Photograph Kobe, Wi_n I

Photograph Kobe, Wi_n I

'/'tl/ik, Ail/llk.,/ J'ILUIIIIlkw Symposium Vienna, March 1-2,1974 Edited by l LZeman and E Ziegler Springer-Verlag Wien GmbH

With 1 Portrait and 67 Figures This work is subject to copyright. Ali 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. Springer-Verlag Wien 1974 Library of Congress Cataloging in Publication Data Main entry under tit1e: Topics in app1ied continuum mechanics. Papers presented at a symposium he1d at the University of Technoil.ogy of Vienna in honor of H. Parkus. Inc1udes bib1iographies. 1. Continm.nn mechanics--congresses. 2. Parku.s, Heinz, 1909- --Bib1iography. I. Zeman, Josef L., 1938- ed. II. Zieg1er, Franz, 1937- ed. III. Parkus, Heinz, 1909- Q,A.808.2.T63 620.1'05 74-12227 ISBN 978-3-211-81260-0 ISBN 978-3-7091-4188-5 (ebook) DOI 10.1007/978-3-7091-4188-5

PRE F ACE On January 31, 1974 Professor Dr.Heinz Parkus celebrated his 65th birthday. In his honour an international symposium on continuum mechanics, sponsored by the Austrian Secretary of Science and Research, was held on Narch 1 and 2, 1974 at the University of Technology of Vienna. Here scientists presented their special fields of interest in a series of lectures, in reviews as well as in reports on latest developments in present day research, experimental as well as theoretical. From these contributions those '"hich seem to be of general interest are collected in this volume. They are arranged starting with experimental results, the basis of any phenomenological theory, followed by theoretical results, by results of application oriented theory and by results of applications '''hich lead to experiments. Of course, none of the papers fits exactly into this scheme, some even cover the entire range themselves. There is not space here to summarize the papers printed in this volume. \ve confine ourself to pointing out the remarkable experiments on plasticity by A.Philli'ps, the fundamental contribution of E.Kroner to self-stresses, the excellent review of electro-magneto-elasticity by J.B.Alblas, the theoretical treatise of distortion in micropolar elasticity by W.Nowacki, the theoretical considerations of J.A.Konig and W.Olszak on the influence of nonhomogeneity on p l a s t the i c two i t engineering ~ oriented papers by W.R.Delameter-G.Herrmann and H.Bargmann covering some modern topics in elasticity, the reviews on plasticity and creep from a more engineering point of view by J.F. Besseling and J.Hult, and the outline of plastokinetics of

IV metal forming by II. Lippmann. A list of references, a subject index and a list of publications of Professor Heinz Parkus have been added. The list of references is complete and the underlined page numbers refer to pages where the complete references may be found. In the subject index only those pages are listed where definitions or general information may be found. In concluding this preface we take the opportunity of expressing our sincerest thanks to the authors, l ~ hhanded o in the manuscripts in time and in a manner such that they could be forwarded to the publisher within short notice, and to Springer-Verlag Wien-New York for making it possible that this interesting collection of different views of the very same subject, applied continuum mechanics, can appear in such a short time. J.L. Zeman F. Ziegler

CON TEN T S PREFACE THE FOUNDATIONS OF THERMOELASTICITY-EXPERIMENTS AND THEORY (A.PHILLIPS) 2. The initial yield surface 3. The subsequent yield surface 4. Some theoretical consequences 4 6 10 13 ON THE PHYSICS AND MATHEMATICS OF SELF-STRESSES (E.KRONER) 22 2. The physical origin of the self-stresses 23 3. Formulation of the mathematical problem of self-stresses 27 4. The method of modified Green's functions 30 5. Concluding remarks 35 38 DISTORTION IN MICROPOLAR ELASTICITY (W.NOWACKI) 1. Fundamental relations and equations 2. Principle of virtual work 3. Theorem of minimum of the complimentary work 4. Reciprocity theorem 5. Equations in displacements and rotations 6. Compatibility equations 39 42 43 44 47 51 57 THE YIELD CRITERION IN THE GENERAL CASE OF NONHOMOGENEOUS STRESS AND DEFORMATION FIELDS (J.A.KONIG and W.OLSZAK) 2. The plasticity condition 3. Special cases of the yield condition 4. Example: Pure bending 5. Criteria for neutral, passive and active processes 58 61 62 63 65

VI 6. The flow law 67 69 ELECTRO-MAGNETO-ELASTICITY (J.B.ALBLAS) 2. Balance equations 3. The jump and boundary conditions 4. The constitutive equations 5. Linearization of the magnetic problem 6. Magneto-elastic waves in the infinite space and in the half-space 71 77 85 91 95 105 114 PLASTICITY AND CREEP THEORY IN ENGINEERING MECHANICS (J. F BESSE LING) 2. Limit analysis 3. Models of material behaviour 4. The geometrically and physically non-linear structural equations 5. Some remarks on the applications in engineering 115 117 126 132 134 136 CREEP IN CONTINUA AND STRUCTURES (J.HULT) 2. Basic laws of deformation and damage 3. Stable creep deformation, methods of analysis 3.1 Elastic analogue 3.2 Reference stress methods 3.3 Energy theorems 4. Ductile instability 5. Brittle instability 6. Mixed type instability 137 139 141 142 143 144 144 149 150 150 WEAKENING OF ELASTIC SOLIDS BY DOUBLY-PERIODIC ARRAYS OF CRACKS (W.R.DELAMETER and G.HERRMANN) 156 2. Formulation of the problems and the method of solution 157

VII 3. Stress intensity factors 159 4. Change in strain energy and effective elastic contstants 162 5. Summary of results 167 168 DYNAMIC THERMAL SHOCK RESISTANCE (H.8ARGMANN) 2. The basic problem of radiation heating 3. Thermal shock resistance of structures 4. Representative materials 174 175 178 179 180 PLA5TOKINETICS OF METAL FORMING (H. LIPPMANN) 2. Some rigorous solutions to kinetically stationary problems 2.1 General 2.2 Plane-strain compression of a layer 2.3 Axially symmetric bulging of a membrane 3. Perturbation method 3.1 General, Indentation of the half-space 3.2 Elementary kinetics of non-stationary forging 4. Further non-stationary solutions 4.1 Hagen-Poiseuille flow 4.2 Flexural waves in plate bulging 4.3 Uniaxial longitudinal waves in upsetting 182 184 184 184 188 191 191 193 196 196 197 201 206 AUTHOR INDEX 209 SU8JECT INDEX 212 LIST OF PUBLICATIONS OF PROFESSOR HEINZ PARKUS 216