Skip to main content
Log in

Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders

  • 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.

10. References

  • J. E. Adkins (1955a), Finite deformation of materials exhibiting curvilinear aeolotropy, Proc. Roy. Soc. Lond. A 229, 119–134.

    Google Scholar 

  • J. E. Adkins (1955b), Some general results in the theory of large elastic deformations, Proc. Roy. Soc. Lond. A 231, 75–90.

    Google Scholar 

  • J. E. Adkins & A. E. Green (1961), The finite flexure of an aeolotropic elastic cuboid, Arch. Rational Mech. Anal. 8, 9–14.

    Google Scholar 

  • J. C. Alexander & S. S. Antman (1983), Global behavior of solutions of nonlinear equations depending on infinite-dimensional parameters, Indiana U. Math. J. 32.

  • J. C. Alexander & J. A. Yorke (1976), The implicit function theorem and global methods of cohomology. J. Functional Analysis 21, 330–339.

    Google Scholar 

  • S. S. Antman (1972), The Theory of Rods, Handbuch der Physik VI a/2, edited by C. Truesdell, Springer-Verlag, 641–703.

  • S. S. Antman (1976), Ordinary differential equations of one-dimensional nonlinear elasticity, Arch. Rational Mech. Anal. 61, 307–393.

    Google Scholar 

  • S. S. Antman (1978), A family of semi-inverse problems of nonlinear elasticity, in de La Penha & Madeiros (1978), 1–24.

  • S. S. Antman (1979), The eversion of thick spherical shells, Arch. Rational Mech. Anal. 70, 113–123.

    Google Scholar 

  • S. S. Antman (1984), Constitutive restrictions permitting cavitation in nonlinearly elastic cylinders, in preparation.

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

    Google Scholar 

  • J. M. Ball (1981a), Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinburgh 88A, 315–328.

    Google Scholar 

  • J. M. Ball (1981b), Remarques sur l'existence et la régularité des solution d'elastostatique nonlinéaire, in Recent Contributions to Nonlinear Partial Differential Equations, edited by H. Berestycki & H. Brezis, Pitman, London.

    Google Scholar 

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

    Google Scholar 

  • H. Brezis (1968), Équations et inéquations nonlinéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier, 18, 115–175.

    Google Scholar 

  • B. Budiansky & G. F. Carrier (1973), The pointless wedge, SIAM J. Appl. Math. 25, 378–387.

    Google Scholar 

  • L. Caprioli (1955), Su un criterio per l'esistenza dell'energia di deformazione. Boll. Un. Mat. Ital. (3) 10, 481–483.

    Google Scholar 

  • B. D. Coleman (1962), Mechanical and thermodynamical admissibility of stress-strain functions, Arch. Rational Mech. Anal. 9, 172–186.

    Google Scholar 

  • G. M. de La Penha & L. A. Madeiros, eds. (1978), Contemporary Developments in Continuum Mechanics and Partial Differential Equations, North Holland, Amsterdam.

    Google Scholar 

  • J. L. Ericksen (1955), Deformations possible in every compressible, perfectly elastic material, J. Math. & Phys. 34, 126–128.

    Google Scholar 

  • J. L. Ericksen (1980), Some phase transitions in crystals, Arch. Rational Mech. Anal. 73, 99–124.

    Google Scholar 

  • J. W. Gibbs & E. B. Wilson (1901), Vector Analysis, Yale Univ. Press.

  • A. E. Green (1965), Finite elastic deformation of compressible isotropic bodies, Proc. Roy. Soc. Lond. A 227, 271–278.

    Google Scholar 

  • A. E. Green & J. E. Adkins (1960), Large Elastic Deformations, Clarendon Press, Oxford.

    Google Scholar 

  • A. E. Green & E. W. Wilkes (1954), Finite plane strain for orthotropic bodies, J. Rational Mech. Anal. 3, 713–723.

    Google Scholar 

  • M. Hayes (1969), Static implications of the strong-ellipticity condition, Arch. Rational Mech. Anal. 33, 181–191.

    Google Scholar 

  • R. Hill (1968), On constitutive inequalities for simple materials — I, J. Mech. Phys. Solids 16, 229–242.

    Google Scholar 

  • W. W. Klingbeil & R. T. Shield (1966), On a class of solutions in plane finite elasticity, Z. Angew. Math. Phys. 17, 489–511.

    Google Scholar 

  • M. A. Krasnosel'skii & Ya. B. Rutitskii (1958), Convex Functions and Orlicz Spaces, in Russian, Fizmatgiz; English transl. by L. F. Boron (1961), Noordhoff, Groningen.

    Google Scholar 

  • J. L. Lions (1969), Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris.

    Google Scholar 

  • E. J. McShane (1938), Some existence theorems for the problems of the calculus of variations, Duke Math. J. 4, 132–156.

    Google Scholar 

  • J. Nečas (1967), Les Méthodes Directes en Théorie des Équations Elliptiques, Masson.

  • R. S. Rivlin (1948), Large elastic deformations of isotropic materials, IV. Further developments of the general theory. Phil. Trans. Roy. Soc. Lond. A 241, 379–397.

    Google Scholar 

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

    Google Scholar 

  • C. Truesdell & W. Noll (1965), The Non-linear Field Theories of Mechanics, Handbuch der Physik III/3, Springer-Verlag.

  • C. Truesdell (1978), Some challenges offered to analysis by rational thermomechanics, in de La Penha & Madeiros (1976), 495–603.

  • C.-C. Wang & C. Truesdell (1973), Introduction to Rational Elasticity, Noordhoff.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Antman, S.S. Regular and singular problems for large elastic deformations of tubes, wedges, and cylinders. Arch. Rational Mech. Anal. 83, 1–52 (1983). https://doi.org/10.1007/BF00281086

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00281086

Keywords

Navigation