A constitutive model for fibrous tissues considering collagen fiber crimp

International Journal of Non-Linear Mechanics

Volumn 42, Issue 2, 2007, Pages 391-402

  Cacho, F ^a,b   Elbischger, P J ^c   Rodriguez J F ^b   Doblare M ^b   Holzapfel, G A ^a,d  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF ZARAGOZA   (Spain)

^c CARINTHIA UNIVERSITY OF APPLIED SCIENCES   (Austria)

^d ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Collagen fiber; Constitutive model; Fiber crimp; Micromechanics; Statistical distribution

Indexed keywords

COLLAGEN; IMAGE ANALYSIS; MATHEMATICAL MODELS; MORPHOLOGY; RANDOM PROCESSES; TISSUE;

COLLAGEN FIBERS; CONSTITUTIVE MODEL; FIBER CRIMP; STATISTICAL DISTRIBUTION;

MICROMECHANICS;

EID: 34247485262     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2007.02.002     Document Type: Article

References (42)

1. Sasaki N., and Odajima S. Stress-strain curve and Young's modulus of a collagen molecule as determined by the X-ray diffraction technique. J. Biomech. 29 (1996) 655-658
2. Vesentini S., Fitie C.F., Montevecchi F.M., and Redaelli A. Molecular assessment of the elastic properties of collagen-like homotrimer sequences. Biomech. Model. Mechanobiol. 3 (2005) 224-234
3. Kato Y.P., Christiansen D.L., Hahn R.A., Shieh S.J., Goldstein J.D., and Silver F.H. Mechanical properties of collagen fibres: a comparison of reconstituted and rat tail tendon fibres. Biomaterials 10 (1989) 38-42
4. An K.N., Sun Y.L., and Luo Z.P. Flexibility of type I collagen and mechanical property of connective tissue. Biorheology 41 (2004) 239-246
5. Schulze-Bauer C.A.J., Regitnig P., and Holzapfel G.A. Mechanics of the human femoral adventitia including high-pressure response. Am. J. Physiol. Heart Circ. Physiol. 282 (2002) H2427-H2440
6. Schulze-Bauer C.A.J., Mörth C., and Holzapfel G.A. Passive biaxial mechanical response of aged human iliac arteries. J. Biomech. Eng. 125 (2003) 395-406
7. Holzapfel G.A., Sommer G., Gasser C.T., and Regitnig P. Determination of the layer-specific mechanical properties of human coronary arteries with non-atherosclerotic intimal thickening, and related constitutive modelling. Am. J. Physiol. Heart Circ. Physiol. 289 (2005) H2048-H2058
8. G. Sommer, T.C. Gasser, P. Regitnig, M. Auer, G.A. Holzapfel, Dissection of the human aortic media: an experimental study, J. Biomech. Eng., 2007, in press.
9. Kratky O., and Porod G. Röntgenuntersuchung gelöster Fadenmoleküle. Recl. Trav. Chim. Pays-Bas. 68 (1949) 1106-1123
10. Marko J.F., and Siggia E.D. Stretching DNA. Macromolecules 28 (1995) 8759-8770
11. Bustamante C., Marko J.F., Siggia E.D., and Smith St.B. Entropic elasticity of λ-phage DNA. Science 265 (1994) 1599-1600
12. Adkins J.E., and Rivlin R.S. Large elastic deformations of isotropic materials X. Reinforcement by inextensible cords. Philos. Trans. R. Soc. A 248 (1955) 201-223
13. A.J.M. Spencer, Constitutive theory for strongly anisotropic solids, in: A.J.M. Spencer (Ed.), Continuum Theory of the Mechanics of Fibre-Reinforced Composites, CISM Courses and Lectures, vol. 282, International Centre for Mechanical Sciences, Springer, Wien, 1984, pp. 1-32.
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. J. Elasticity 61 (2000) 1-48
15. In: Holzapfel G.A., and Ogden R.W. (Eds). Biomechanics of Soft Tissue in Cardiovascular Systems (2003), Springer, Wien, New York
16. In: Holzapfel G.A., and Ogden R.W. (Eds). Mechanics of Biological Tissue (2006), Springer, Heidelberg
17. Holzapfel G.A. Nonlinear Solid Mechanics, A Continuum Approach for Engineering (2000), Wiley, Chichester
18. Horgan C.O., and Saccomandi G. A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomech. Model. Mechanobiol. 1 (2003) 251-266
19. Lanir Y. A structural theory for the homogeneous biaxial stress-strain relationships in flat collagenous tissues. J. Biomech. 12 (1979) 423-436
20. Lanir Y. Constitutive equations for fibrous connective tissues. J. Biomech. 16 (1983) 1-12
21. Zulliger M.A., Fridez P., Hayashi K., and Stergiopulos N. A strain energy function for arteries accounting for wall composition and structure. J. Biomech. 37 (2004) 989-1000
22. Wuyts F.L., Vanhuyse V.J., Langewouters G.J., Decraemer W.F., Raman E.R., and Buyle S. Elastic properties of human aortas in relation to age and atherosclerosis: a structural model. Phys. Med. Biol. 40 (1995) 1577-1597
23. Hurschler C., Loitz-Ramage B., and Vanderby Jr. R. A structurally based stress-stretch relationship for tendon and ligament. J. Biomech. Eng. 119 (1997) 392-399
24. Freed A.D., and Doehring T.C. Elastic model for crimped collagen fibrils. J. Biomech. Eng. 127 (2005) 587-593
25. Freed A.D., Einstein D.R., and Vesely I. Invariant formulation for dispersed transverse isotropy in aortic heart valves: an efficient means for modeling fiber splay. Biomech. Model. Mechanobiol. 4 (2005) 100-117
26. F. Cacho, Constitutive models for fiber-reinforced soft biological tissues, Ph.D. Thesis, University of Zaragoza, Spain, 2006.
27. Gasser T.C., Ogden R.W., and Holzapfel G.A. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3 (2006) 15-35
28. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, vol. 55, New York, 1972.
29. Trotter J.A., Thurmond F.A., and Koob T.J. Molecular structure and functional morphology of echinoderm collagen fibrils. Conn. Tiss. Res. 275 (1994) 451-458
30. P.J. Elbischger, Computer vision methods for the automatic analysis of fibrous structures in biological soft tissues, Ph.D. Thesis, Graz University of Technology, 2005.
31. Sasaki N., and Odajima S. Elongation mechanism of collagen fibrils and force-strain relations of tendon at each level of the structural hierarchy. J. Biomech. 29 (1996) 1131-1136
32. Holzapfel G.A., and Weizsäcker H.W. Biomechanical behavior of the arterial wall and its numerical characterization. Comput. Biol. Med. 28 (1998) 377-392
33. R.W. Ogden, G. Saccomandi, Introducing mesoscopic information into constitutive equations for arterial walls, Biomech. Model. Mechanobiol. 2007, DOI 10.1007/s10237-006-0064-8.
34. J.J. Filliben, A. Heckert, NIST/SEMATECH e-Handbook of Statistical Methods, Chapter 1: Exploratory Data Analysis, 2006. 〈http://www.itl.nist.gov/div898/handbook/index.htm〉.
35. Lake L.W., and Armeniades C.D. Structure-property relations of aortic tissue. Trans. Am. Soc. Artif. Intern. Organs 18 (1972) 202-209
36. Rodríguez J.F., Cacho F., Bea J.A., and Doblaré M. A stochastic-structurally based three dimensional finite-strain damage model for fibrous soft tissue. J. Mech. Phys. Solids 54 (2006) 864-886
37. M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, F. Rossi. GNU Scientific Library Reference Manual-Revised Second Edition (v1.8). Network Theory Ltd., 2006.
38. Decraemer W.F., Maes M.A., and Vanhuyse V.J. An elastic stress-strain relation for soft biological tissues based on a structural model. J. Biomech. 13 (1980) 463-468
39. Decraemer W.F., Maes M.A., Vanhuyse V.J., and Vanpeperstraete P. A non-linear viscoelastic constitutive equation for soft biological tissues, based upon a structural model. J. Biomech. 13 (1980) 559-564
40. Bischoff J.E., Arruda E.M., and Grosh K. Orthotropic hyperelasticity in terms of an arbitrary molecular chain model. J. Appl. Mech. 69 (2002) 198-201
41. Bischoff J.E., Arruda E.M., and Grosh K. A microstructurally based orthotropic hyperelastic constitutive law. J. Appl. Mech. 69 (2002) 570-579
42. Kuhl E., Garikipati K., Arruda E.M., and Grosh K. Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. J. Mech. Phys. Solids 53 (2005) 1552-1573