Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues

Biomechanics and Modeling in Mechanobiology

Volumn 4, Issue 2-3, 2005, Pages 190-199

  Sun, Wei ^a   Sacks, Michael S ^a  

^a MCGOWAN INSTITUTE FOR REGENERATIVE MEDICINE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMATERIALS; FINITE ELEMENT METHOD; MATRIX ALGEBRA; REGRESSION ANALYSIS; STIFFNESS;

FUNG-ELASTIC MODEL; PLANAR SOFT TISSUES; TISSUE-DERIVED BIOMATERIALS;

TISSUE;

FIBRILLAR COLLAGEN;

ANISOTROPY; ARTICLE; BIOLOGICAL MODEL; CHEMISTRY; COMPUTER PROGRAM; CONNECTIVE TISSUE; ELASTICITY; FINITE ELEMENT ANALYSIS; MECHANICAL STRESS; PHYSIOLOGY; REGRESSION ANALYSIS; SHEAR STRENGTH;

ANISOTROPY; CONNECTIVE TISSUE; ELASTICITY; FIBRILLAR COLLAGENS; FINITE ELEMENT ANALYSIS; MODELS, BIOLOGICAL; REGRESSION ANALYSIS; SHEAR STRENGTH; SOFTWARE; STRESS, MECHANICAL;

EID: 30344473313     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-005-0075-x     Document Type: Article

References (38)

1. Billiar KL, Sacks MS (2000) Biaxial mechanical properties of the native and glutaraldehyde-treated aortic valve cusp: Part II-A structural constitutive model. J Biomech Eng 122(4):327-335
2. Chew PH, Yin FC, Zeger SL (1986) Biaxial stress-strain properties of canine pericardium. J Mol Cell Cardiol 18(6):567-578
3. Criscione JC, Humphrey JD, Douglas AD, Hunter WC (2000) An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. J Mech Phys Solids 48:2445-2465
4. Criscione JC, Sacks MS, Hunter WC (2003a) Experimentally tractable, pseudo-elastic constitutive law for biomembranes: I. Theory. J Biomech Eng 125(1):94-99
5. Criscione JC, Sacks MS, Hunter WC (2003b) Experimentally tractable, pseudo-elastic constitutive law for biomembranes: II. Application. J Biomech Eng 125(1):100-105
6. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York
7. Fung Y, Tong P (eds) (2001) Classical and computational solid mechanics. Advanced series in engineering science. World Scientific Publishing
8. Gardiner JC, Weiss JA (2001) Simple shear testing of parallel-fibered planar soft tissues. J Biomech Eng 123(2):170-175
9. Hildebrand F (1980) Advanced calculus for applications
10. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, Chichester New York
11. Holzapfel GA, Gasser TC (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity 61:1-48
12. Holzapfel GA, Eberlein R, Wriggers P, Weizascker HW (1996) Large strain analysis of soft biological membranes: formulatin and finite element analysis. Comput Methods Appl Mech Eng 132:45-61
13. Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues, and organs. Springer, New York
14. Humphrey JD, Na S (2002) Elastodynamics and arterial wall stress. Ann Biomed Eng 30(4):509-523
15. Humphrey JD, Vawter DL, Vito RP (1987) Pseudoelasticity of excised visceral pleura. J Biomech Eng 109:115-120
16. Humphrey JD, Strumpf RK, Yin FC (1990a) Determination of a constitutive relation for passive myocardium: I. A new functional form. J Biomech Eng 112(3):333-339
17. Humphrey JD, Strumpf RK, Yin FC (1990b) Determination of a constitutive relation for passive myocardium: II. Parameter estimation. J Biomech Eng 112(3):340-346
18. Humphrey JD, Strumpf RK, Yin FCP (1992) A constitutive theory for biomembranes: application to epicardial mechanics. J Biomech Eng 114:461-466
19. Kyriacou SK, Shah AD, Humphrey JD (1997) Inverse finite element characterization of nonlinear hyperelastic membranes. J Appl Mech 64(June):257-262
20. Lanir Y (1994) Plausibility of structural constitutive equations for isotropic soft tissues in finite static deformations. J Appl Mech 61:695-702
21. Lanir Y (1996) Plausibility of structural constitutive equations for swelling tissues - implications of the C-N and S-E conditions. J Biomech Eng 118:10-16
22. Lanir Y, Lichtenstein O, Imanuel O (1996) Optimal design of biaxial tests for structural material characterization of flat tissues. J Biomech Eng 118:41-47
23. Marsden JE, Hughes TJR (1983) Mathematical foundations of elasticity. Dover, Don Mills
24. Nielsen PMF, Hunter PJ, Smaill BH (1991) Biaxial testing of membrane biomaterials: testing equipment and procedures. J Biomech Eng 113:295-300
25. Ogden RW (1997) Non-linear elastic deformations. Dover, Toronto
26. Ogden R (2003) Nonlinear elasticity, anisotropy, material stability, and residual stresses in soft tissue. In: Ogden R (ed) Biomechanics of soft tissue in cardiovascular system. Springer, New York
27. Sacks MS (1999) A method for planar biaxial mechanical testing that includes in-plane shear. J Biomech Eng 121(5):551-555
28. Sacks MS (2000) Biaxial mechanical evaluation of planar biological materials. J Elasticity 61:199-246
29. Sacks MS (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng 125(2):280-287
30. Sacks MS, Chuong CJ (1998) Orthotropic mechanical properties of chemically treated bovine pericardium. Ann Biomed Eng 26(5):892-902
31. Sacks MS, Sun W (2003) Multiaxial mechanical behavior of biological materials. Annu Rev Biomed Eng
32. Schroder J, Neff P (2003) Aspects of formulation of hyperelastic soft tissues with polyconvex anisotropic strain energies. Second MIT conference on computational fluid and solid mechanics. MIT, Cambridge MA
33. Sun W, Sacks MS, Sellaro TL, Slaughter WS, Scott MJ (2003) Biaxial mechanical response of bioprosthetic heart valve biomaterials to high in-plane shear. J Biomech Eng 125:372-380
34. Sun W, Scott MJ, Sacks MS (2005) Effects of boundary conditions on the planar biaxial mechanical properties of soft tissues. ASME J Biomech Eng (in press)
35. Tong P, Fung YC (1976) The stress-strain relationship for the skin. J Biomech 9(10):649-657
36. Truesdell C, Noll W (1965) The Nonlinear Field Theories. Handbuch der Physik. S Flugge. Springer, Berlin, pp 119-126
37. Weiss JA, Maker BN, Govindjee S (1996) Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput Methods Biomech Biomed Eng 135:107-128
38. Wilber JP, Walton JR (2002) The convexity properties of a class of constitutive models for biological soft tissues. Math Mech Solids 7:217-236