Regularity of solutions to a one dimensional plasticity model
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 5, p. 521-537
@article{M2AN_1998__32_5_521_0,
author = {Babu\v ska, I. and Shi, P.},
title = {Regularity of solutions to a one dimensional plasticity model},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {Dunod},
volume = {32},
number = {5},
year = {1998},
pages = {521-537},
zbl = {0906.73028},
mrnumber = {1643489},
language = {en},
url = {http://www.numdam.org/item/M2AN_1998__32_5_521_0}
}

Babuška, I.; Shi, P. Regularity of solutions to a one dimensional plasticity model. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 32 (1998) no. 5, pp. 521-537. http://www.numdam.org/item/M2AN_1998__32_5_521_0/

[1] I. Babuška, Y. Li and K. L. Jerina, Rehability of computational analysis of plasticity problems, In Non-linear Computational Mechanics, P. Wriggers and W. Wagner Eds, Springer-verlag, 1991.

[2] I. Babuška and P. Shi, A continuous Galerkin method in one dimensional plasticity, in preparation.

[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. | MR 922980 | Zbl 0652.35043

[4] G. Duvault and J. L. Lions, Inequalities in mechanics and physics, Springer-Verlag, Berlin-New York, 1976. | MR 600341 | Zbl 0331.35002

[5] I. Ekeland and R. Temam, Convex analysis and variational problems, North-Holland, 1976. | MR 463994 | Zbl 0322.90046

[6] W. Han and B. D. Reddy, Computational plasticity: the variational basis and numerical analysis, Computational Mechanics Advances, 2, No. 2, 1995. | MR 1361227 | Zbl 0847.73078

[7] I. Hlaváček, J. Haslinger, J. Nečas and J. Lovišek, Solutions of variational inequalities in mechanics, Springer-Verlag, 1988. | MR 952855 | Zbl 0654.73019

[8] C. Johnson, Existence theorems for plasticity problems, J. Math. Pure et Appl., 55, pp. 431-444 (1976). | MR 438867 | Zbl 0351.73049

[9] C. Johnson, On plasticity with hardening, J. Math. Anal. Appl., 62, pp. 333-344 (1978). | MR 489198 | Zbl 0373.73049

[10] M. A. Krasnosel'Skii and A. V. Pokrovskii, Systems with Hysteresis (in Russian), Nauka, Moscow, 1983 (English edition: Springer 1989). | MR 987431

[11] P. Krejćĭ, Hysteresis, Convexity, and Dissipation in Hyperbolic Equations, Springer, 1996. | MR 2466538 | Zbl pre05376857

[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. | MR 1451111 | Zbl 0879.73070

[13] J. Lubliner, Plasticity Theory, Macmillan Publishing Company, New York, 1990. | Zbl 0745.73006

[14] J. Lemaitre and J. L. Chaboche, Mechanics of Solid Materials, Cambridge University Press, 1985. | Zbl 0743.73002

[15] G. Maugin, The Thermodynamics of Plasticity and Fracture, Cambridge University Press, 1992. | MR 1173212 | Zbl 0753.73001

[16] A. Visintin, Differential Models of Hysteresis, Springer, 1994. | MR 1329094 | Zbl 0820.35004

[17] M. Zyzckowski, Combined Loading in the Theory of Plasticity, PWN-Polish Scientific Publisher, Warszawa, 1981. | Zbl 0497.73036