; NONLINEAR SYSTEM; PROCESS MODEL; PROTEIN STRUCTURE; RABBIT; THERMODYNAMICS; VISCOELASTICITY; ALGORITHM; ANIMAL; BIOLOGICAL MODEL; BIOMEDICAL ENGINEERING; ELASTICITY; IN VITRO STUDY; PHYSIOLOGY; VISCOSITY; YOUNG MODULUS;

ORYCTOLAGUS CUNICULUS;

ACHILLES TENDON; ALGORITHMS; ANIMALS; BIOMECHANICS; BIOMEDICAL ENGINEERING; COLLAGEN; ELASTIC MODULUS; ELASTICITY; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; RABBITS; STRESS, MECHANICAL; THERMODYNAMICS; VISCOSITY;

EID: 77958469166     PISSN: 01480731     EISSN: 15288951     Source Type: Journal    
DOI: 10.1115/1.4002552     Document Type: Article

References (35)

1. Wang J.H.C. Mechanobiology of Tendon. J. Biomech. 2006, 39(9):1563-1582. JBMCB5, 0021-9290, 10.1016/j.jbiomech.2005.05.011
2. Woo S.L.Y. Abramowitch S.D. Kilger R.C. Liang R. Biomechanics of Knee Ligaments: Injury, Healing, and Repair. J. Biomech. 2006, 39(1):1-20. JBMCB5, 0021-9290, 10.1016/j.jbiomech.2004.10.025
3. Djian P. Bellier G. Christel P. Aspects Biologiques de la Reconstruction du Ligament Croisé Antérieur par une Greffe Tendineuse Autologue. Ann. Soc. fr. Arthroscopie 1999.
4. De Vita R. Slaughter W.S. A Structural Constitutive Model for the Strain Rate-Dependent Behavior of Anterior Cruciate Ligaments. Int. J. Solids Struct. 2006, 43(6):1561-1570. IJSOAD, 0020-7683, 10.1016/j.ijsolstr.2005.04.022
5. Peña E. Calvo B. Martinez M.A. Doblaré M. An Anisotropic Visco-Hyperelastic Model for Ligaments at Finite Strains. Formulation and Computational Aspects. Int. J. Solids Struct. 2007, 44(3-4):760-778. IJSOAD, 0020-7683, 10.1016/j.ijsolstr.2006.05.018
6. Pioletti D.P. Viscoelastic Properties of Soft Tissues: Application to Knee Ligaments and Tendons. 1997, Ph.D. thesis, EPFL, Lausanne, Switzerland.
7. Pioletti D.P. Rakotomanana L.R. Non-Linear Viscoelastic Laws for Soft Biological Tissues. Eur. J. Mech. A/Solids 2000, 19(5):749-759. EJASEV, 0997-7538, 10.1016/S0997-7538(00)00202-3
8. Fratzl P. Misof K. Zizak I. Rapp G. Amenitsch H. Bernstorff S. Fibrillar Structure and Mechanical Properties of Collagen. J. Struct. Biol. 1997, 122(1-2):119-122. JSBIEM, 1047-8477, 10.1006/jsbi.1998.3966
9. Fung Y.C. Biomechanics: Mechanical Properties of Living Tissues 1993, 2nd ed., Springer-Verlag, New York.
10. Magnenet V. Rahouadj R. Bacher P. Cunat C. Inelastic Constitutive Relations for Foamed Materials: A Statistical Approach and Its Application to Open-Cell Melamine. Mech. Mater. 2008, 40(9):673-684. MSMSD3, 0167-6636, 10.1016/j.mechmat.2008.03.003
11. Provenzano P. Lakes R. Keenan T. Vanderby Jr R. Nonlinear Ligament Viscoelasticity. Ann. Biomed. Eng. 2001, 29:908-914. ABMECF, 0090-6964, 10.1114/1.1408926
12. Ciarletta P. Dario P. Micera S. Pseudo-Hyperelastic Model of Tendon Hysteresis From Adaptative Recruitment of Collagen Type I Fibrils. Biomaterials 2008, 29:764-770. BIMADU, 0142-9612, 10.1016/j.biomaterials.2007.10.020
13. Lakes R.S. Vanderby Jr R. Interrelation of Creep and Relaxation: A Modeling Approach for Ligaments. J. Biomech. Eng. 1999, 121:612-615. JBENDY, 0148-0731, 10.1115/1.2800861
14. Arieby R. Caractérisation Mécanique et Modélisation Thermodynamique du Comportement Anisotrope du Polyéthylène à Haute Densité. Intégration des effets d'Endommagement. 2007, Ph.D. thesis, Nancy-Université, Nancy, France.
15. Mrabet K. Rahouadj R. Cunat C. An Irreversible Thermodynamic Model for Semicrystalline Polymers Submitted to Multisequence Loading at Large Strain. Polym. Eng. Sci. 2005, 45(1):42-51. PYESAZ, 0032-3888, 10.1002/pen.20228
16. Cunat C. Approche Statistique des Propriétés Thermodynamiques des Etats Liquides et Vitreux-Relaxation des Liquides et Transition Vitreuse-Influence des Associations Chimiques. 1985, Ph.D. thesis, University of Nancy 1, Nancy, France.
17. De Donder T. Thermodynamic Theory of Affinity: A Book of Principle 1936, Oxford University Press, Oxford, UK.
18. Cunat C. Thermodynamic Treatment of Relaxation in Frozen-In Systems-Universality of the Fluctuation Distribution Law for Relaxation Time. Z. Phys. Chem., Neue Folge 1998, 157:419-423. ZPCFAX, 0044-3336
19. Pioletti D.P. Rakotomanana L.R. Benvenuti J.F. Leyvraz P.F. Viscoelastic Constitutive Law in Large Deformations: Application to Human Knee Ligaments and Tendons. J. Biomech. 1998, 31(8):753-757. JBMCB5, 0021-9290, 10.1016/S0021-9290(98)00077-3
20. Woo S.L. Y. Gomez M.A. Akeson W.H. The Time and History-Dependent Viscoelastic Properties of the Canine Medial Collateral Ligaments. J. Biomech. Eng. 1981, 103:293-298. JBENDY, 0148-0731, 10.1115/1.3138295
21. Johnson G.A. Livesay G.A. Woo S.L. Y. Rajagopal K.R. A Single Integral Finite Strain Viscoelastic Model of Ligaments and Tendons. J. Biomech. Eng. 1996, 118(2):221-226. JBENDY, 0148-0731, 10.1115/1.2795963
22. Weiss J.A. Gardiner J.C. Computational Modeling of Ligament Mechanics. Biomed. Eng. (NY) 2001, 29(1):1-70. 0006-3398
23. Berisio R. Vitagliano L. Mazzarella L. Zagari A. Crystal Structure of a Collagen-Like Polypeptide With Repeating Sequence Pro-Hyp-Gly at 1.4 A Resolution: Implications for Collagen Hydratation. Biopolymers 2000, 56(1):8-13. BIPMAA, 0006-3525, 10.1002/1097-0282(2000)56:1<8::AID-BIP1037>3.0.CO;2-W
24. Kramer R.Z. Venugopal M.G. Bella J. Mayville P. Brodsky B. Berman H.M. Staggered Molecular Packing in Crystals of a Collagen-Like Peptide With a Single Charged Pair. J. Mol. Biol. 2000, 301(5):1191-1205. JMOBAK, 0022-2836, 10.1006/jmbi.2000.4017
25. Kramer R.Z. Bella J. Brodsky B. Berman H.M. The Crystal and Molecular Structure of a Collagen-Like Peptide With a Biologically Relevant Sequence. J. Mol. Biol. 2001, 311(1):131-147. JMOBAK, 0022-2836, 10.1006/jmbi.2001.4849
26. Sasaki N. Odajima S. Stress-Strain Curve and Young's Modulus of a Collagen Molecule as Determined by the X-Ray Diffraction Technique. J. Biomech. 1996, 29(5):655-658. JBMCB5, 0021-9290, 10.1016/0021-9290(95)00110-7
27. Vesentini S. Fitié C.F. C. Montevecchi F.M. Redaelli A. Molecular Assessment of the Elastic Properties of Collagen-Like Homotrimer Sequences. Biomech. Model. Mechanobiol. 2005, 3(4):224-234. BMMICD, 1617-7959, 10.1007/s10237-004-0064-5
28. Fessel G. Müller R. Snedeker J.G. Decorin Mediated Collagen Fibril Load Sharing in Tendon; Protein Level Models and Experiments. J. Biomech. 2008, 41:S314. JBMCB5, 0021-9290, 10.1016/S0021-9290(08)70313-0
29. Redaelli A. Vesentini S. Soncini M. Vena P. Mantero S. Montevecchi F.M. Possible Role of Decorin Glycosaminoglycans in Fibril Force Transmission in Relative Mature Tendons: A Computational Study From Molecular to Microstructural Level. J. Biomech. 2003, 36(10):1555-1569. JBMCB5, 0021-9290, 10.1016/S0021-9290(03)00133-7
30. Abramowitch S.D. Woo S.L. Y. An Improved Method to Analyze the Stress Relaxation of Ligaments Following a Finite Ramp Time Based on the Quasi-Linear Viscoelastic Theory. J. Biomech. Eng. 2004, 126(1):92-97. JBENDY, 0148-0731, 10.1115/1.1645528
31. Gentleman E. Livesay G.A. Dee K.C. Nauman E.A. Development of Ligament-Like Structural Organization and Properties in Cell-Seeded Collagen Scaffolds In Vitro. Ann. Biomed. Eng. 2006, 34(5):726-736. ABMECF, 0090-6964, 10.1007/s10439-005-9058-4
32. Cunat C. Lois constitutives de matériaux complexes stables ou vieillissants, Apport de la thermodynamique de la relaxation. Rev. Gen. Therm. 1996, 35(418-419):680-685. RGTHA7, 0035-3159
33. Cunat C. The DNLR Approach and Relaxation Phenomena. Part I: Historical Account and DNLR Formalism. Mech. Time-Depend. Mater. 2001, 5(1):39-65. MTDMFH, 1385-2000, 10.1023/A:1009899519935
34. El Alam H. Rahouadj R. Haboussi M. Cunat C. Extension du formalisme thermodynamique DNLR aux transformations finies. 2002, and Proc. Premier congrès interdisciplinaire sur les matériaux en France, Tours, France.
35. Onsager L. Reciprocal Relation in Irreversible Process. Phys. Rev. 1931, 38:2265-2279. PHRVAO, 0031-899X, 10.1103/PhysRev.38.2265