Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-31T02:20:31.524Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Mróz model

Published online by Cambridge University Press:  26 September 2008

Martin Brokate ,
Klaus Dressler  and
Pavel Krejčí
Martin Brokate
Affiliation:
Institut für Informatik und Praktische Mathematik, Universität Kiel, 24098 Kiel, Germany
Klaus Dressler
Affiliation:
Tecmath GmbH, Sauerwiesen 2, 67661 Kaiserslautern, Germany
Pavel Krejčí
Affiliation:
Institute of Mathematics, Academy of Sciences, Žitná 25, 11567 Prague, Czech Republic
Get access Rights & Permissions [Opens in a new window]

Abstract

We treat the mathematical properties of the one-parameter version of the Mróz model for plastic flow. We present continuity results and an energy inequality for the hardening rule, and discuss different versions of the flow rule regarding their relation to the basic laws of thermodynamics.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 5 , October 1996 , pp. 473 - 497
Copyright
Copyright © Cambridge University Press 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

[1]Mróz, Z. (1967) On the description of anisotropic workhardening. J. Mech. Phys. Solids 15, 163–175.CrossRefGoogle Scholar
[2]Lemaitre, J. & Chaboche, J.-L. (1990) Mechanics of Solid Materials. Cambridge University Press. (French edition: Dunod, 1985.)CrossRefGoogle Scholar
[3]Chu, C. C. (1984). A three-dimensional model of anisotropic hardening in metals and its application to the analysis of sheet metal formability. J. Mech. Phys. Solids 32, 197–212.CrossRefGoogle Scholar
[4]Chu, C. C. (1987) The analysis of multiaxial cyclic problems with an anisotropic hardening model. Int. J. Solids Structures 23, 567–579.Google Scholar
[5]Prandtl, L. (1928) Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85–106. (In German.)CrossRefGoogle Scholar
[6]Preisach, F. (1935) Über die magnetische Nachwirkung. Z. Physik 94, 277–302. (In German.)CrossRefGoogle Scholar
[7]Ishlinskii, A. Yu. (1944) Some applications of statistical methods to describing deformations of bodies. Izv. AN SSSR, Techn. Ser. No. 9, 580–590. (In Russian.)Google Scholar
[8]Krasnosel'skii, M. A. & Pokrovskii, A. V. (1989) Systems with Hysteresis. Springer-Verlag. (Russian edition: Nauka, 1983)CrossRefGoogle Scholar
[9]Brokate, M. & Visintin, A. (1989) Properties of the Preisach model for hysteresis. J. Reine Angew. Math. 402, 1–40.Google Scholar
[10]Visintin, A. (1994) Differential Models of Hysteresis. Springer-Verlag.CrossRefGoogle Scholar
[11]Brokate, M. (1994) Hysteresis operators. In: Phase Transitions and Hysteresis, Visintin, A. (ed.), Lecture Notes in Mathematics 1584. Springer-Verlag, 1–40.CrossRefGoogle Scholar
[12]Krejčí, P. (1991) Hysteresis memory preserving operators. Applic. Math. 36, 305–326.CrossRefGoogle Scholar
[13]P., Krejčí (1996) Hysteresis, convexity and energy dissipation in hyperbolic equations. Monograph (to appear).Google Scholar
[14]Clormann, U. H. & Seeger, T. (1986) RAINFLOW-HCM: Ein Zählverfahren für Be-triebsfestigkeitsnachweise auf werkstoffmechanischer Grundlage. Stahlbau 55, 65–71. (In German.)Google Scholar
[15]Brokate, M., Dreßler, K. & Krejčí, P. (1996) Rainflow counting and energy dissipation for hysteresis models in elastoplasticity. Submitted.Google Scholar
[16]Murakami, Y. (ed.) (1992) The Rainflow Method in Fatigue. Butterworth–Heinemann.Google Scholar
[17]Krejčí, P. (1991) Vector hysteresis models. Euro. J. Appl. Math. 2, 281–292.CrossRefGoogle Scholar
[18]Hildebrandt, T. H. (1963) Introduction to the Theory of Integration. Academic Press.Google Scholar
[19]Betten, J. (1986) Elastizitäts- und Plastizitätslehre. Vieweg. (In German.)CrossRefGoogle Scholar
[20]Ziegler, H. (1983) An Introduction to Thermomechanics, 2nd ed.North Holland.Google Scholar