@article{AIHPC_2004__21_3_271_0, author = {Mora, Maria Giovanna and M\"uller, Stefan}, title = {A nonlinear model for inextensible rods as a low energy $\Gamma $-limit of three-dimensional nonlinear elasticity}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {271--293}, publisher = {Elsevier}, volume = {21}, number = {3}, year = {2004}, doi = {10.1016/j.anihpc.2003.08.001}, zbl = {1109.74028}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2003.08.001/} }
TY - JOUR AU - Mora, Maria Giovanna AU - Müller, Stefan TI - A nonlinear model for inextensible rods as a low energy $\Gamma $-limit of three-dimensional nonlinear elasticity JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 271 EP - 293 VL - 21 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2003.08.001/ DO - 10.1016/j.anihpc.2003.08.001 LA - en ID - AIHPC_2004__21_3_271_0 ER -
%0 Journal Article %A Mora, Maria Giovanna %A Müller, Stefan %T A nonlinear model for inextensible rods as a low energy $\Gamma $-limit of three-dimensional nonlinear elasticity %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 271-293 %V 21 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2003.08.001/ %R 10.1016/j.anihpc.2003.08.001 %G en %F AIHPC_2004__21_3_271_0
Mora, Maria Giovanna; Müller, Stefan. A nonlinear model for inextensible rods as a low energy $\Gamma $-limit of three-dimensional nonlinear elasticity. Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 3, pp. 271-293. doi : 10.1016/j.anihpc.2003.08.001. http://www.numdam.org/articles/10.1016/j.anihpc.2003.08.001/
[1] A variational definition for the strain energy of an elastic string, J. Elasticity 25 (1991) 137-148. | MR | Zbl
, , ,[2] The Theory of Rods, Handbuch der Physik, vol. VIa, Springer-Verlag, 1972.
,[3] Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995. | MR | Zbl
,[4] Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods, J. Elasticity 19 (1988) 111-161. | MR | Zbl
, , , , ,[5] An Introduction to Γ-convergence, Birkhäuser, Boston, 1993. | Zbl
,[6] 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
, , ,[7] The Föppl von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 201-206. | Zbl
, , ,[8] G. Friesecke, R.D. James, S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence, in preparation. | Zbl
[9] Über das Gleichgewicht und die Bewegungen eines unendlich dünnen Stabes, J. Reine Angew. Math. (Crelle) 56 (1859) 285-313. | Zbl
,[10] On Saint-Venant's problem for an elastic strip, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988) 161-181. | MR | Zbl
,[11] Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity, Arch. Rational Mech. Anal. 102 (1988) 205-229. | MR | Zbl
,[12] M.G. Mora, S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by Γ-convergence, Calc. Var., in press. | Zbl
[13] Comportement asymptotique des solutions du système de l'élasticité linéarisée anisotrope hétérogène dans des cylindres minces, C. R. Acad. Sci. Paris, Sér. I Math. 328 (1999) 179-184. | MR | Zbl
, ,[14] Effets non locaux dans le passage 3d-1d en élasticité linéarisée anisotrope hétérogène, C. R. Acad. Sci. Paris, Sér. I Math. 330 (2000) 745-750. | MR | Zbl
, ,[15] Mathematical Problems in Elasticity and Homogenization, North-Holland, 1992. | MR | Zbl
, , ,[16] O. Pantz, Le modèle de poutre inextensionnelle comme limite de l'élasticité non-linéaire tridimensionnelle, Preprint, 2002.
[17] Mathematical Models for Elastic Structures, Cambridge University Press, 1997. | MR | Zbl
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