Universal Solutions and Relations in Finite Elasticity

  • Giuseppe Saccomandi
Part of the International Centre for Mechanical Sciences book series (CISM, volume 424)


Let us consider an isotropic, uniform, unconstrained hyperelastic material.


Strain Energy Density Cauchy Stress Tensor Incompressible Material Response Coefficient Universal Relation 
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.


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  1. Antman, S.S, Nonlinear Problems in Elasticity, Springer-Verlag, N.Y. 1995CrossRefGoogle Scholar
  2. Aron, M. (1994) On a class of plane deformations of compressible nonlinearly elastic solids, [MA J. of Appl. Math. 52, 289–296.Google Scholar
  3. Beatty, M.F. (1996) Introduction to nonlinear elasticity in Nonlinear Effects in Fluids and Solids edited by M.M. Carroll and M.A. Hayes (1996) pp 16–112 Plenum Press N.Y.Google Scholar
  4. Beatty, M.F. (1987) A class of universal relations in isotropic elasticity J. of Elasticity 17, 113–121.MathSciNetCrossRefMATHGoogle Scholar
  5. Beatty, M.F. and Hayes, M.A. (1992) Deformations of an elastic, internally constrained material, part 1: homogeneous deformations, J. of Elasticity 29, 1–84.MathSciNetCrossRefMATHGoogle Scholar
  6. Beatty, M.F. and Hayes, M.A. (1992) Deformations of an elastic, internally constrained material, part 2: nonhomogeneous deformations, Q. Jl. Mech. appl. Math. 45, 663–709.MathSciNetCrossRefMATHGoogle Scholar
  7. Beatty, M.F. and Saccomandi, G (2000) Universal Relations for Fiber Reinforced Materials, to appear.Google Scholar
  8. Carroll, M.M. (1995) On obtaining closed form solutions for compressible elastic materials, ZAMP 46 s126 - s145.Google Scholar
  9. Currie, P.K. and Hayes, M. (1981) On non-universal finite elastic deformations,in Finite Elasticity, Carlson and Shield (eds) Martinus Nijhoff Publishers The Hague (NL)Google Scholar
  10. Ericksen J.L. (1954) Deformations possible in every isotropic, incompressible, perfectly elastic body,ZAMP 5 466–488.MathSciNetCrossRefMATHADSGoogle Scholar
  11. Ericksen J.L. (1955) Deformations possible in every isotropic, compressible, perfectly elastic material, J. Math. Phys. 34 126–128.MathSciNetGoogle Scholar
  12. Fosdick, R.L. (1966) Remarks on compatibility in Modern Developments in the Mechanics of Continua pp109–127 Academic Press N.Y.Google Scholar
  13. Fosdick, R.L. and Schuler, K.W. (1969) On Ericksen’s problem for plane deformations with uniform transverse stretch, Int. J. of Engng. Sci 7, 217–233.CrossRefMATHGoogle Scholar
  14. Hayes, M.A and Knops R.J. (1966) On universal relations in Elasticity theory ZAMP 17, 636–639.CrossRefADSGoogle Scholar
  15. Hayes, M.A. and Saccomandi, G., The Cauchy stress tensor for a material subject to an isotropic internal constraint, J. Engng. Math, 37 (2000) 85–92.MathSciNetCrossRefMATHGoogle Scholar
  16. Horgan, C.O. (1995) Antiplane-shear deformations in linear and nonlinear solid mechanics, SIAM Review 37, 53–81.MathSciNetCrossRefMATHGoogle Scholar
  17. Horgan, C. O.(1995) On axisymmetric solutions for compressible nonlinearly elastic solids, ZAMP 46 S107 - S125MathSciNetCrossRefGoogle Scholar
  18. Horgan, C.O. and Saccomandi, G., Simple torsion of isotropic, hyperelastic, incompressible materials with limiting chain extensibility, Journal of Elasticity 56 (1999) 159–170.CrossRefMATHGoogle Scholar
  19. Jiang, Q. and Beatty, M.F. On compressible materials capable of sustaining axisymmetric shear deformations (Part 1), J. of Elasticity 39 (1995) 75–95.MathSciNetCrossRefMATHGoogle Scholar
  20. Marris, A.W. and Shiau, J.F (1970), Universal deformations in isotropic incompressible hyperelastic materials when the deformation tensor has equal proper values, Arch. Rat. Mech. Anal. 36, 135–160.MathSciNetMATHGoogle Scholar
  21. Ogden R.W. (1984) Non-linear Elastic Deformations, Ellis Horwood, Chichester.Google Scholar
  22. Pucci, E. and Saccomandi, G. (1996) Universal relations in constrained elasticity, Math and Mech of Solids, 1, 207–217.MathSciNetCrossRefMATHGoogle Scholar
  23. Pucci, E. and Saccomandi, G. (1997) On universal relations in continuum mechanics, Continuum Mechanics and Thermodynamics, 9, 61–72.MathSciNetCrossRefMATHADSGoogle Scholar
  24. Pucci, E. and Saccomandi, G. (1998) Universal generalized plane deformations in constrained elasticity, Math and Mech of Solids, 3, 201–216.MathSciNetCrossRefGoogle Scholar
  25. Pucci, E. and Saccomandi, G. (1999) Universal solutions in constrained simple materials, Int. J. of Nonlin. Mech., 34, 469–484.MathSciNetCrossRefMATHGoogle Scholar
  26. Saccomandi G. and Vianello, M. A Universal relation characterizing transversely hemitropic hyperelastic materials, Math. and Mech. of Solids 2 (1997) 181–188.MathSciNetCrossRefMATHGoogle Scholar
  27. Singh, M and Pipkin, A.C. (1965) Note on Ericksen’s problem ZAMP 16, 706–709.CrossRefADSGoogle Scholar
  28. Truesdell, C. and Noll, W. 1965 The Nonlinear Field Theories of Mechanics, Handbuch der Physik IIU3, Springer-Verlag, New York.Google Scholar
  29. Wang, C.C. and Truesdell C. (1973) Introduction to Rational Elasticity, Noordhoff Int. Publ. Leyden.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Giuseppe Saccomandi
    • 1
  1. 1.Dipartimento di Ingegneria dell’InnovazioneUniversità degli Studi di LecceItaly

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