Incompressible limit behaviour of slightly compressible nonlinear elastic materials

H. Le Dret

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1986)

  • Volume: 20, Issue: 2, page 315-340
  • ISSN: 0764-583X

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Le Dret, H.. "Incompressible limit behaviour of slightly compressible nonlinear elastic materials." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 20.2 (1986): 315-340. <http://eudml.org/doc/193479>.

@article{LeDret1986,
author = {Le Dret, H.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear elastostatics; incompressibility as limit compressibility; penalised coercive polyconvex incompressible strain energy function; minimizers for the penalised (compressible) energy; converge weakly; incompressible energy minimizer; Strong convergence; existence theorems of Ball; formal asymptotic expansion; strong solution to the equilibrium equations; incompressible equilibrium equations},
language = {eng},
number = {2},
pages = {315-340},
publisher = {Dunod},
title = {Incompressible limit behaviour of slightly compressible nonlinear elastic materials},
url = {http://eudml.org/doc/193479},
volume = {20},
year = {1986},
}

TY - JOUR
AU - Le Dret, H.
TI - Incompressible limit behaviour of slightly compressible nonlinear elastic materials
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1986
PB - Dunod
VL - 20
IS - 2
SP - 315
EP - 340
LA - eng
KW - nonlinear elastostatics; incompressibility as limit compressibility; penalised coercive polyconvex incompressible strain energy function; minimizers for the penalised (compressible) energy; converge weakly; incompressible energy minimizer; Strong convergence; existence theorems of Ball; formal asymptotic expansion; strong solution to the equilibrium equations; incompressible equilibrium equations
UR - http://eudml.org/doc/193479
ER -

References

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  1. [1] R. A. ADAMS, Sobolev spaces, Academic Press, New York (1975). Zbl0314.46030MR450957
  2. [2] J. M. BALL, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal. 63 (1977), pp. 307-403. Zbl0368.73040MR475169
  3. [3] J. M. BALL, J. C. CURRIE, P. J. OLVER, Null Lagrangians, weak continuity and variational problems of arbitrary order, J. Functional Analysis 41 (1981), pp. 135-174. Zbl0459.35020MR615159
  4. [4] J. M. BALL, J. E. MARSDEN, Quasiconvexity at the boundary, positivity of the second variation and elastic stability, Arch. Rat. Mech. Anal. 86 (1984), pp. 251-277. Zbl0552.73006MR751509
  5. [5] P. G. CIARLET, G. GEYMONAT, Sur les lois de comportement en élasticité non linéaire compressible, C.R. Acad. Sci. Paris, Série A, 295 (1982), pp. 423-426. Zbl0497.73017MR695540
  6. [6] D. G. EBIN, The motion of slightly compressible fluids viewed as a motion with strong constraining force, Ann of Math 105 (1977), pp. 141-200. Zbl0373.76007MR431261
  7. [7] G. GEYMONAT, E. SANCHEZ PALENCIA, Spectral properties of certain stiff problems in elasticity and acoustics part II, Pubblicaziom dell' Istituto Matematico del Politecnico di Torino, Serie II, No 21 (1982). Zbl0561.35059
  8. [8] H. LE DRET, Constitutive laws and existence questions in incompressible nonlinear elasticity, J Elasticity 15 (1985), pp. 369-387. Zbl0648.73013MR817376
  9. [9] P. LE TALLEC, Les problèmes d'équilibre d'un corps hypérelastique incompressible en grandes déformations, These d'État, Université Pierre et Marie Curie, Paris (1981). 
  10. [10] J. L. LIONS, Réduction à des problèmes de Cauchy-Kowalewska, 2e cicle, CIME, Numerical analysis of partial differential equations, Ispra 1967, Cremonese, Roma (1968). Zbl0179.22502MR244605
  11. [11] L. NIRENBERG, Topics in nonlinear functional analysis, N Y U Courant Institute Lecture Notes, New York (1974). Zbl0286.47037MR488102
  12. [12] R. W. OGDEN, Large deformation isotropic elasticity on the correlation of theory and experiment for compressible rubberlike solids, Proc R Soc Lond A 328 (1972), pp. 567-583. Zbl0245.73032
  13. [13] M. G. PELISSIER, Résolution numérique de quelques problèmes raides en mécanique des milieux faiblement compressibles Calcolo 12 (1975), pp. 275-314. Zbl0328.65060MR421247
  14. [14] J. M. POUYOT, Études numériques de problèmes d'élasticité non lineaire application au calcul d'elastomeres dans des configurations sévères, These de 3e cycle, Université de Bordeaux I (1984). 
  15. [15] R. TEMAM, Une méthode d'approximation de la solution des équations de Navier-Stokes, Bull S M F 96 (1968), pp. 115-152. Zbl0181.18903MR237972
  16. [16] C. TRUESDELL, W. NOLL, The nonlinear field théories of mechanics, Handbuch der Physik vol III/3, Springer Verlag, Berlin (1965). Zbl0779.73004MR1215940
  17. [17] T. VALENT, Sulla differenziabilita dell'operatore di Nemytsky, Rend Acc Naz Lincei 65 (1978), pp. 15-26. Zbl0424.35084

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