Elastic instabilities for strain-stiffening rubber-like spherical and cylindrical thin shells under inflation

International Journal of Non-Linear Mechanics

Volumn 42, Issue 2, 2007, Pages 204-215

  Kanner, Landon M ^a   Horgan, Cornelius O ^a  

^a UNIVERSITY OF VIRGINIA   (United States)

Author keywords

Incompressible rubber like materials and soft biological tissues; Inflation of spherical and cylindrical thin shells; Instabilities; Strain stiffening constitutive models

Indexed keywords

BIOMECHANICS; ELASTICITY; STABILITY; STIFFNESS; STRAIN; TISSUE;

CYLINDRICAL THIN SHELLS; INFLATION; SOFT TISSUES; STRAIN STIFFENING CONSTITUTIVE MODELS;

ELASTIC DEFORMATION;

EID: 34247510522     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2006.10.010     Document Type: Article

References (45)

1. Gent A.N. Elastic instabilities in rubber. Int. J. Non-Linear Mech. 40 (2005) 165-175
2. Gent A.N. Elastic instabilities of inflated rubber shells. Rubber Chem. Technol. 72 (1999) 263-268
3. Holzapfel G.A. Nonlinear Solid Mechanics: A Continuum Approach for Engineering (2000), Wiley, Chichester
4. R.W. Ogden, Nonlinear Elastic Deformations, Ellis Horwood, Chichester 1984, reprinted by Dover, New York, 1997.
5. Humphrey J.D. Cardiovascular Solid Mechanics (2002), Springer, New York
6. Humphrey J.D. Continuum biomechanics of soft biological tissues. Proc. R. Soc. London A 459 (2003) 1-44
7. Humphrey J.D., Canham P.B., and Structure. mechanical properties and mechanics of intercranial saccular aneurysms. J. Elasticity 61 (2000) 49-81
8. Horgan C.O., and Saccomandi G. A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomechan. Model Mechanbiol. 1 (2003) 251-266
9. G.A. Holzapfel, Similarities between soft biological tissues and rubberlike materials, in: P.-E. Austrell, L. Kari (Eds.), Constitutive Models for Rubber IV, Proceedings of the Fourth European Conference on "Constitutive Models for Rubber", (ECCMR 2005), Stockholm, Sweden, Taylor and Francis, London, 2005, pp. 607-617.
10. Needleman A. Inflation of spherical rubber balloons. Int. J. Solids Struct. 13 (1977) 409-421
11. Beatty M.F. Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl. Mech. Rev. 40 (1987) 1699-1733 reprinted with minor modifications as "Introduction to nonlinear elasticity" in: M.M. Carroll, M.A. Hayes (Eds.), Nonlinear Effects in Fluids and Solids, Plenum Press, NY, 1996, pp. 16-112
12. B. Erman, Molecular aspects of rubber elasticity, in: G. Saccomandi, R.W. Ogden (Eds.), Mechanics and Thermomechanics of Rubberlike Solids, CISM Lecture Notes, vol. 452, Springer, Vienna, 2004, pp. 63-89.
13. Haward R.N. The application of non-Gaussian chain statistics to ultralow density polyethylenes and other thermoplastic polymers. Polymer 40 (1999) 5821-5832
14. Hearle J.W.S. A critical review of the structural mechanics of wool and hair fibers. Int. J. Biol. Macromol. 27 (2000) 123-138
15. Marko J.F., and Siggia E.D. Stretching DNA. Macromolecules 28 (1995) 8759-8770
16. Gent A.N. A new constitutive relation for rubber. Rubber Chem. Technol. 69 (1996) 59-61
17. Ogden R.W., Saccomandi G., and Sgura I. Fitting hyperelastic models to experimental data. Comput. Mech. 34 (2004) 484-502
18. Pucci E., and Saccomandi G. A note on the Gent model for rubber-like materials. Rubber Chem. Technol. 75 (2002) 839-851
19. Arruda E.M., and Boyce M.C. A three-dimensional constitutive model for the large deformation stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41 (1993) 389-412
20. Boyce M.C. Direct comparison of the Gent and Arruda-Boyce constitutive models. Rubber Chem. Technol. 69 (1996) 781-785
21. Boyce M.C., and Arruda E.M. Constitutive models of rubber elasticity: a review. Rubber Chem. Technol. 73 (2000) 504-523
22. Horgan C.O., and Saccomandi G. A molecular-statistical basis for the Gent constitutive model of rubber elasticity. J. Elasticity 68 (2002) 167-176
23. C.O. Horgan, G. Saccomandi, Constitutive models for atactic elastomers, in: R. Monaco, S. Rionero, T. Ruggeri (Eds.), Proceedings of the Symposium on "Waves and Stability in Continuous Media", (WASCOM 2003), Sardinia, Italy, World Scientific, Singapore, 2004, pp. 281-293.
24. C.O. Horgan, G. Saccomandi, Hyperelastic limiting chain extensibility constitutive models for rubber: a brief review, in: P.-E. Austrell, L. Kari (Eds.), Constitutive Models for Rubber IV, Proceedings of the Fourth European Conference on "Constitutive Models for Rubber", (ECCMR 2005), Stockholm, Sweden, Taylor and Francis, London, 2005, pp. 607-617.
25. Horgan C.O., and Saccomandi G. Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chem. Technol. 79 (2006) 152-169
26. Horgan C.O., and Schwartz J.G. Constitutive modeling and the trousers test for fracture of rubber-like materials. J. Mech. Phys. Solids 53 (2005) 545-564
27. Horgan C.O., and Saccomandi G. Constitutive modeling of rubber-like and biological materials with limiting chain extensibility. Math. Mech. Solids 7 (2002) 353-371
28. M.M. Carroll, Elastic polymers with limiting chain extensibility, preprint, 2001.
29. Murphy J.G. Some remarks on kinematic modeling of limiting chain extensibility. Math. Mech. Solids 11 (2006) 629-641
30. Fung Y.C.B. Elasticity of soft tissues in simple elongation. Am. J. Physiol. 213 (1967) 1532-1544
31. Knowles J.K. The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. Int. J. Fract. 13 (1977) 611-639
32. Horgan C.O., and Saccomandi G. Anti-plane shear deformations of non-Gaussian isotropic incompressible hyperelastic materials. Proc. R. Soc. London, Ser. A 457 (2001) 1999-2017
33. Chagnon G., Marckham G., and Verron E. Equivalence of the Hart-Smith model with Arruda-Boyce and Gent formulations of rubber elasticity. Rubber Chem. Technol. 77 (2004) 724-735
34. Adkins J.E., and Rivlin R.S. Large elastic deformations of isotropic materials IX. The deformations of thin shells. Proc. R. Soc. London, Ser. A 244 (1952) 505-531
35. R.W. Ogden, Elastic deformations of rubberlike solids, in: H.G. Hopkins, M.J. Sewell (Eds.), Mechanics of Solids, (the Rodney Hill 60th Anniversary Volume), Pergamon Press, 1982, pp. 499-537.
36. E. Pucci, G. Saccomandi, Some remarks on the Gent model of rubber elasticity, in: E.M. Croitero (Ed.), Proceedings of the First Canadian Conference on Nonlinear Solid Mechanics (CNSM), Victoria, University of Victoria Press, Victoria, 1999, pp. 163-171.
37. Carroll M.M. Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders. Qt. Appl. Math. 45 (1987) 141-154
38. Alexander H. Tensile instability of initially spherical balloons. Int. J. Eng. Sci. 9 (1971) 151-162
39. Müller I. Two instructive instabilities in non-linear elasticity: biaxially loaded membrane and rubber balloons. Meccanica 31 (1996) 387-395
40. Müller I., and Struchtrup H. Inflating a rubber balloon. Math. Mech. Solids 7 (2002) 569-577
41. Horgan C.O., and Saccomandi G. Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility. J. Elasticity 56 (1999) 159-170
42. Wineman A. Some results for generalized neo-Hookean elastic materials. Int. J. Non-Linear Mech. 40 (2005) 271-280
43. G. Saccomandi, Universal results in finite elasticity, in: Y.B. Fu, R.W. Ogden (Eds.), Nonlinear Elasticity: Theory and Applications, London Mathematical Society Lecture Notes, vol. 283, Cambridge University Press, 2001, pp. 97-134.
44. J.M. Hill, Exact integrals and solutions for finite deformations of the incompressible Varga elastic materials, in: Y.B. Fu, R.W. Ogden (Eds.), Nonlinear Elasticity: Theory and Applications, London Mathematical Society Lecture Notes, vol. 283, Cambridge University Press, 2001, pp. 160-200.
45. Charrier J.-M. Large elastic deformation theories and unstable deformations of rubber structures-thin tubes. Rubber Chem. Technol. 47 (1974) 788-802