At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials

Computational Mechanics

Volumn 52, Issue 4, 2013, Pages 959-969

  Destrade, M ^a,b   Donald, B Mac ^c   Murphy, J G ^a,c   Saccomandi, G ^d  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b UNIVERSITY COLLEGE DUBLIN   (Ireland)

^c DUBLIN CITY UNIVERSITY   (Ireland)

^d UNIVERSITY OF PERUGIA   (Italy)

Author keywords

Biomechanics; Constitutive laws; Finite element

Indexed keywords

BIOMECHANICS; DEFORMATION; FINITE ELEMENT METHOD; NUMERICAL MODELS; STRAIN ENERGY;

ANISOTROPIC INVARIANTS; CONSTITUTIVE LAW; MATERIAL CHARACTERISATION; MODERATE DEFORMATIONS; STRAIN ENERGY FUNCTIONS; TRANSVERSELY ISOTROPIC; TRANSVERSELY ISOTROPIC MATERIALS; VERTICAL DISPLACEMENTS;

TESTING;

EID: 84885295547     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-013-0857-4     Document Type: Article

References (32)

1. Rivlin RS (1997). In: Barenblatt GI, Joseph DD (eds) Collected papers of R.S. Rivlin, vol 1. Springer, New York
2. Spencer AJM (1972) Deformations of fibre-reinforced materials. Oxford University Press, Oxford
3. Pagano NJ, Halpin JC (1968) Influence of end constraint in the testing of anisotropic bodies. J Compos Mater 2:18-31
4. Marín JC, Cañas J, París F, Morton J (2002) Determination of G 12 by means of the off-axis tension test. Part I: review of gripping systems and correction factors. Compos A 33:87-100
5. Xiao Y, Kawai M, Hatta H (2010) An integrated method for off-axis tension and compression testing of unidirectional composites. J Compos Mater 45:657-669
6. Moon H, Truesdell C (1974) Interpretation of adscititious inequalities through the effects pure shear stress produces upon an isotropic elastic solid. Arch Ration Mech Anal 55:1-17
7. Rajagopal KR, Wineman AS (1987) New universal relations for nonlinear isotropic elastic materials. J Elast 17:75-83
8. Mihai LA, Goriely A (2012) Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials. Proc R Soc A (to appear)
9. Destrade M, Murphy JG, Saccomandi G (2012) Simple shear is not so simple. Int J Nonlinear Mech 47:210-214
10. Rivlin RS (1948) Large elastic deformations of isotropic materials. IV. Further developments of the general theory. Philos Trans R Soc Lond A 241:379-397
11. Gent AN, Suh JB, Kelly SG III (2007) Mechanics of rubber shear springs. Int J Nonlinear Mech 42:241-249
12. Horgan CO, Murphy JG (2010) Simple shearing of incompressible and slightly compressible isotropic nonlinearly elastic materials. J Elast 98:205-221
13. Humphrey JD, Yin FCP (1987) A new constitutive formulation for characterizing the mechanical behavior of soft tissues. Biophys J 52:563-570
14. Humphrey JD, Strumpf RK, Yin FCP (1990) Determination of a constitutive relation for passive myocardium: I. New Funct Form J Biomech Eng 112:333-339
15. Horgan CO, Murphy JG (2012) On the modeling of extension-torsion experimental data for transversely isotropic biological soft tissues. J Elast 108:179-191
16. Wenk JF, Ratcliffe MB, Guccione JM (2012) Finite element modeling of mitral leaflet tissue using a layered shell approximation. Med Biol Eng Comput 50:1071-1079
17. Ning X, Zhu Q, Lanir Y, Margulies SS (2006) A transversely isotropic viscoelastic constitutive equation for brainstem undergoing finite deformation. J Biomech Eng 128:925-933
18. Destrade M, Gilchrist MD, Prikazchikov DA, Saccomandi G (2008) Surface instability of sheared soft tissues. J Biomech Eng 130:0610071-0610076
19. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1-48
20. Holzapfel GA, Ogden RW, Gasser TC (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3:15-35
21. Ogden RW (2003) Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue. In: Biomechanics of soft tissue in cardiovascular systems, CISM courses and lectures series no. 441. Springer, Wien, pp 65-108
22. Holzapfel GA, Ogden RW (2009) On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework. Math Mech Solids 14:474-489
23. Ogden RW, Saccomandi G, Sgura I (2004) Fitting hyperelastic models to experimental data. Comput Mech 34:484-502
24. Nì Annaidh A, Bruyère K, Destrade M, Gilchrist MD, Maurini C, Otténio M, Saccomandi G (2012) Automated estimation of collagen fibre dispersion in the dermis and its contribution to the anisotropic behaviour of skin. Ann Biomed Eng 40:1666-1678
25. Moulton MJ, Creswell LL, Actis RL, Myers KW, Vannier MW, Szabo BA, Pasque MK (1995) An inverse approach to determining myocardial material properties. J Biomech 28:935-948
26. Yeoh OH, Fleming PD (1997) A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity. J Polym Sci B 35:1919-1931
27. Yamamoto E, Hayashi K, Yamamoto N (1999) Mechanical properties of collagen fascicles from the rabbit patellar tendon. J Biomech Eng 121:124-131
28. Van Kerckhoven R, Kalkman EAJ, Saxena PR, Schoemaker RG (2000) Altered cardiac collagen and associated changes in diastolic function of infarcted rat hearts. Cardiovasc Res 46:316-323
29. Guo D-L, Chen B-S, Liou N-S (2007) Investigating full-field deformation of planar soft tissue under simple-shear tests. J Biomech 40:1165-1170
30. Atkin RJ, Fox N (1980) An introduction to the theory of elasticity. Longman, London
31. Dokos S, Smaill BH, Young AA, LeGrice IJ (2002) Shear properties of passive ventricular myocardium. Am J Physiol Heart Circ Physiol 283:H2650-H2659
32. Horgan CO, Murphy JG (2011) Simple shearing of soft biological tissues. Proc R Soc A 467:760-777