Skip to main content
SpringerLink
Log in

Normal configurations and the nonlinear elastostatic problems of bending, torsion, expansion, and eversion for compressible bodies

  • 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. Truesdell, C., & W. Noll, The Non-Linear Field Theories of Mechanics. In: Flügge's Handbuch der Physik, Bd. III/3. Springer, 1965.

  2. Wang, C.-C., & C. Truesdell, Introduction to Rational Elasticity. Noordhoff, 1973.

  3. Ericksen, J. L., Deformation possible in every compressible, isotropic, perfectly elastic material. J. Math. Phys. 34, 126–128 (1955).

    Google Scholar 

  4. Carroll, M. M., Finite strain solutions in compressible isotropic elasticity. J. Elasticity 20, 65–92 (1988).

    Google Scholar 

  5. Wang, C.-C., Universal solutions for incompressible laminated bodies. Arch. Rational Mech. Anal. 29, 161–192 (1968).

    Google Scholar 

  6. Rivlin, R. S., Torsion of a rubber cylinder. J. Appl. Phys. 18, 444–449 (1947).

    Google Scholar 

  7. Rivlin, R. S., Large elastic deformations of isotropic materials, IV. Further developments of the general theory. Phil. Trans. Roy. Soc. A 195, 463–473 (1949).

    Google Scholar 

  8. Rivlin, R. S., Large elastic deformations of isotropic materials, V. The problem of flexure. Proc. Roy. Soc. A 195, 463–473 (1949).

    Google Scholar 

  9. Rivlin, R. S., Large elastic deformations of isotropic materials, VI. Further results in the theory of torsion, shear, and flexure. Phil. Trans. Roy. Soc. A 242, 173–195 (1949).

    Google Scholar 

  10. Ericksen, J. L., Deformation possible in every isotropic, incompressible, perfectly elastic body. Z. angew. Math. Phys. 5, 466–489 (1954).

    Google Scholar 

  11. Singh, M., & A. C. Pipkin, Note on Ericksen's problem. Z. angew. Math. Phys. 16, 706–709 (1965).

    Google Scholar 

  12. Marris, A. W., Steady universal motions of Rivlin-Ericksen fluids. Arch. Rational Mech. Anal. 69, 335–380 (1979).

    Google Scholar 

  13. Wang, C.-C., & A. W. Marris, Proof that motions obtained in the preceding paper by Marris are universal for all incompressible isotropic simple materials. Arch. Rational Mech. Anal. 69, 381–390 (1979).

    Google Scholar 

  14. Ericksen, J. L., General solutions in the hydrostatic theory of liquid crystals. Trans. Soc. Rheology 11, 5–14 (1967).

    Google Scholar 

  15. Naghdi, P. M., & P.Y. Tang, Large deformation possible in every isotropic elastic membrane. Phil. Trans. Roy. Soc. A 287, 145–187 (1977).

    Google Scholar 

  16. Wang, C.-C., & J. J. Cross, Universal solutions for isotropic elastic membranes. Arch. Rational Mech. Anal. 65, 73–86 (1977).

    Google Scholar 

  17. Yin, W.-L., Universal solutions for general and area-preserving isotropic elastic membranes. Arch. Rational Mech. Anal. 77, 37–45 (1981).

    Google Scholar 

  18. Ogden, R. W., Nonlinear Elastic Deformations. Wiley, 1984.

  19. Antman, S. S., A family of semi-inverse problems of nonlinear elasticity. In: Contemporary Developments in Continuum Mechanics and Partial Differential Equations, (G. M. de la Penha & L. A. Madeiros, eds.) North Holland, 1978, 1–24.

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

    Google Scholar 

  21. Szeri, A. I., On the everted states of cylindrical and spherical shells. Quart. Appl. Math. 17, 49–58 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Rice University, Houston, Texas

    C. -C. Wang

Authors
  1. C. -C. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, C.C. Normal configurations and the nonlinear elastostatic problems of bending, torsion, expansion, and eversion for compressible bodies. Arch. Rational Mech. Anal. 114, 195–236 (1991). https://doi.org/10.1007/BF00385969

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00385969

Keywords

Search

Navigation