Phenomenology of Rubber-Like Materials

  • Giuseppe Saccomandi
Part of the International Centre for Mechanical Sciences book series (CISM, volume 452)


These lectures are devoted to an overview of the basic balance laws and constitutive requirements of continuum mechanics. Some solutions of simple boundary value problems are considered and a critical review of strain-energy density functions is proposed.


Nonlinear Elasticity Anti Plane Shear Incompressible Material Antiplane Shear Finite Elasticity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Aberayatne, R. and Knowles, J. (2001) in: Y. Fu, R. Ogden (Eds.), Non-linear Elasticity, Cambridge University Press, Cambridge.Google Scholar
  2. Arruda, E. M. and Boyce, M. C. (1993) A three dimensional constitutive model for the large deformation stretch behavior of rubber elastic materials, J. Mech. Phys. Solids 41, 389–412.CrossRefGoogle Scholar
  3. Ball, J. M. (2003) Some open problems in elasticity, in: P. Newton, P. Holmes, A. Weinstein (Eds.) Geometry, Mechanics and Dynamics, Springer, New-York.Google Scholar
  4. Benvenuto, E. (1998) A. J. C. Barrè de Saint-Venant: the man, the scientist, the engineer, in: Il problema di de Saint-Venant: aspetti teorici ad applicativi, Atti dei Convegni Lincei 140, Accademia dei Lincei, Roma.Google Scholar
  5. Bischoff, E. J., Arruda, E. M. and Grosh, K. (2001) A new constitutive model for the compressibility of elastomers at finite deformations, Rubber Chemistry and Technology 74, 541–559.CrossRefGoogle Scholar
  6. Boyce, M. C. and Arruda, E. M. (2000) Constitutive models of rubber elasticity: a review, Rubber Chemistry and Technology 73, 504–523.CrossRefGoogle Scholar
  7. Chen, Y. C. and Rajagopal, K. R. (2001) Boundary layer solutions in elastic solids, J. of Elasticity 62, 203–216.MathSciNetCrossRefzbMATHGoogle Scholar
  8. Coleman, B. D. and Noll, W. (1963) The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 245–261.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Criscione, J. C., Humphrey, J. D., Douglas, A. S. and Hunter, W. C. (2000) An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity, J. Mech. and Phys. of Solids, 48, 2445–2465.CrossRefzbMATHGoogle Scholar
  10. Criscione, J. C., McCulloch, A. D., and Hunter, W. C. (2002) Constitutive framework optimized for myocardium and other high-strain laminar materials with one fiber family, J. Mech. and Phys. of Solids, 50, 1681–1702.MathSciNetCrossRefzbMATHGoogle Scholar
  11. Dorfmann, A. and Muhr, A., (Eds.)(1999) Constitutive Models for Rubber,Balkema, Rotterdam.Google Scholar
  12. Ericksen, J. L. (1997) Introduction to the Thermodynamics of Solids, Springer, New-York.Google Scholar
  13. Fosdick, R. L. and Kao, B. G. (1978) Transverse deformations associated with rectilinear shear in elastic solids, J. of Elasticity, 8 117–142.MathSciNetCrossRefzbMATHGoogle Scholar
  14. Gent, A. N. (1996) A new constitutive relation for rubber, Rubber Chemistry and Technology, 69, 59–61.MathSciNetCrossRefGoogle Scholar
  15. Holzapfel, G. A. (2001) Nonlinear Solid Mechanics, Wiley, Chichester.Google Scholar
  16. Horgan, C. 0. (1995) Antiplane shear deformation in linear and nonlinear solid mechanics, SIAM Rev. 37, 53–81Google Scholar
  17. Horgan, C. 0. and Saccomandi, G. (1999) Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility, J. of Elasticity, 56 159–170.zbMATHGoogle Scholar
  18. Horgan, C. 0. and Saccomandi, G. (2002a) Constitutive modelling of rubber-like and biological materials with limiting chain extensibility, Mathematics and Mechanics of Solids, 7 353–371.MathSciNetzbMATHGoogle Scholar
  19. Horgan, C. 0. and Saccomandi, G. (2002b) A molecular-statistical basis for the Gent constitutive model of rubber elasticity, Journal of Elasticity, 68 167–176.MathSciNetzbMATHGoogle Scholar
  20. Horgan, C. 0. and Saccomandi, G. (2003) Finite thermoelasticity with limiting chain extensibility, Journal of Mechanics and Physics of Solids, 75, 839–851.Google Scholar
  21. Horgan, C. 0. and Saccomandi, G. (2004) Coupling of anti-plane shear deformations with plane deformations in generalized neo-Hookean isotropic, incompressible, hyperelastic materials, submitted.Google Scholar
  22. Horgan, C. 0., Saccomandi, G. and Sgura, I. (2003) Finite thermoelasticity with limiting chain extensibility, SIAM Journal on Applied Mathematics, 65, 1712–1727.Google Scholar
  23. Knowles, J. K. (1977) The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids, Int. J. of Fracture 13, 611–639.MathSciNetCrossRefGoogle Scholar
  24. Martin, S.E. and Carlson, D. E. (1977) The behavior of elastic heat conductors with second order response functions, ZAMP 28, 311–329.CrossRefzbMATHGoogle Scholar
  25. Müller, I. (1985) Thermodynamics, Pitman, Boston-London-Melbourne.zbMATHGoogle Scholar
  26. Murnaghan, F. D. (1937) Finite deformation of an elastic solid, Amer. J. Math. 59, 235–260.MathSciNetCrossRefzbMATHGoogle Scholar
  27. Murphy J. and Rogerson G. (2002) A method to model simple tension experiments using finite elasticity theory with an application to some polyurethane foams, Int. J.of Engngr. Sci 40, 499–510.CrossRefGoogle Scholar
  28. Mollica, F. and Rajagopal, K. R. (1997) Secondary deformations due to axial shear of the annular region between two eccentricaly place cylinder, J. of Elasticity 48 103–123.MathSciNetCrossRefzbMATHGoogle Scholar
  29. Murray, J. D. (1984) Asymptotic Analysis, Springer, New-York.CrossRefzbMATHGoogle Scholar
  30. Ogden, R. W. (1972) Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids, Proc. Roy. Soc. London A 328, 567–584.CrossRefzbMATHGoogle Scholar
  31. Ogden, R. W. (1984) Non-Linear Elastic Deformations, Ellis Horwood, Chichester. Reprinted by Dover (1997).Google Scholar
  32. Ogden, R.W. (1986) Recent advances in the theory of phenomenological theory of rubber elasticity, Rubber Chemistry and Technology, 59, 361–383CrossRefGoogle Scholar
  33. Pedregal, P. (2000) Variational methods in nonlinear elasticity, SIAM, Philadelphia.CrossRefzbMATHGoogle Scholar
  34. Peng, T. J. and Landel, R. F. (1972) Stored energy function of rubberlike materials derive from tensile data, J. of Appl. Phys. 43, 3064–3067.CrossRefGoogle Scholar
  35. Perrin, G. (2000) Analytic stress-strain relationship for isotropic network model of rubber elasticity, C.R. Acad. Sci. Paris 328, Série II, 5–10.Google Scholar
  36. Pucci, E. and Saccomandi, G. (1999) Some remarks on the Gent model of rubber elasticity, CanCNSM proceedings (edited by Elena M. Croitoro), University of Victoria Press, Victoria, Canada, 163–172.Google Scholar
  37. Pucci, E. and Saccomandi, G. (2002) A note on the Gent model for rubber-like materials, to appear in Rubber Chemistry and Technology, 75 839–851.CrossRefGoogle Scholar
  38. Rajagopal, K. R. and Srinivasa, A. R. (2000) A thermodynamic frame work for rate type fluid models, J. Non_Newtonian Fluid. Mech. 88, 207–227.Google Scholar
  39. Rivlin, R. S. (1960) Some topics in finite elasticity in Proc. of the First Naval Symp. on Structural Mech., pp. 169–198, Pergamon Press, New York.Google Scholar
  40. Saccomandi, G. (2001) Universal results in finite elasticiy, in: Y. Fu, R. Ogden (Eds.), Non-linear Elasticity, Cambridge University Press, Cambridge.Google Scholar
  41. Signorini, A. (1955) Trasformazioni termoelastiche finite, Ann. di Mat. Pura Appl. 39, 147–201.MathSciNetCrossRefzbMATHGoogle Scholar
  42. Singh, S. (1967) Small finite deformations of elastic dielectrics, Quart. Appl. Math. 25, 275–284.zbMATHGoogle Scholar
  43. Spencer. A. J. M. (1972) Deformations of fibre-reinforced materials,Oxford University Press.Google Scholar
  44. Valanis, K. C. and Landel, R. F. (1967) The strain-energy function of a hyperelastic materials in terms of extension ratios, J. of Appl. Phys., 38, 2997–3002.CrossRefGoogle Scholar
  45. Zhang, J. P. and Rajagopal, K. R. (1992) Some inhomogeneous motions and deformations within the context of a nonlinear elastic solid, Int. J. Engngr. Sci., 30 919–938.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • Giuseppe Saccomandi
    • 1
  1. 1.Dipartimento di Ingegneria dell’Innovazione, Sezione di Ingegneria IndustrialeUniversità di LecceLecceItaly

Personalised recommendations