Nonlinear transversely isotropic elastic solids: An alternative representation

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 61, Issue 2, 2008, Pages 129-149

  Shariff, M H B M ^a  

^a KHALIFA UNIVERSITY   (United Arab Emirates)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONSTITUTIVE EQUATIONS; ELASTICITY; MATHEMATICAL MODELS; STRESS-STRAIN CURVES;

PRINCIPAL AXES TECHNIQUES; STRAIN ENERGY FUNCTION; TRANSVERSELY ISOTROPIC ELASTIC SOLIDS;

STRAIN ENERGY;

EID: 43049101695     PISSN: 00335614     EISSN: 14643855     Source Type: Journal    
DOI: 10.1093/qjmam/hbm028     Document Type: Article

References (25)

1. G. Saccomandi, Phenomenology of rubber-like materials, Mechanics and Thermomechanics of Rubberlike Solids, CISM Courses and Lectures Series 452 (ed. G. Saccomandi & R. W. Ogden; Springer, Wien 2004) 91-134.
2. R. W. Ogden, Elastic deformations of rubberlike solids, Mechanics of Solid, The Rodney Hill 60th Anniversary Volume (ed. H. G. Hopkins & M. J. Sewell; Pergamon Press, New York 1982 ) 499-537.
3. R. W. Ogden Large dwformation isotropic elasticity: On the correlation of theory and experinmet for incompressible rubberlike solids, Proc R. Soc. Lond. A 326 (1972) 565-584.
4. K. C. Valanis and R. F. Landel, The strain-energy function of hyperelastic material in terms of the extension ratios, J. Appl. Phys. 38 (1967) 2997-3002.
5. M. H. B. M. Shariff, Strain energy function for filled and unfilled rubberlike material, Rubber Chem. Technol. 73 (2000) 1-21
6. G. Marckmann and E. Verron, Comparison of hyperelastic models for rubber-like materials, ibid. 79, (2006) 835-858.
7. A. J. M. Spencer, Constitutive theory for strongly anisotropic solid, Continuum Theory of the Mechanics of Fiber-Reinforced Composites (Chapter I), CISM Courses and Lectures 282 (ed. A. J. M. Spencer, Springer, Wein 1984) 1-32.
8. J. C. Criscione, A. S. Douglas and W. C. hunter, Physically based invariants set for materials exhibiting transversely isotropic behaviour, J. Mech. Phys. Solids 49 (2001) 871-891.
9. J. Lu and L. Zhang, Physically motivated invariant formulation for transversely isotrpic hyperelasticity, Int. J. Solids Struct. 42 (2005) 6015-6031.
10. Z. Y. Guo, X. O. Peng and B. Moran, A Composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibroses, J. Mech. Phys. Solids 54 (2006) 1952-1971.
11. G. deBotton. L. Hariton and E. A. Socolsky, Neo-Hookean fiber-reinforced composites in finite elasticity, ibid. 54 (2006) 533-559.
12. M. B. Rubin and M. Jabarcen, Physically based invariants for nonlinear elastic orthotropic solids, J. Elast. 90 (2008) 1-18.
13. M. H. B. M. Shariff and D. F. Parker, An extension of Key's principle to nonlinear elasticity, J. Engng. Math 37, (2000) 171-190.
14. A. J. M. Spencer. Theory of invariants, Continnum Physics, Vol. 1 (ed. A. C. Eringen; Academic Press, New York 1971 ) 239-253.
15. R. S. Rivlin, The Valanis-Landel strain energy function. J. Elast. 73 (2003) 291-297.
16. M. H. B. M. Shariff, An anisotropic model of the Mullins effect, J. Engng. Math. 56 (2006) 415-435.
17. R. W. Ogden, Non-Linear Elastic Deformations (Ellis Horwood, Chicheser 1984). linear elastic solids, Int. J. Non-Linear Mech. 40 (2005) 213-227.
18. J. Merodio and R. W. Ogden, Mechanical response of fiber-reinforced incompressible non-linear elastic solids, Int. J. Non-Linear Mech. 40 (2005) 213-227.
19. M. H. B. M. Shariff, Transversely isotropic strain energy with physical invariants. Constitutive Models for Rubber V ( ed. A. Boukamel, L. Laiarinandrasana, S. Meo & E. Verron; Taylor & Francis, London 2007) 67-72.
20. M. H. B. M. Shariff, Physical parameters strain energy function for rubberlike materials, Constitutive Models for Rubber (ed. A. Dorfmann & A. Muhr; Balkema, Rotterdam 1999) 131-137.
21. S. D. Conte and C. de Boor, Elementary Numerical Analysis (McGraw-Hill, Kogkusa 1965).
22. R. W. Ogden, Recent advances in the phenomenological theory of rubber elasticity, Rubber Chem. Technol. 59, (1986) 361-383.
23. R. S. Rivlin and D. W. Saunders, Large elastic deformations of isotropic materials: VII. Experiments on the deformation of rubber, Philos. Trans. R. Soc. Lond. A 243 (1951) 251-288.
24. J. C. Criscione, J. D. Humphrey, A. S. Douglas and W. C. Hunter, An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelatsticity, J. Mech. Phys. Solids 48 (2000) 2445-2465.
25. J. C. Criscione, Rivlin's representation formula is ill-conceived for the determination of response functions via biaxial testing, J. Elast. 70 (2003) 129-147.