Skip to main content
Log in

Cavitation and phase transition of hyperelastic fluids

  • 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

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

Instant access to the full article PDF.

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. J. M. Ball, Strict convexity, strong ellipticity, and regularity in the calculus of variations, Math. Proc. Camb. Phil. Soc. 87 (1980), pp. 501–513.

    Google Scholar 

  3. J. M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. (London) A 306 (1982), pp. 557–611.

    Google Scholar 

  4. J. Carr, M. E. Gurtin & M. Slemrod, One-dimensional structured phase transformations under prescribed loads, MRC Report no. 2559, Mathematics Research Center, University of Wisconsin-Madison, 1983.

  5. B. Dacorogna, Weak continuity and weak semicontinuity of non-linear functionals, Lecture Notes in Mathematics no. 922, Springer-Verlag, Berlin, 1982.

    Google Scholar 

  6. B. Dacorogna, A relaxation theorem and its application to the equilibrium of gases, Arch. Rational Mech. Anal. 77 (1981), pp. 359–386.

    Google Scholar 

  7. B. Dacorogna, Quasiconvexity and relaxation of nonconvex problems in the calculus of variations, J. Funct. Anal. 46 (1982), pp. 102–118.

    Google Scholar 

  8. J. L. Ericksen, Equilibrium of bars, J. Elasticity 5 (1975), pp. 191–201.

    Google Scholar 

  9. M. E. Gurtin, An introduction to continuum mechanics, Academic Press, New York, 1981.

    Google Scholar 

  10. G. H. Hardy, J. E. Littlewood & G. Polya, Inequalities, Cambridge University Press, Cambridge, 1952.

    Google Scholar 

  11. C. B. Morrey, Quasi-convexity and the lower semicontinuity of multiple integrals, Pacific J. Math. 2 (1952), pp. 25–53.

    CAS  PubMed  Google Scholar 

  12. J. E. Marsden & T. J. R. Hughes, Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, 1983.

    Google Scholar 

  13. P. Podio-Guidugli, G. Vergara Caffarelli & E. G. Virga, Discontinuous energy minimizers in nonlinear elastostatics: an example of J. Ball revisited, to appear in J. Elasticity, 1984.

  14. C. Truesdell & R. A. Toupin, The classical field theories, Handbuch der Physik III/1, S. Flügge Ed., Springer-Verlag, Berlin, 1960.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Walter Noll on his sixtieth birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Podio-Guiougli, P., Vergara Caffarelli, G. & Virga, E.G. Cavitation and phase transition of hyperelastic fluids. Arch. Rational Mech. Anal. 92, 121–136 (1986). https://doi.org/10.1007/BF00251253

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00251253

Keywords

Navigation