[Quelques inégalités de Korn unilatérales et leur application à un problème de contact avec inclusions]
Dans une première partie sont démontrées quelques inégalités de Korn unilatérales qui semblent nouvelles.
Ces inégalités sont alors utilisées de façon essentielle dans la démontration de lʼexistence dʼune solution pour un problème de contact unilatéral dans une matrice avec des inclusions de diverses formes (les conditions dépendent de façon remarquable de la forme de chaque inclusion).
In the first part of this note, some unilateral inequalities of the Korn type are established. These inequalities seem to be new.
In the second part, these inequalities are used in an essential way to prove the existence of a solution (which is not necessarily unique) for a unilateral contact problem involving a matrix material with inclusions of various shapes (the conditions depend on the shape of each inclusion in a remarkable way).
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@article{CRMATH_2012__350_17-18_861_0,
author = {Damlamian, Alain},
title = {Some unilateral {Korn} inequalities with application to a contact problem with inclusions},
journal = {Comptes Rendus. Math\'ematique},
pages = {861--865},
publisher = {Elsevier},
volume = {350},
number = {17-18},
year = {2012},
doi = {10.1016/j.crma.2012.09.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.09.006/}
}
TY - JOUR AU - Damlamian, Alain TI - Some unilateral Korn inequalities with application to a contact problem with inclusions JO - Comptes Rendus. Mathématique PY - 2012 SP - 861 EP - 865 VL - 350 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.09.006/ DO - 10.1016/j.crma.2012.09.006 LA - en ID - CRMATH_2012__350_17-18_861_0 ER -
%0 Journal Article %A Damlamian, Alain %T Some unilateral Korn inequalities with application to a contact problem with inclusions %J Comptes Rendus. Mathématique %D 2012 %P 861-865 %V 350 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.09.006/ %R 10.1016/j.crma.2012.09.006 %G en %F CRMATH_2012__350_17-18_861_0
Damlamian, Alain. Some unilateral Korn inequalities with application to a contact problem with inclusions. Comptes Rendus. Mathématique, Tome 350 (2012) no. 17-18, pp. 861-865. doi : 10.1016/j.crma.2012.09.006. http://www.numdam.org/articles/10.1016/j.crma.2012.09.006/
[1] D. Cioranescu, A. Damlamian, J. Orlik, Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptot. Anal., in press.
[2] Les inéquations en mécanique et en physique, Travaux et Recherches Mathématiques, vol. 21, Dunod, Paris, 1972
[3] Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno, Atti Acc. Naz. Lincei (s. VIII), Volume VII (1964)
[4] Elastostatics problems with unilateral constraints, Séminaire Jean Leray, Volume 3 (1966–1967), pp. 64-68
[5] Unilateral constraints in elasticity, Actes Congrès Int. Math. (Nice 1970), vol. 3, Gauthier–Villars, Paris, 1970, pp. 79-84
[6] Une inégalité fondamentale de la théorie de lʼélasticité, Bull. Soc. Roy. Sci. Liège, Volume 31 (1962), pp. 182-191
[7] Numerical methods for unilateral problems in solid mechanics, Handbook of Numerical Analysis, vol. IV, North-Holland, Amsterdam, 1996, pp. 313-485
[8] Solution of Variational Inequalities in Mechanics, Applied Mathematical Sciences, vol. 66, Springer-Verlag, New York, 1988 (x+275 pp. Translated from Slovak by J. Jarník) (ISBN: 0-387-96597-1)
[9] Contact Problems in Elasticity, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1988
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