×

Variational inequality formulation in strain space and finite element solution of an elasto-plastic problem with hardening. (English) Zbl 0747.73047


MSC:

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74B99 Elastic materials

Keywords:

flow theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Nečas, J., Variational inequalities in elasticity and plasticity with application to Signiorini’s problems and to flow theory of plasticity, Z. Angew. Math. Mech., 60, T20-T26 (1980) · Zbl 0451.73100
[2] Nečas, J.; Hlaváček, I., Mathematical Theory of Elastic and Elasto Plastic Bodies: An Introduction (1981), Elsevier: Elsevier Amsterdam · Zbl 0448.73009
[3] Hlaváček, I., A finite element solution for plasticity with strain-hardening, RAIRO Anal. Numér., 14, 347-368 (1970) · Zbl 0471.73078
[4] Nayak, G. C.; Zienkiewicz, O. C., Elastic-plastic stress analysis. A generalization for various constitutive relations including strain softening, Internat. J. Numer. Methods Engrg., 5, 113-135 (1972) · Zbl 0241.73034
[5] Owen, D. R.J.; Hinton, E., Finite Elements in Plasticity (1980), Pineridge: Pineridge Swansea · Zbl 0482.73051
[6] Beagles, A. E.; Walton, J. R.; Warby, M. K.; Whiteman, J. R., Some numerical results in nonlinear and viscoelastic fracture, (BICOM 88/4 (1988), Institute of Computational Mathematics, Brunel University) · Zbl 0666.73072
[7] A.E. Beagles and J.R. Whiteman, Elasto-plastic finite element results produced with the MODLEP code (to appear).; A.E. Beagles and J.R. Whiteman, Elasto-plastic finite element results produced with the MODLEP code (to appear). · Zbl 0626.65112
[8] I. Hlaváček and J.R. Whiteman, Existence and uniqueness of solutions in strain space of elasto-plastic problems with hardening (to appear).; I. Hlaváček and J.R. Whiteman, Existence and uniqueness of solutions in strain space of elasto-plastic problems with hardening (to appear).
[9] Fichera, G., Boundary value problems of elasticity with unilateral constraints, (Flügge, S., Handbuch der Physik, Vol. VIa/2 (1972), Springer: Springer Berlin)
[10] Naghdi, P. M., Stress-strain relations in plasticity and thermo-plasticity, (Plasticity, Proc. 2nd Symp. Naval Structural Mechanics. Plasticity, Proc. 2nd Symp. Naval Structural Mechanics, Rhode Island, 1960 (1960), Pergamon: Pergamon Oxford) · Zbl 0556.73031
[11] Hodge, P. G., Continuum Mechanics. An Introductory Text for Engineers (1970), McGraw-Hill: McGraw-Hill New York
[12] Hill, P., The Mathematical Theory of Plasticity (1950), Clarendon Press: Clarendon Press Oxford · Zbl 0041.10802
[13] Samuelsson, A.; Fröier, M., Finite Elements in plasticity—A variational inequality approach, (Whiteman, J. R., The Mathematics of Finite Elements and Applications III, MAFELAP 1978 (1978), Academic Press: Academic Press London) · Zbl 0437.73058
[14] Casey, G.; Naghdi, P. H., On the nonequivalence of the stress space and strain space formulation of plasticity theory, ASME Trans. J. Appl. Mech., 50, 350 (1983) · Zbl 0518.73027
[15] Malvern, L. E., Introduction to the Mechanics of a Continuous Medium (1969), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0181.53303
[16] Kestřánek, Z., Variational principles in plasticity with strain hardening-equilibrium finite element approach, Apl. Mat., 4, 270-281 (1986) · Zbl 0608.73040
[17] Naghdi, P. M.; Trapp, J. A., The significance of formulating plasticity theory with reference to loading surfaces in strain space, Internat. J. Engrg. Sci, 13, 785-797 (1975) · Zbl 0315.73050
[18] Theocaris, P. S.; Marketos, E., Elasto-plastic analysis of performed thin strips of a strain hardening material, J. Mech. Phys. Solids, 12, 377 (1964)
[19] Zienkiewicz, O. C.; Valliapan, S.; King, I. P., Elasto-plastic solutions of engineering problems; Initial stress finite element approach, Internat. J. Numer. Methods Engrg., 1, 75-100 (1969) · Zbl 0247.73087
[20] Korn’eev, V. G.; Langer, U., Approximate Solution of Plastic Flow Theory Problems, (Teubner-Texte zur Mathematik, 69 (1984), Teubner: Teubner Leipzig)
[21] Miyoshi, T., Foundation of the Numerical Analysis of Plasticity (1985), North-Holland: North-Holland Amsterdam
[22] Desai, C. S.; Abel, J. F., Introduction to the Finite Element Method (1972), Van Nostrand: Van Nostrand New York
[23] Gröger, K., Initial boundary value problems for elastoplastic and elasto-viscoplastic problems, (Proc. Summer School Horni Bradlo. Proc. Summer School Horni Bradlo, 1978. Proc. Summer School Horni Bradlo. Proc. Summer School Horni Bradlo, 1978, Teubner-Texte zur Mathematik (1979), Teubner: Teubner Leipzig), 95-127
[24] Hunter, S. C., Mechanics of Continuous Media (1976), Ellis Horwood: Ellis Horwood Chichester · Zbl 0385.73002
[25] Januszewicz, W., Continuum Mechanics (1967), Macmillan: Macmillan New York
[26] Mason, J., Variational Incremental and Energy Methods in Solid Mechanics and Shell Theory (1980), Elsevier: Elsevier Amsterdam · Zbl 0571.73008
[27] Mendelson, A., Plasticity: Theory and Application (1968), Macmillan: Macmillan New York
[28] Prager, W., An Introduction to Plasticity (1959), Addison-Wesley: Addison-Wesley New York · Zbl 0089.42004
[29] Washizu, K., Variational Methods in Elasticity and Plasticity (1968), Pergamon: Pergamon Oxford · Zbl 0164.26001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.