Critical points in the energy of hyperelastic materials

P. Quintela-Estevez

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1990)

  • Volume: 24, Issue: 1, page 103-132
  • ISSN: 0764-583X

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Quintela-Estevez, P.. "Critical points in the energy of hyperelastic materials." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 24.1 (1990): 103-132. <http://eudml.org/doc/193585>.

@article{Quintela1990,
author = {Quintela-Estevez, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {W(sup 1, infinity)-topology; W(sup 1,p)-topology; positivity of the second variation of the energy; local minimizers; inverse function theorem; pure displacement problem; small body forces; polconvexity},
language = {eng},
number = {1},
pages = {103-132},
publisher = {Dunod},
title = {Critical points in the energy of hyperelastic materials},
url = {http://eudml.org/doc/193585},
volume = {24},
year = {1990},
}

TY - JOUR
AU - Quintela-Estevez, P.
TI - Critical points in the energy of hyperelastic materials
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1990
PB - Dunod
VL - 24
IS - 1
SP - 103
EP - 132
LA - eng
KW - W(sup 1, infinity)-topology; W(sup 1,p)-topology; positivity of the second variation of the energy; local minimizers; inverse function theorem; pure displacement problem; small body forces; polconvexity
UR - http://eudml.org/doc/193585
ER -

References

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  2. J. M. BALL[ 1977] : Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63, 337-403. Zbl0368.73040MR475169
  3. J. M. BALL, J. C. CURRIE, P. J. OLVER [ 1981] : Null Lagrangians, weak continuity and variational problems of arbitrary order. J. Functional Analysis -41, 135-174. Zbl0459.35020MR615159
  4. J. M. BALL, R. J. KNOPS, J. E. MARSDEN [ 1978] : Two examples in nonlinear elasticity. Proceedings, Conferences on Nonlinear Analysis, Besançon 1977, pp. 41-49, Springer-Verlag, Berlin. Zbl0386.73012MR519421
  5. P. G. CIARLET [ 1986] : Élasticité Tridimensionnelle, Collection Recherches en Mathématiques Appliquées, Masson. Zbl0572.73027MR819990
  6. P. G. CIARLET [ 1987] : Mathematical Elasticity, vol. I. North Holland, Amsterdam. Zbl0648.73014MR936420
  7. P. G. CIARLET, G. GEYMONAT [ 1982] : Sur les lois de comportement en élasticité non linéaire compressible. C.R. Acad. Sci. Paris. Ser. A 295, 423-426. Zbl0497.73017MR695540
  8. P. G. CIARLET, J. NECAS [ 1985] : Global invertibility and self-contact conditions, in nonlinear, three-dimensional elasticity, to appear. Zbl0585.73018
  9. D. R. J. CHILLINGWORTH, J. E. MARSDEN, Y. H. WAN [ 1982] : Symmetry and bifurcation in three dimensional elasticity. Part. I. Arch. Rational Mech. Anal. 80, 295-331. Zbl0509.73018MR677564
  10. D. R. J. CHILLINGWORTH, J. E. MARSDEN, Y. H. WAN[ 1983] : Symmetry and bifurcation in three dimensional elasticity. Part II. Arch. Rational Mech. Anal. 83, 363-395. Zbl0536.73010MR714980
  11. R. J. KNOPS, L. E. PAYNE [ 1978] : On potential wells and stability in nonlinear elasticity. Math. Proc. Camb. Phil. Soc. 84, 177-190. Zbl0384.73026MR471533
  12. LE DRET [ 1987] : Structure of the set of equilibrated loads in nonlinear elasticity and applications to existence and nonexistence. J. Elasticity 17, 123-141. Zbl0654.73029MR885602
  13. J. E. MARSDEN, T. J. R. HUGHES [ 1983] : Mathematical Foundations of Elasticity. Prentice-Hall, Englewood Cliffs. Zbl0545.73031
  14. A. RAOULT [ 1986] : Non-polyconvexity of the stored energy function of a St. Venant-Kirchhoff material. Aplikace Matematiky. Zbl0608.73023
  15. T. VALENT [ 1979] : Teoremi di esistenza e unicita in elastostatica finita. Rend. Sem. Mat. Univ. Padova 60, 165-181. Zbl0425.73011
  16. C.-C. WANG, C. TRUESDELL [ 1973] : Introduction to Rational Elasticity. Noordhoff, Groningen. Zbl0308.73001MR468442

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