An energetic approach to the analysis of anisotropic hyperelastic materials

International Journal of Engineering Science

Volumn 46, Issue 2, 2008, Pages 164-181

  Federico, Salvatore ^a   Grillo, Alfio ^b,c   Imatani, Shoji ^d   Giaquinta, Gaetano ^b,c   Herzog, Walter ^a  

^a UNIVERSITY OF CALGARY   (Canada)

^b UNIVERSITY OF CATANIA   (Italy)

^c CNR   (Italy)

^d KYOTO UNIVERSITY   (Japan)

Author keywords

Anisotropy; Convexity; Elastic potential; Hyperelasticity

Indexed keywords

ANISOTROPY; COMPUTER SOFTWARE; PROBLEM SOLVING; STRESS-STRAIN CURVES; TENSORS;

ANISOTROPIC HYPERELASTIC MATERIALS; ELASTIC POTENTIAL; LINEAR ELASTICITY TENSOR;

ELASTIC MODULI;

EID: 37049005184     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2007.09.005     Document Type: Article

References (41)

1. ABAQUS v6.3 Theory Manual, 2002. ABAQUS, Inc.
2. Almeida E.S., and Spilker R.L. Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues. Computer Methods in Applied Mechanics and Engineering 151 (1998) 513-538
3. Bettendorff-Bakman D.-E., Schmid P., Lunkenheimer P.P., and Niederer P. A finite element study relating to the rapid filling phase of the human ventricles. Journal of Theoretical Biology 238 2 (2006) 303-316
4. Bischoff J.E., Arruda E.M., and Grosh K. Finite element simulations of orthotropic hyperelasticity. Finite Elements in Analysis and Design 38 (2002) 983-998
5. Bonet J., and Burton A.J. A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations. Computer Methods in Applied Mechanics and Engineering 162 (1998) 151-164
6. Bursać P.M., Obitz T.W., Eisenberg S.R., and Stamenović D. Confined and unconfined stress relaxation of cartilage: appropriateness of a transversely isotropic analysis. Journal of Biomechanics 32 (1999) 1125-1130
7. Carpinteri A. Structural Mechanics: A Unified Approach (1997), Taylor & Francis, Abingdon, UK
8. B. Cohen, Anisotropic Hydrated Soft Tissues in Finite Deformation and the Biomechanics of the Grow Plate, PhD thesis, Columbia University, 1992.
9. Cohen B., Lai W.M., and Mow V.C. A transversely isotropic biphasic model for unconfined compression of growth plate and chondroepiphysis. Journal of Biomechanical Engineering 120 (1998) 491-496
10. Donzelli P.S., and Spilker R.L. A contact finite element formulation for biological soft hydrated tissues. Computer Methods in Applied Mechanics and Engineering 153 1-2 (1998) 63-79
11. Federico S., Grillo A., and Herzog W. A transversely isotropic composite with a statistical distribution of spheroidal inclusions: a geometrical approach to overall properties. Journal of the Mechanics and Physics of Solids 52 10 (2004) 2309-2327
12. Federico S., Grillo A., La Rosa G., Giaquinta G., and Herzog W. A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage. Journal of Biomechanics 38 10 (2005) 2008-2018
13. S. Federico, A. Grillo, G. Giaquinta, W. Herzog, Convex fung-type potentials for biological tissues, Meccanica, in press, doi:10.1007/s11012-007-9090-6.
14. Fosdick R.L., and Serrin J. On the impossibility of linear Cauchy and Piola-Kirchhoff constitutive theories for stress in solids. Journal of Elasticity 9 1 (1979) 83-89
15. Fung Y.C., Fronek K., and Patitucci P. Pseudoelasticity of arteries and the choice of its mathematical expression. American Journal of Physiology 237 (1979) H620-H631
16. Guilak F., and Mow V.C. The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage. Journal of Biomechanics 33 (2000) 1663-1673
17. Griffel D.H. Applied Functional Analysis (1981), Ellis Horwood, Chirchester, UK
18. Gurvich M.R. A constitutive model of hyperelastic anisotropic materials: approach and implementation in ABAQUS. Proceedings of the 2004 ABAQUS Users' Conference (2004) 281-289
19. Gurvich M.R. On characterization of anisotropic elastomeric materials for structural analysis. Rubber Chemistry and Technology 77 1 (2004) 115-130
20. Han S.-K., Federico S., Grillo A., Giaquinta G., and Herzog W. The mechanical behaviour of chondrocytes predicted with a micro-structural model of articular cartilage. Biomechanics and Modeling in Mechanobiology 6 3 (2006) 139-150
21. Holmes M.H., and Mow V.C. The non-linear characteristics of soft gels and hydrated connective tissues in ultrafiltration. Journal of Biomechanics 23 (1990) 1145-1156
22. Holzapfel G.A., Eberlein R., Wriggers P., and Weizsäcker H.W. Large strain analysis of soft biological membranes: Formulation and finite element analysis. Computer Methods in Applied Mechanics and Engineering 132 1-2 (1996) 45-61
23. Holzapfel G.A., and Gasser T.C. A viscoelastic model for fiber-reinforced composites at finite strains: Continuum basis, computational aspects and applications. Computer Methods in Applied Mechanics and Engineering 190 34 (2001) 4379-4403
24. 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
25. Hughes T.J.R. The Finite Element Method (1987), Prentice-Hall, Englewood Cliffs, NJ, USA
26. Humphrey J.D. Mechanics of arterial wall: review and directions. Critical Reviews in Biomedical Engineering 23 (1995) 1-162
27. Marsden J.E., and Hughes T.J.R. Mathematical Foundations of Elasticity (1983), Prentice-Hall, Englewood Cliffs, NJ, USA
28. Moore R., Davids N., and Friedenberg R. Study of a biological model of membrane function by finite element analysis. Biosystems 3 2 (1969) 156-168
29. Ogden R.W. Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society London Series A 326 (1972) 565-584
30. Ogden R.W. Large deformation isotropic elasticity - on the correlation of theory and experiment for compressible rubberlike solids. Proceedings of the Royal Society London Series A 328 (1972) 567-583
31. Ogden R.W. Non-Linear Elastic Deformations (1984), Dover Publications, Inc., Mineola, New York, USA
32. Owen D.R.J., Prakash A., and Zienkiewicz O.C. Finite element analysis of non-linear composite materials by use of overlay systems. Computers and Structures 4 (1974) 1251-1276
33. Peña E., Calvo B., Martínez 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
34. Quintanilla R., and Saccomandi G. The importance of the compatibility of nonlinear constitutive theories with their linear counterparts. Journal of Applied Mechanics 74 (2007) 455-460
35. Saravanan U., and Rajagopal K.R. A comparison of the response of isotropic inhomogeneous elastic cylindrical and spherical shells and their homogenized counterparts. Journal of Elasticity 71 1-3 (2003) 205-233
36. Saravanan U., and Rajagopal K.R. Inflation, extension, torsion and shearing of an inhomogeneous compressible elastic right circular annular cylinder. Mathematics and Mechanics of Solids 10 6 (2005) 603-650
37. Walpole L.J. Elastic behavior of composite materials: theoretical foundations. Advances in Applied Mechanics 21 (1981) 169-242
38. Wang C.C.-B., Chahine N.O., Hung C.T., and Ateshian G.A. Optical determination of anisotropic material properties of bovine articular cartilage in compression. Journal of Biomechanics 36 (2003) 339-353
39. Weiss J.A., Maker B.N., and Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering 135 1-2 (1996) 107-128
40. Wu J.Z., and Herzog W. Finite element simulation of location- and time-dependent mechanical behavior of chondrocytes in unconfined compression tests. Annals of Biomedical Engineering 28 (2000) 318-330
41. Wu J.Z., and Herzog W. Analysis of the mechanical behavior of chondrocytes in unconfined compression tests for cyclic loading. Journal of Biomechanics 39 4 (2006) 603-616