A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity

Maria Giovanna Mora; Stefan Müller

Annales de l'I.H.P. Analyse non linéaire (2004)

  • Volume: 21, Issue: 3, page 271-293
  • ISSN: 0294-1449

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Mora, Maria Giovanna, and Müller, Stefan. "A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity." Annales de l'I.H.P. Analyse non linéaire 21.3 (2004): 271-293. <http://eudml.org/doc/78619>.

@article{Mora2004,
author = {Mora, Maria Giovanna, Müller, Stefan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
language = {eng},
number = {3},
pages = {271-293},
publisher = {Elsevier},
title = {A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity},
url = {http://eudml.org/doc/78619},
volume = {21},
year = {2004},
}

TY - JOUR
AU - Mora, Maria Giovanna
AU - Müller, Stefan
TI - A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2004
PB - Elsevier
VL - 21
IS - 3
SP - 271
EP - 293
LA - eng
UR - http://eudml.org/doc/78619
ER -

References

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  2. [2] Antman S.S, The Theory of Rods, Handbuch der Physik, vol. VIa, Springer-Verlag, 1972. 
  3. [3] Antman S.S, Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995. Zbl0820.73002MR1323857
  4. [4] Cimetière A, Geymonat G, Le Dret H, Raoult A, Tutek Z, Asymptotic theory and analysis for displacements and stress distribution in nonlinear elastic straight slender rods, J. Elasticity19 (1988) 111-161. Zbl0653.73010MR937626
  5. [5] Dal Maso G, An Introduction to Γ-convergence, Birkhäuser, Boston, 1993. Zbl0816.49001
  6. [6] 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. Zbl1021.74024MR1916989
  7. [7] Friesecke G, James R.D, Müller S, The Föppl von Kármán plate theory as a low energy Γ-limit of nonlinear elasticity, C. R. Acad. Sci. Paris, Ser. I335 (2002) 201-206. Zbl1041.74043
  8. [8] G. Friesecke, R.D. James, S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence, in preparation. Zbl1100.74039
  9. [9] Kirchhoff G, Über das Gleichgewicht und die Bewegungen eines unendlich dünnen Stabes, J. Reine Angew. Math. (Crelle)56 (1859) 285-313. 
  10. [10] Mielke A, On Saint-Venant's problem for an elastic strip, Proc. Roy. Soc. Edinburgh Sect. A110 (1988) 161-181. Zbl0657.73003MR963848
  11. [11] Mielke A, Saint-Venant's problem and semi-inverse solutions in nonlinear elasticity, Arch. Rational Mech. Anal.102 (1988) 205-229. Zbl0651.73006MR944546
  12. [12] M.G. Mora, S. Müller, Derivation of the nonlinear bending-torsion theory for inextensible rods by Γ-convergence, Calc. Var., in press. Zbl1053.74027
  13. [13] Murat F, Sili A, 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. Zbl0929.74010MR1669058
  14. [14] Murat F, Sili A, 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. Zbl0962.74009MR1763923
  15. [15] Oleinik O.A, Shamaev A.S, Yosifian G.A, Mathematical Problems in Elasticity and Homogenization, North-Holland, 1992. Zbl0768.73003MR1195131
  16. [16] O. Pantz, Le modèle de poutre inextensionnelle comme limite de l'élasticité non-linéaire tridimensionnelle, Preprint, 2002. 
  17. [17] Villaggio P, Mathematical Models for Elastic Structures, Cambridge University Press, 1997. Zbl0978.74002MR1486043

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