Qualitative properties of a continuum theory for thin films
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 43-75.
@article{AIHPC_2008__25_1_43_0,
     author = {Schmidt, Bernd},
     title = {Qualitative properties of a continuum theory for thin films},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {43--75},
     publisher = {Elsevier},
     volume = {25},
     number = {1},
     year = {2008},
     doi = {10.1016/j.anihpc.2006.09.001},
     mrnumber = {2383078},
     zbl = {1142.74026},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.001/}
}
TY  - JOUR
AU  - Schmidt, Bernd
TI  - Qualitative properties of a continuum theory for thin films
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2008
SP  - 43
EP  - 75
VL  - 25
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.001/
DO  - 10.1016/j.anihpc.2006.09.001
LA  - en
ID  - AIHPC_2008__25_1_43_0
ER  - 
%0 Journal Article
%A Schmidt, Bernd
%T Qualitative properties of a continuum theory for thin films
%J Annales de l'I.H.P. Analyse non linéaire
%D 2008
%P 43-75
%V 25
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.001/
%R 10.1016/j.anihpc.2006.09.001
%G en
%F AIHPC_2008__25_1_43_0
Schmidt, Bernd. Qualitative properties of a continuum theory for thin films. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 43-75. doi : 10.1016/j.anihpc.2006.09.001. http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.001/

[1] Ball J.M., Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 63 (1977) 337-403. | MR | Zbl

[2] Blanc X., Lebris C., Lions P.-L., Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus, C. R. Acad. Sci. Paris, Ser. I 332 (2001) 949-956. | MR | Zbl

[3] Blanc X., Lebris C., Lions P.-L., From molecular models to continuum mechanics, Arch. Rational Mech. Anal. 164 (2002) 341-381. | MR | Zbl

[4] Braides A., Nonlocal variational limits of discrete systems, Commun. Contemp. Math. 2 (2000) 285-297. | MR | Zbl

[5] Braides A., Gelli M.S., Limits of discrete systems with long-range interactions, J. Convex Anal. 9 (2002) 363-399. | MR | Zbl

[6] Braides A., Gelli M.S., Continuum limits of discrete systems without convexity hypotheses, Math. Mech. Solids 7 (2002) 41-66. | MR | Zbl

[7] Ciarlet P.G., Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity, North-Holland, Amsterdam, 1988. | MR | Zbl

[8] Ciarlet P.G., Mathematical Elasticity. Vol. II: Theory of Plates, North-Holland, Amsterdam, 1997. | MR | Zbl

[9] Dacorogna B., Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989. | MR | Zbl

[10] Dal Maso G., An Introduction to Γ-Convergence, Birkhäuser, Boston, 1993. | MR | Zbl

[11] Dolzmann G., Variational Methods for Crystalline Microstructure - Analysis and Computation, Springer-Verlag, Berlin, 2003. | MR | Zbl

[12] Friesecke G., James R.D., A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods, J. Mech. Phys. Solids 48 (2000) 1519-1540. | MR | Zbl

[13] Friesecke G., James R.D., Müller S., Rigorous derivation of nonlinear plate theory and geometric rigidity, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 173-178. | MR | Zbl

[14] Friesecke G., James R.D., Müller S., A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Comm. Pure Appl. Math. 55 (2002) 1461-1506. | MR | Zbl

[15] Friesecke G., James R.D., Müller S., A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence, Arch. Rational Mech. Anal. 180 (2006) 183-236. | MR | Zbl

[16] Friesecke G., James R.D., Mora M.G., Müller S., Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence, C. R. Acad. Sci. Paris, Ser. I 336 (2003) 697-702. | MR | Zbl

[17] Le Dret H., Raoult A., La modèle membrane non linéaire comme limite variationnelle de l'élasticité non linéaire tridimensionnelle, C. R. Acad. Sci. Paris, Ser. I 317 (1993) 221-226. | MR | Zbl

[18] Le Dret H., Raoult A., The nonlinear membrane model as a variational limit of three-dimensional elasticity, J. Math. Pures Appl. 74 (1995) 549-578. | MR | Zbl

[19] Le Dret H., Raoult A., The membrane shell model in nonlinear elasticity: a variational asymptotic derivation, J. Nonlinear Sci. 6 (1996) 59-84. | MR | Zbl

[20] Love A.E.H., A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press, Cambridge, 1927. | JFM

[21] B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig. | MR | Zbl

[22] B. Schmidt, Effective theories for thin elastic films, PhD thesis, Universität Leipzig, 2006. | Zbl

[23] Weiner J.H., Statistical Mechanics of Elasticity, J. Wiley & Sons, New York, 1983. | Zbl

Cité par Sources :