Résumé
En 1977, John Ball a obtenu une série de résultats d'existence très importants en hyperélasticité. L'objet de cet article est l'extension de ses résultats dans deux directions, premièrement en considérant des conditions aux limites unilatérales correspondant au contact sans frottement, deuxièmement en admettant une contrainte de “blocage” dans l'ensemble des déformations admissibles.
Abstract
In 1977 John Ball obtained a series of very important existence results in hyperelasticity. The objective of the present paper is to extend his results in two directions, first by considering unilateral boundary conditions corresponding to contact without friction, secondly by allowing “locking” constraints in the set of admissible deformations.
This is a preview of subscription content, log in via an institution to check access.
References
Ball, J. M. [1977]: Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63, 337–403.
Ciarlet, P. G. [1983]: Lectures on Three-Dimensional Elasticity, Tata Institute Lectures on Mathematics, Springer-Verlag, Berlin.
Ciarlet, P. G. [1985]: Topics in Mathematical Elasticity, Vol. 1, North-Holland, Amsterdam.
Ciarlet, P. G. & Geymonat, G. [1982]: Sur les lois de comportement en élasticité non-linéaire compressible, C. R. Acad. Sci. Paris Sér. A 295, 423–426.
Ciarlet, P. G. & Nečas, J. [1984]: Problèmes unilatéraux en élasticité non linéaire tri-dimensionnelle, C. R. Acad. Sci. Paris, Sér. A 298, 189–192.
Duvaut, G. & Lions, J. L. [1972]: Les Inéquations en Mécanique et en Physique, Dunod, Paris.
Fichera, G. [1972]: Boundary value problems of elasticity with unilateral constraints, Handbuch der Physik, Vol. VIa/2, 391–424, Springer-Verlag, Berlin, Heidelberg, New-York.
Germain, P. [1972]: Mécanique des Milieux Continus, Tome 1, Masson, Paris.
Guo Zhong-Heng [1980]: The unified theory of variational principles in nonlinear elasticity, Arch. Mech. 32, 577–596.
Gurtin, M. E. [1981]: Introduction to Continuum Mechanics, Academic Press, New York.
Hlaváček, I.; Haslinger, J.; Nečas, J. & Lovíšek, J. [1982]: Solution of Variational Inequalities in Mechanics, Alfa, Bratislava.
Marsden, J. E. & Hughes, T. J. R. [1983]: Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs.
Nečas, J. [1967]: Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris.
Nečas, J. [1983]: Introduction to the Theory of Nonlinear Equations, Teubner Texte zur Mathematik, Band 52, Leipzig.
Nečas, J. & Hlaváček, I. [1981]: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier, Amsterdam.
Ogden, R. W. [1972]: Large deformation isotropic elasticity: On the correlation of theory and experiment for compressible rubberlike solids, Proc. Roy. Soc. London A 328, 567–583.
Prager, W. [1957]: On ideal locking materials, Transaction of the Society of Rheology 1, 169–175.
Truesdell, C. & Noll, W. [1965]: The non-linear field theories of mechanics, Handbuch der Physik, Vol. III/3, 1–602.
Wang, C.-C. & Truesdell, C. [1973]: Introduction to Rational Elasticity, Noordhoff, Groningen.
Author information
Authors and Affiliations
Additional information
Communicated by S. Antman
Rights and permissions
About this article
Cite this article
Ciarlet, P.G., Nečas, J. Unilateral problems in nonlinear, three-dimensional elasticity. Arch. Rational Mech. Anal. 87, 319–338 (1985). https://doi.org/10.1007/BF00250917
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00250917