On modelling nonlinear viscoelastic effects in ligaments

Journal of Biomechanics

Volumn 41, Issue 12, 2008, Pages 2659-2666

  Pena E ^a,b   Pena J A ^c   Doblare M ^a,b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b BIOMATERIALES Y NANOMEDICINA CIBER BBN   (Spain)

^c UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

Anisotropy; Finite element analysis; Hyperelasticity; Large deformation; Ligaments; Nonlinear viscoelasticity

Indexed keywords

BIOMECHANICS; DEFORMATION; FIBERS; FOOD ADDITIVES; LIGAMENTS; MODEL STRUCTURES; STANDARDS; STRESS RELAXATION;

ADDITIVE DECOMPOSITION; ANISOTROPY; COLLAGEN FIBERS; EXPERIMENTAL DATA; FINITE DEFORMATIONS; FINITE ELEMENT ANALYSIS; FREE-ENERGY DENSITY; HYPERELASTICITY; KELVIN-VOIGT; LARGE DEFORMATION; MEDIAL COLLATERAL LIGAMENT; MODEL PARAMETERS; MULTI-AXIAL LOADINGS; NON-EQUILIBRIUM; NON-LINEAR BEHAVIORS; NONLINEAR STRESSES; NONLINEAR VISCOELASTIC; NONLINEAR VISCOELASTICITY; QUASI-LINEAR VISCOELASTICITY; STRAIN DEPENDENCIES; STRAIN-DEPENDENT; STRESS TENSORS; STRUCTURAL MODEL; VISCOELASTIC BEHAVIORS; VISCOUS MODELS;

STRAIN RATE;

ANISOTROPY; ARTICLE; BONE GRAFT; COMPUTER MODEL; LIGAMENT; PATELLA TENDON; PRIORITY JOURNAL; SIMULATION; VISCOELASTICITY;

COMPRESSIVE STRENGTH; COMPUTER SIMULATION; ELASTIC MODULUS; HUMANS; LIGAMENTS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; STRESS, MECHANICAL; TENSILE STRENGTH; VISCOSITY;

EID: 49449093111     PISSN: 00219290     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jbiomech.2008.06.019     Document Type: Article

References (50)

1. Beynnon B., Johnson R., Fleming B.C., Kannus P., Kaplan M., Samani J., and Renström P. Anterior cruciate ligament replacement: comparison of bone-patellar tendon-bone graft with two-strand hamstring grafts. Journal of Bone and Joint Surgery 84-A (2002) 1503-1513
2. Bonifasi-Lista C., Lake S.P., Small M.S., and Weiss J.A. Viscoelastic properties of the human medial collateral ligament under longitudinal, transverse and shear loading. Journal of Orthopaedic Research 23 (2005) 67-76
3. Calvo B., Peña E., Martínez M.A., and Doblaré M. An uncoupled directional damage model for fibered biological soft tissues. Formulation and computational aspects. International Journal of Numerical Methods in Engineering 69 (2006) 2036-2057
4. Carew T.E., Vaishnav R.N., and Patel D.J. Compressibility of the arterial wall. Circulation Research 23 (1968) 61-86
5. Drapaca C.S., Sivaloganathan S., and Tenti G. Nonlinear constitutive laws in viscoelasticity. Mathematics and Mechanics of Solids 12 (2007) 475-501
6. Fu F.H., Harner C., and Vince K.G. Knee Surgery (1994), Williams and Wilkins, Baltimore
7. Fung Y.C. Biomechanics. Mechanical Properties of Living Tissues (1993), Springer, Berlin
8. Grashow J.S., Yoganathan A.P., and Sacks M. Biaxial stress-stretch behavior of the mitral valve anterior leaflet at physiologic strain rates. Annals of Biomedical Engineering 34 (2006) 315-325
9. Haslach H.W. Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomechanics and Modeling in Mechanobiology 3 (2005) 172-189
10. Hayes W.C., and Mockros L.F. Viscoelastic constitutive relations for human articular cartilage. Journal of Applied Physiology 18 (1971) 562-568
11. Hibbit, Karlsson and Sorensen, Inc., 2006. Abaqus user's guide, v. 6.5. HKS inc. Pawtucket, RI, USA.
12. Hingorani R.V., Provenzano P.P., Lakes R.S., Escarcega A., and Vanderby Jr. R. Nonlinear viscoelasticity in rabbit medial collateral ligament. Annals of Biomedical Engineering 32 (2004) 306-312
13. Holzapfel G.A. Nonlinear Solid Mechanics (2000), Wiley, New York
14. Holzapfel G.A., Gasser T.C., and Ogden R.W. A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 61 (2000) 1-48
15. Holzapfel G.A., Gasser C.T., Sommer G., and Regitnig P. Determination of the layer-specific mechanical properties of human coronary arteries with non-atherosclerotic intimal thickening, and related constitutive modelling. American Journal of Physiology 289 (2005) H2048-H2058
16. Humphrey J.D. Mechanics of the arterial wall: review and directions. Critical Reviews in Biomedical Engineering 23 (1995) 1-162
17. Johnson G.A., Livesay G.A., Woo S.L.Y., and Rajagopal K.I.R. A single integral finite strain viscoelastic model of ligaments and tendons. ASME Journal of Biomechanical Engineering 118 (1996) 221-226
18. Kaliske M. A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains. Computational Methods in Applied Mechanical Engineering 185 (2000) 225-243
19. Kampen A.V., Wymenga A.B., vad der Heide H.J.L., and Bakens H.J.A.M. The effect of different graft tensioning in anterior cruciate ligament reconstruction: a prospective randomized study. Arthroscopy 14 (1998) 845-850
20. Marquardt D.W. An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal of Applied Mathematics 11 (1963) 431-441
21. Merodio J., and Goicolea J.M. On thermodynamically consistent constitutive equations for fiber-reinforced nonlinearly viscoelastic solids with application to biomechanics. Mechanics Research Communications 34 (2007) 561-571
22. Merodio J., and Rajagopal K.R. On constitutive equations for anisotropic nonlinearly viscoelastic solids. Mathematics and Mechanics of Solids 12 (2007) 131-147
23. Natali A.N., Pavan P.G., Carniel E.L., and Dorow C. Viscoelastic response of the periodontal ligament: an experimental-numerical analysis. Connective Tissue Research 45 (2004) 222-230
24. Natali A.N., Pavan P.G., Carniel E.L., Luisiano M.E., and Taglialavoro G. Anisotropic elasto-damage constitutive model for the biomechanical analysis of tendons. Medical Engineering and Physics 27 (2005) 209-214
25. Natali A.N., Carniel E.L., Pavan P.G., Sander F.G., Dorow C., and Geiger M. A visco-hyperelastic-damage constitutive model for the analysis of the biomechanical response of the periodontal ligament. ASME Journal of Biomechanical Engineering 130 (2008) 031004
26. Ning X., Zhu Q., Lanir Y., and Margulies S.S. A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. ASME Journal of Biomechanical Engineering 128 (2006) 925-933
27. Peña E., Martinez M.A., Calvo B., Palanca D., and Doblaré M. A finite element simulation of the effect of graft stiffness and graft tensioning in ACL reconstruction. Clinical Biomechanics 20 (2005) 636-644
28. Peña E., Calvo B., Martinez M.A., and Doblaré M. A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. Journal of Biomechanics 39 9 (2006) 1686-1701
29. Peña E., Calvo B., Martínez M.A., and Doblaré M. An anisotropic visco-hyperelastic model for ligaments at finite strains: formulation and computational aspects. International Journal of Solids and Structures 44 (2007) 760-778
30. Peña E., del Palomar A.P., Calvo B., Martínez M.A., and Doblaré M. Computational modelling of diarthrodial joints. Physiological, pathological and post-surgery simulations. Archives of Computational Methods in Engineering 14 1 (2007) 47-91
31. Peña E., Calvo B., Martínez M.A., and Doblaré M. On finite strain damage of viscoelastic fibred materials. Application to soft biological tissues. International Journal of Numerical Methods in Engineering 74 (2008) 1198-1218
32. Pinsky P.M., and Datye V. A microstructurally-based finite element model of the incised human cornea. Journal of Biomechanics 10 (1991) 907-922
33. Pioletti, D.P., 1997. Viscoelastic properties of soft tissues. Ph.D. Thesis, The University of Lausanne.
34. Pioletti D.P., Rakotomanana L., Benvenuti J.F., and Leyvraz P.F. Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons. Journal of Biomechanics 31 (1998) 753-757
35. Provenzano P.P., Lakes R.S., Corr D.T., and Vanderby R. Application of nonlinear viscoelastic models to describe ligament behavior. Biomechanics and Modeling in Mechanobiology 1 (2002) 45-47
36. Puso M.A., and Weiss J.A. Finite element implementation of anisotropic quasilinear viscoelasticity. ASME Journal of Biomechanical Engineering 120 (1998) 162-170
37. Puxkandl R., Zizak I., Paris O., Tesch W., Bernstorff S., Purslow P., and Fratzl1 P. Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Philosophical Transactions of the Royal Society of London Series B 357 (2002) 191-197
38. Quapp K.M., and Weiss J.A. Material characterization of human medial collateral ligament. ASME Journal of Biomechanical Engineering 120 (1998) 757-763
39. Sacks M. Biaxial mechanical evaluation of planar biological materials. Journal of Elasticity 61 (2000) 199-246
40. Sasaki N., and Odajima S. Stress-strain curve and Youngś modulus of a collagen molecule as determined by X-ray diffraction technique. Journal of Biomechanics 29 (1996) 655-658
41. Schapery R.A. On the characterization of nonlinear viscoelastic materials. Polymer Engineering Science 9 (1969) 295-310
42. Silver F.H., Snowhill P.B., and Foran D.J. Mechanical behavior of vessel wall: a comparative study of aorta, vena cava, and carotid artery. Annals of Biomedical Engineering 31 (2003) 793-803
43. Simo J.C. On a fully three-dimensional finite-strain viscoelastic damage model: formulation and computational aspects. Computational Methods in Applied Mechanical Engineering 60 (1987) 153-173
44. Simo J.C., and Hughes T.J.R. Computational Inelasticity (1998), Springer, New York
45. Simo J.C., and Taylor R.L. Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms. Computational Methods in Applied Mechanical Engineering 85 (1991) 273-310
46. Spencer A.J.M. Theory of invariants. Continuum Physics (1954), Academic Press, New York 239-253
47. Vena P., Gastaldi D., and Contro R. A constituent-based model for the nonlinear viscoelastic behavior of ligaments. ASME Journal of Biomechanical Engineering 128 (2006) 449-457
48. Vita R.D., and Slaughter W.S. A structural constitutive model for the strain rate-dependent behavior of anterior cruciate ligaments. International Journal of Solids and Structures 43 (2006) 1561-1570
49. Weiss J.A., Maker B.N., and Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Computational Methods in Applied Mechanical Engineering 135 (1996) 107-128
50. Woo S.L.Y., and Young E.P. Structure and function of tendons and ligaments. Basic Orthopeadics Biomechanics (1991), Raven Press, New York 199-244