Plasticity
The theory of plasticity represents even in the classical continuum mechanics a field in which certain fundamental problems are not solved. The existing engineering theories give for practical purposes sufficiently good results, but such theories represen
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L E C T U RES
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No. 27
RASTKO STOJANOVIC UNIVERSITY OF BELGRADE
RECENT DEVELOPMENTS IN THE THEORY OF POLAR CONTINUA
COURSE HELD AT THE DEPARTMENT FOR MECHANICS OF DEFORMABLE BODIES JUNE -JULY 1970
UDINE 1970
SPRINGER-VERLAG WIEN GMBH
ISBN 978-3-211-81144-3 ISBN 978-3-7091-4309-4 (eBook) DOI 10.1007/978-3-7091-4309-4
Copyright by Springer-Verlag Wien 1970 Originally published by Springer Vienna in 1970
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P r e f a a e This aourse of 21 ~eatures on RECENT DEVELOPMENTS IN THE THEORY OF POLAR CONTINUA is based most~y on the former aourse I had the p~easure to give at the Internationa~ Centre for Meahaniaa~ Saienaes in Udine during the September-October session in 1969. Being aware of many important topics in the mechanics of polar continua whiah I did not ina~ude in my former course, and even more being aware of the p~enty of mistakes, and most of them were not of the typographi£ a~ nature, I was very g~ad to receive the invitation of the Reator of CISM to give another course of lectures on the same subject as I did nine months ago. Owing to the ~ack of time at home, I had to prepare this course in Udine. The Rector, W. Olszak, the Secretary Genera~, Professor L. Sobrero, together with the complete technical and administrative staff of CISM did everything possib~e to make my stay and work here not only efficient, but a~so a p~easure. I mostly admire their support and assistance. In parallel to this course, at CISM were he~d the courses by the most distinguished scie~ tists, Professors Eringen, Nowacki, Mindlin and Sokolowski on more specia~ized topics of polar continua. Therefore, I have omitted from my ~ectures the chapters dealing with the applications of linearized theories to some specia~ problems, such as wave propaga-
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Preface
tion, stPess aonaentPation, singulaP foPaes eta. I have added a ahapteP on some aspeats of the shell the oPy,· and 2 ahaptePs on polaP fluids and on the theopy of plastiaity, as welL as some otheP minoP aoPPeations and additions (e.g. on inaompatible stPains with appliaations to thePmoelastiaity and to the theoPy of disloaations). Also the list of PefePenaes is aoPPea! ed and the PefePenaes aPe also given to some Peaently published papePs. I mostly appPeaiate the help of MP.J. JaPic, M. Sa. in aoPPeating the list of PefePenaes and in aheaking the proofs in the main text, as well as the help of Mr. M. Miaunovia, B. Eng. in WPiting the foPmulae. The International CentPe foP Meahaniaal Saienaes in Udine paid for the seaond time in one year its attention to the meahanias of polar aontinua. Appreaiating very muah this interest in this modern branah of meahanias, I hope that this aou~se of leatures (whiah !.delivered with the greatest pleasure) will be, besides all imperfeations and may be even aonaeptual errors, at least a small aontPibution to the furtheP development of aontinuum meahanias. Udine, July 16, 1970 R. Stojanovic
l. Introduction
Classical continuum mechanics
consider~
material
continua as point-continua with points having three degrees of freedom, and t
