10. References
J. E. Adkins (1955a), Finite deformation of materials exhibiting curvilinear aeolotropy, Proc. Roy. Soc. Lond. A 229, 119–134.
J. E. Adkins (1955b), Some general results in the theory of large elastic deformations, Proc. Roy. Soc. Lond. A 231, 75–90.
J. E. Adkins & A. E. Green (1961), The finite flexure of an aeolotropic elastic cuboid, Arch. Rational Mech. Anal. 8, 9–14.
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.
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.
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.
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.
J. M. Ball (1981a), Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinburgh 88A, 315–328.
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.
J. M. Ball (1982), Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil, Trans. Roy. Soc. London A 306, 557–611.
H. Brezis (1968), Équations et inéquations nonlinéaires dans les espaces vectoriels en dualité, Ann. Inst. Fourier, 18, 115–175.
B. Budiansky & G. F. Carrier (1973), The pointless wedge, SIAM J. Appl. Math. 25, 378–387.
L. Caprioli (1955), Su un criterio per l'esistenza dell'energia di deformazione. Boll. Un. Mat. Ital. (3) 10, 481–483.
B. D. Coleman (1962), Mechanical and thermodynamical admissibility of stress-strain functions, Arch. Rational Mech. Anal. 9, 172–186.
G. M. de La Penha & L. A. Madeiros, eds. (1978), Contemporary Developments in Continuum Mechanics and Partial Differential Equations, North Holland, Amsterdam.
J. L. Ericksen (1955), Deformations possible in every compressible, perfectly elastic material, J. Math. & Phys. 34, 126–128.
J. L. Ericksen (1980), Some phase transitions in crystals, Arch. Rational Mech. Anal. 73, 99–124.
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.
A. E. Green & J. E. Adkins (1960), Large Elastic Deformations, Clarendon Press, Oxford.
A. E. Green & E. W. Wilkes (1954), Finite plane strain for orthotropic bodies, J. Rational Mech. Anal. 3, 713–723.
M. Hayes (1969), Static implications of the strong-ellipticity condition, Arch. Rational Mech. Anal. 33, 181–191.
R. Hill (1968), On constitutive inequalities for simple materials — I, J. Mech. Phys. Solids 16, 229–242.
W. W. Klingbeil & R. T. Shield (1966), On a class of solutions in plane finite elasticity, Z. Angew. Math. Phys. 17, 489–511.
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.
J. L. Lions (1969), Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris.
E. J. McShane (1938), Some existence theorems for the problems of the calculus of variations, Duke Math. J. 4, 132–156.
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.
M. Syngh & A. C. Pipkin (1965), Note on Ericksen's problem, Z. angew. Math. Phys. 16, 706–709.
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.
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00281086