Abstract
We formally state and prove the wellposedness and the local Lipschitz continuity of the multisurface stress-strain law of nonlinear kinematic hardening type due to Chaboche within the space of time-dependent tensor-valued absolutely continuous functions. The results also include the more general case of a continuous family of auxiliary surfaces.
Supported by the BMBF, Grant No. 03-BR7KIE-9, within “Anwendungsorientierte Verbund projekte auf dem Gebiet der Mathematik”.
Supported by the BMBF during his stay at Kiel.
Partially supported by the Grant Agency of the Czech Republic under Grant No. 201/95/0568.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R.J. ARMSTRONG and CO. FREDERICK, 1966, A mathematical representation of the multiaxial Bauschinger effect, C.E.G.B., Report RD/B/N 731.
M. BROKATE, P. KREJČĺ, Wellposedness of kinematic hardening models in elastoplasticity, Math. Model. Numer. Anal., to appear.
M. BROKATE, J. SPREKELS, 1996, Hysteresis and phase transitions, Springer-Verlag, Berlin.
J.-L. CHABOCHE, 1989, Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plasticity, 5, pp. 247–302.
J.-L. CHABOCHE, 1991, On some modifications of kinematic hardening to improve the description of ratchetting effects, Int. J. Plasticity, 7, pp. 661–678.
J.-L. CHABOCHE, 1994, Modeling of ratchetting: evaluation of various approaches, Eur. J. Mech., A/Solids, 13, pp. 501–518.
M. KAMLAH, M. KORZEN and CH. TSAKMAKIS, Uniaxial ratchetting in rate-independent plasticity laws, Acta Mechanica, to appear.
M.A. KRASNOSEL’SKII and A.V. POKROVSKII, 1989, Systems with hysteresis, Springer-Verlag, Berlin. Russian edition: Nauka, Moscow 1983.
P. KREJCI, 1996, Hysteresis, convexity and dissipation in hyperbolic equations, Gakkotosho, Tokyo.
J. LEMAITRE and J.-L. CHABOCHE, 1990, Mechanics of solid materials, Cambridge University Press, Cambridge 1990. French edition: Dunod, Paris 1985.
G.A. MAUGIN, 1992, The thermomechanics of plasticity and fracture, Cambridge University Press, Cambridge 1992.
E. MELAN, 1938, Zur Plastizitat des raumlichen Kontinuums, Ingenieur-Archiv, 9, 116–126.
W. PRAGER, 1949, Recent developments in the mathematical theory of plasticity, J. Appl. Phys., 20, pp. 235–241.
A. VISINTIN, 1994, Differential models of hysteresis, Springer-Verlag, Berlin.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Basel AG
About this paper
Cite this paper
Brokate, M., Krejčí, P. (1998). On the Wellposedness of the Chaboche Model. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems. International Series of Numerical Mathematics, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8849-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8849-3_5
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9800-3
Online ISBN: 978-3-0348-8849-3
eBook Packages: Springer Book Archive