Regularity of solutions to a one dimensional plasticity model

I. Babuška; P. Shi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1998)

  • Volume: 32, Issue: 5, page 521-537
  • ISSN: 0764-583X

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Babuška, I., and Shi, P.. "Regularity of solutions to a one dimensional plasticity model." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.5 (1998): 521-537. <http://eudml.org/doc/193885>.

@article{Babuška1998,
author = {Babuška, I., Shi, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {H(2)-regularity; H(1)-regularity; quasi-static model; multilinear kinematic law; system of variational inequalities},
language = {eng},
number = {5},
pages = {521-537},
publisher = {Dunod},
title = {Regularity of solutions to a one dimensional plasticity model},
url = {http://eudml.org/doc/193885},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Babuška, I.
AU - Shi, P.
TI - Regularity of solutions to a one dimensional plasticity model
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 5
SP - 521
EP - 537
LA - eng
KW - H(2)-regularity; H(1)-regularity; quasi-static model; multilinear kinematic law; system of variational inequalities
UR - http://eudml.org/doc/193885
ER -

References

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  2. [2] I. BABUŠKA and P. SHI, A continuous Galerkin method in one dimensional plasticity, in preparation. 
  3. [3] P. BENILAN, M. G. GRANDALL and P. SACKS, Some Ll existence and dependence results for semilinear elliptic equationsunder non linear boundary conditions, Appl. Math. Optim. Vol. 17. 1988, pp. 203-224. Zbl0652.35043MR922980
  4. [4] G. DUVAULT and J. L. LIONS, Inequalities in mechanics and physics, Springer-Verlag, Berlin-New York, 1976. Zbl0331.35002MR600341
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  6. [6] W. HAN and B. D. REDDY, Computational plasticity: the variational basis and numerical analysis, Computational Mechanics Advances, 2, No. 2, 1995. Zbl0847.73078MR1361227
  7. [7] I. HLAVÁČEK, J. HASLINGER, J. NEČAS and J. LOVIŠEK, Solutions of variational inequalities in mechanics, Springer-Verlag, 1988. Zbl0654.73019MR952855
  8. [8] C. JOHNSON, Existence theorems for plasticity problems, J. Math. Pure et Appl., 55, pp. 431-444 (1976). Zbl0351.73049MR438867
  9. [9] C. JOHNSON, On plasticity with hardening, J. Math. Anal. Appl., 62, pp. 333-344 (1978). Zbl0373.73049MR489198
  10. [10] M. A. KRASNOSEL'SKII and A. V. POKROVSKII, Systems with Hysteresis (in Russian), Nauka, Moscow, 1983 (English edition: Springer 1989). MR987431
  11. [11] P. KREJĆĬ, Hysteresis, Convexity, and Dissipation in Hyperbolic Equations, Springer, 1996. Zbl1187.35003MR2466538
  12. [12] Y. LI and I. BABUŠKA, A convergence analysis of an H-version finite element method with high order elements for two dimensional elasto-plastic problems, SIAM J. Numer. Anal., to appear. Zbl0879.73070MR1451111
  13. [13] J. LUBLINER, Plasticity Theory, Macmillan Publishing Company, New York, 1990. Zbl0745.73006
  14. [14] J. LEMAITRE and J. L. CHABOCHE, Mechanics of Solid Materials, Cambridge University Press, 1985. Zbl0743.73002
  15. [15] G. MAUGIN, The Thermodynamics of Plasticity and Fracture, Cambridge University Press, 1992. Zbl0753.73001MR1173212
  16. [16] A. VISINTIN, Differential Models of Hysteresis, Springer, 1994. Zbl0820.35004MR1329094
  17. [17] M. ZYZCKOWSKI, Combined Loading in the Theory of Plasticity, PWN-Polish Scientific Publisher, Warszawa, 1981. Zbl0497.73036

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