Plane strain bending of strain-stiffening rubber-like rectangular beams

International Journal of Solids and Structures

Volumn 45, Issue 6, 2008, Pages 1713-1729

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

^a University of Virginia   (United States)

Author keywords

Bending of rectangular beams by an end moment; Incompressible hyperelastic rubber like materials and soft biological tissues; Strain stiffening constitutive models

Indexed keywords

BENDING (DEFORMATION); BIOMECHANICS; CONSTITUTIVE MODELS; ELASTICITY; STRAIN; STRAIN ENERGY;

END MOMENT; INCOMPRESSIBLE HYPERELASTIC RUBBER LIKE MATERIALS; RECTANGULAR BEAMS; SOFT BIOLOGICAL TISSUES; STRAIN STIFFENING CONSTITUTIVE MODELS;

BEAMS AND GIRDERS;

EID: 38649134773     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.10.022     Document Type: Article

References (45)

1. 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
2. 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: Carroll, M.M., Hayes, M.A. (Eds.), Nonlinear Effects in Fluids and Solids, Plenum Press, NY, 1996, pp. 16-112
3. Beatty M.F. On the radial oscillations of incompressible, isotropic, elastic and limited elastic thick-walled tubes. Int. J. Nonlinear Mech. 42 (2007) 283-297
4. Beatty, M.F., in press. On constitutive models for limited elastic, molecular based materials. Math. Mech. Solids.
5. Boyce M.C. Direct comparison of the Gent and Arruda-Boyce constitutive models. Rubber Chem. Technol. 69 (1996) 781-785
6. Boyce M.C., and Arruda E.M. Constitutive models of rubber elasticity: a review. Rubber Chem. Technol. 73 (2000) 504-523
7. 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
8. Fung Y.C.B. Elasticity of soft tissues in simple elongation. Am. J. Physiol. 213 (1967) 1532-1544
9. Gent A.N. A new constitutive relation for rubber. Rubber Chem. Technol. 69 (1996) 59-61
10. Gent A.N. Elastic instabilities of inflated rubber shells. Rubber Chem. Technol. 72 (1999) 263-268
11. Gent A.N. Elastic instabilities in rubber. Int. J. Nonlinear Mech. 40 (2005) 165-175
12. Haward R.N. The application of non-Gaussian chain statistics to ultralow density polyethylenes and other thermoplastic polymers. Polymer 40 (1999) 5821-5832
13. Hearle J.W.S. A critical review of the structural mechanics of wool and hair fibers. Int. J. Biol. Macromol. 27 (2000) 123-138
14. Holzapfel G.A. Nonlinear Solid Mechanics: A Continuum Approach for Engineering (2000), Wiley, Chichester
15. Holzapfel G.A. Similarities between soft biological tissues and rubber like materials. In: Austrell P.-E., and Kari L. (Eds). Constitutive Models for Rubber IV (ECCMR 2005) (2005), Taylor and Francis, London 607-617
16. Horgan C.O., and Murphy J.G. Limiting chain extensibility constitutive models of Valanis-Landel type. J. Elasticity 86 (2007) 101-111
17. Horgan C.O., Ogden R.W., and Saccomandi G. A theory of stress softening of elastomers based on finite chain extensibility. Proc. R. Soc. Lond. A 460 (2004) 1737-1754
18. Horgan C.O., and Saccomandi G. Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility. J. Elasticity 56 (1999) 159-170
19. Horgan C.O., and Saccomandi G. Pure axial shear of isotropic incompressible nonlinearly elastic materials with limiting chain extensibility. J. Elasticity 57 (1999) 307-319
20. Horgan C.O., and Saccomandi G. Pure azimuthal shear of isotropic incompressible hyperelastic materials with limiting chain extensibility. Int. J. Nonlinear Mech. 36 (2001) 465-475
21. Horgan C.O., and Saccomandi G. Anti-plane shear deformations of non-Gaussian isotropic, incompressible hyperelastic materials. Proc. R. Soc. Lond. A 457 (2001) 1999-2017
22. 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
23. Horgan C.O., and Saccomandi G. A molecular-statistical basis for the Gent constitutive model of rubber elasticity. J. Elasticity 68 (2002) 167-176
24. Horgan C.O., and Saccomandi G. Helical shear for hardening generalized neo-Hookean elastic materials. Math. Mech. Solids 8 (2003) 539-559
25. Horgan C.O., and Saccomandi G. A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomech. Model. Mechanobiol. 1 (2003) 251-266
26. Horgan C.O., and Saccomandi G. Constitutive models for atactic elastomers. In: Monaco R., Rionero S., and Ruggeri T. (Eds). Proceedings of the Symposium on "Waves and Stability in Continuous Media", (WASCOM 2003), Sardinia, Italy (2004), World Scientific, Singapore 281-293
27. Horgan C.O., and Saccomandi G. Hyperelastic limiting chain extensibility constitutive models for rubber: a brief review. In: Austrell P.-E., and Kari L. (Eds). Constitutive Models for Rubber IV (ECCMR 2005) (2005), Taylor and Francis, London 607-617
28. Horgan C.O., and Saccomandi G. Phenomenological hyperelastic strain-stiffening constitutive models for rubber. Rubber Chem. Technol. 79 (2006) 152-169
29. 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
30. Humphrey J.D. Cardiovascular Solid Mechanics (2002), Springer, New York
31. Humphrey J.D. Continuum biomechanics of soft biological tissues. Proc. R. Soc. Lond. A 459 (2003) 1-44
32. Kanner L.M., and Horgan C.O. Elastic instabilities for strain-stiffening rubber-like spherical and cylindrical thin shells under inflation. Int. J. Nonlinear Mech. 42 (2007) 204-215
33. Lai W.M., Rubin D., and Krempl E. Introduction to Continuum Mechanics. third ed. (1993), Pergamon, New York
34. Marko J.F., and Siggia E.D. Stretching DNA. Macromolecules 28 (1995) 8759-8770
35. Murphy J.G. Some remarks on kinematic modeling of limiting chain extensibility. Math. Mech. Solids 11 (2006) 629-641
36. Ogden, R.W., 1984. Nonlinear Elastic Deformations. Ellis Horwood, Chichester. Reprinted by Dover, New York, 1997.
37. Ogden R.W., and Saccomandi G. Introducing mesoscopic information into constitutive equations for arterial walls. Biomech. Model. Mechanobiol. 6 (2007) 333-344
38. Ogden R.W., Saccomandi G., and Sgura I. Fitting hyperelastic models to experimental data. Comput. Mech. 34 (2004) 484-502
39. Ogden R.W., Saccomandi G., and Sgura I. On worm-like chain models within the three-dimensional continuum mechanics framework. Proc. R. Soc. Lond. A 462 (2006) 749-768
40. Ogden R.W., Saccomandi G., and Sgura I. Computational aspects of the worm-like chain interpolation formulas. Comput. Math. Appl. 53 (2007) 276-286
41. Pucci E., and Saccomandi G. A note on the Gent model for rubber-like materials. Rubber Chem. Technol. 75 (2002) 839-851
42. Rivlin R.S. Large elastic deformations of isotropic materials, part V, the problem of flexure. Proc. R. Soc. Lond. A 195 (1949) 463-473
43. Rivlin R.S. Large elastic deformations of isotropic materials, part VI, further results in the theory of torsion, shear, and flexure. Phil. Trans. R. Soc. Lond. A242 (1949) 173-195
44. Saccomandi G. Universal results in finite elasticity. In: Fu Y.B., and Ogden R.W. (Eds). Nonlinear Elasticity: Theory and Applications. London Mathematical Society Lecture Notes vol. 283 (2001), Cambridge University Press 97-134
45. Taber L.A. Nonlinear Theory of Elasticity: Applications in Biomechanics (2004), World Scientific Publishing Co., Singapore