Bifurcation Problems in Plasticity
The text of the following chapters comprises six lectures given at the International Centre for Mechanical Sciences (CISM) in Udine, July 19 – 30, 1982, as part of the course “The Constitutive Law in Thermoplasticity” which has been coordinated by Profess
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No.
281
THE CONSTITU TIVE LAW IN THERMOP LASTICIT Y
EDITEDBY
Th. LEHMANN RUHR-UNIVERSITY BOCHUM
SPRINGER-VERLA G WIEN GMBH
Tbia volume contains 111 illustrations.
This work is subject to copyright.
All rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 1984 by
Springer-Verlag Wien
Originally published by Springer Verlag Wien-New York in 1984
ISBN 978-3-211-81796-4 DOI 10.1007/978-3-7091-2636-3
ISBN 978-3-7091-2636-3 (eBook)
CONTENTS
The Constitutive Law in Thermplasticity - an Introduction by T. Lehmann . . . . . . . . . . . . . . . . . . . . . . .
. . . 1
Thermodynamic Theories of Thermoelasticity and Special Gases of Thermoplasticity by 1 Müller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
Physical Theory of Plasticity in Crystalline Solids by V. Gerold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . lÖS Plasticity and Nonequilibrium Thermodynamics by G.A. Kluitenberg . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 157
Thermodynamic Aspects of Cyclic and Monotone Plasticity by B. Raniecki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Foundations of Large Deformations by K. Thermann . . . . . . . . . .
. . . . . . 323
Weil Posedness of Constitutive Equations of the Kinematical Hardening Type G. Del Piere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 General Frame for the Definition of Constitutive Laws for Large Non-isothermic Elastic-plastic and Elastic-visco-plastic Deformations by T. Lehmann . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . 379
Bifurcation Problems in Plasticity by O.T. Bruhns . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . 465
Constitutive Law in Inelastic Structural Mechanics B.F. Besseling
. . . . . . . . . . . . . . . . . . . 541
THE CONSTITUTIVE LAW IN THERMOPLASTICITY AN INTRODUCTION
TUEODOR LEUMANN Ruhr-University Bochum D-4630 Bochum
Within this course we are dealing mainly with non-isothermic inelastic deformations of such solid borlies which can be considered phenomenologically as classical continua. This mearis, we assume that the deformations of the considered borlies are completely derivable from the description of the motion of the material points in a well defined space of observation (space-fixed coordinate system). We shall see, however, that the description of the deformations can also be based merely on the consideration of the deformations of a comoving body-fixed coordinate system. The restriction to classical continua is, of course, significant. Certain problems concerning deformations of structured media cannot be treated within this frame. This is, for instance, true for certain
2
T. Lehmann
problems in rock mechanics. Such problems require an extended concept ·for the description of defo
