Skip to main content
SpringerLink
Log in

Extreme elastic deformations

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63, 1977, pp. 337–403.

    Google Scholar 

  2. P. G. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity. North-Holland, 1988.

  3. P. Podio-Guidugli, Polyconvex energies and symmetry requirements. To appear in J. Elasticity.

  4. S. S. Antman, Fundamental mathematical problems in the theory of nonlinea relasticity, pp. 35–54 of Numerical Solution of Partial Differential Equations, III. North-Holland, 1976.

  5. S. S. Antman, Ordinary differential equations of non-linear elasticity, I & II. Arch. Rational Mech. Anal. 61, 1976, pp. 307–393.

    Google Scholar 

  6. S. S. Antman, Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders. Arch. Rational Mech. Anal. 83, 1983, pp. 1–52. Corrigenda, ibid. 95, 1986, pp. 391–393,

    Google Scholar 

  7. S. S. Antman, The influence of elasticity on analysis: modern developments. Bull. Amer. Math. Soc. 9, 1983, pp. 267–291.

    Google Scholar 

  8. P. Podio-Guidugli, On energy-growth conditions in elasticity. To appear in Rend. Sem. Mat. Torino, 1990.

  9. P. Podio-Guidugli, G. Vergara Caffarelli, & E. G. Virga, Cavitation and phase transition of hyperelastic fluids. Arch. Rational Mech. Anal. 92, 1986, pp. 121–136.

    Google Scholar 

  10. C. Truesdell, Some challenges offered to analysis by rational thermomechanics. Lecture 1: Comments on elasticity, pp. 495–540 of Contemporary Developments in Continuum Mechanics and Partial Differential Equations, G. M. de la Penha & L. A. Medeiros Eds., North-Holland, 1978.

  11. J. L. Ericksen, Some simpler cases of the Gibbs problem for thermoelastic solids. J. Thermal Stresses 4, 1981, pp. 13–30.

    Google Scholar 

  12. P. G. Flory, Thermodynamics relations for high elastic materials. Trans. Faraday Soc. 57, 1961, pp. 829–838.

    Google Scholar 

  13. M. Chipot & D. Kinderlehrer, Equilibrium configurations of crystals. Arch. Rational Mech. Anal. 103, 1988, pp. 237–277.

    Google Scholar 

  14. I. Fonseca, The lower quasi-convex envelope of stored energy function for an elastic crystal. J. Math. Pures Appl. 67, 1988, pp. 175–195.

    Google Scholar 

  15. P. Podio-Guidugli, Il criterio di snervamento della sottoenergia, pp. 559–568 of G. Ceradini's Anniversary Volume, Tip. Esagrafica: Roma, 1988.

    Google Scholar 

  16. W. Noll, On the foundations of the mechanics of continuous media. Carnegie Inst. Tech. Dept. Math. Rep. No. 17, June 1957.

  17. W. Noll, A mathematical theory of the behavior of continuous media. Arch. Rational Mech. Anal. 2, 1958, pp. 197–226.

    Google Scholar 

  18. C. Truesdell, A theorem on the isotropy groups of a hyperelastic material. Proc. Nat. Acad. Sci. U.S.A. 52, 1964, pp. 1081–1083.

    Google Scholar 

  19. M. E. Gurtin, An Introduction to Continuum Mechanics. Academic Press, 1981.

  20. C. Truesdell & W. Noll, The Non-Linear Field Theories of Mechanics. Handbuch der Physik III/3, S. Flügge Ed. Springer-Verlag, 1965.

  21. P. R. Halmos, Finite-Dimensional Vector Spaces. Van Nostrand, 1958.

  22. P. Lancaster & M. Tismenetsky, The Theory of Matrices. Academic Press, 1985.

  23. M. Giaquinta, G. Modica & J. Souček, Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 106, 1989, pp. 97–159. Erratum and addendum, ibid. 109, 1990, pp. 385–392.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Civile, Università di Roma, 00173, Tor Vergata, Roma

    P. Podio-Guidugli & G. Vergara Caffarelli

  2. Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma, 00161, La Sapienza, Roma

    P. Podio-Guidugli & G. Vergara Caffarelli

Authors
  1. P. Podio-Guidugli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Vergara Caffarelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by M. E. Gurtin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Podio-Guidugli, P., Caffarelli, G.V. Extreme elastic deformations. Arch. Rational Mech. Anal. 115, 311–328 (1991). https://doi.org/10.1007/BF00375278

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00375278

Keywords

Search

Navigation