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A finite element analysis for elasto-plastic bodies obeying Hencky’s law. (English) Zbl 0467.73096


MSC:

74S05 Finite element methods applied to problems in solid mechanics
49S05 Variational principles of physics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
49J40 Variational inequalities
49M15 Newton-type methods
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:

[1] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique. Paris, Dunod 1972. · Zbl 0298.73001
[2] B. Mercier: Sur la théorie et l’analyse numérique de problèmes de plasticité. Thesis, Université Paris VI, 1977.
[3] P. Suquet: Existence and regularity of solutions for plasticity problems. (Preprint). Proc. IUTAM Congress in Evanston - 1978. · Zbl 0453.73040
[4] R. Falk B. Mercier: Estimation d’erreur en élastoplasticité. C. R. Acad. Sc. Paris, 282, A, (1976), 645-648. · Zbl 0329.73031
[5] R. Falk B. Mercier: Error estimates for elasto-plastic problems. R.A.I.R.O. Anal. Numer., 11 (1977), 135-144. · Zbl 0357.73062
[6] V. B. Watwood B. J. Hartz: An equilibrium stress field model for finite element solution of two-dimensionalelastostatic problems. Inter. J. Solids Structures 4, (1968), 857-873. · Zbl 0164.26201 · doi:10.1016/0020-7683(68)90083-8
[7] C. Johnson B. Mercier: Some equilibrium finite element methods for two-dimensional elasticity problems. Numer. Math. 30 (1978), 103-116. · Zbl 0427.73072 · doi:10.1007/BF01403910
[8] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris 1971. · Zbl 0211.17402
[9] F. Brezzi W. W. Hager P. A. Raviart: Error estimates for the finite element solution of variational inequalities. Part I. Primal Theory. Numer. Math. 28, (1977), 431 - 443. · Zbl 0369.65030 · doi:10.1007/BF01404345
[10] M. Křížek: An equilibrium finite element method in three-dimensional elasticity. Apl. Mat. 27 (1982).
[11] P. A. Raviart J. M. Thomas: A mixed finite element method for 2-nd order elliptic problems. Math. Aspects of Fin. El. Meth. Rome 1975, Springer-Verlag 1977, 292-315.
[12] H. Brezis K. Stampacchia: Sur la regularité de la solution d’inéquations elliptiques. Bull. Soc. Math. France 96, (1968), 153-180.
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