Fundamental Equations
The derivation of the fundamental equations of the couple-stress theory presented in this section is mainly based on paper [1] by W. T. Koiter with certain modifications. The indicial notation (Cartesian tensors) is used throughout the paner. The summatio
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MAREK SOKOLOWSKI POLISH ACADEMY OF SCIENCES
THEORY OF COUPLE- STRESSES IN BODIES WITH CONSTRAINED ROTATIONS
COURSE HELD AT THE DEPARTMENT FOR MECHANICS OF DEFORMABLE BODIES JULY 1970
UDINE 1970
SPRINGER-VERLAG WIEN GMBH
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©
1972 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien New York in 1972
ISBN 978-3-211-81143-6 DOI 10.1007/978-3-7091-2943-2
ISBN 978-3-7091-2943-2 (eBook)
PREFACE
These notes represent the material of the author's leatures given at the CISM summer aourses in Udine 1970.
The author is indebted to Prof. Luigi Sobrero, Searetary General of CISM for his kind invitation to deliver these leatures. As always, the staff of CISM should be thanked for the trouble they take in printing, proofreading and publishing these leatures.
Udine, July 1970
M. Sokolowsky.
1. Introduction
In the last ten, twelve years a rapid development of the theory of Gosserat-type media, bodies with additional internal degrees of freedom, the couple-stress theory and the theory of bodies with internal microstructure can be observed. It is not the aim of this series of lectures to characterize generally
the above mentioned theories, to outline their fundamental
physical and mathematical assumptions and to discuss the possibilities of their practical applications in numerous fields of technology. Some of these problems are subject to detailed discussion in the lecture to be held in the same period of time at Udine by Professor R. Stojanovic and Professor W. Nowacki; some of these problems arenot completely cleared in the world literature so far- like, for instance, the extent of possible technological applications of the couple-stress theory to real polycrystalline bodies. Generally speaking, two trends can be observed in the current development of the theories mentioned above; one of them consists in a constant broadening of their mathematical and physical basis; increasing the number of internal degrees of freedom, introducing a number of new elastic and material constants; trying to embrace the largest possible number of physical phenomena and to generalize most of the results known
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Problems of Couple-Stress Theory...
from the classical theories of deformable bodies. The other tendency can be characterized by the efforts to obtain certain new solutions in this domain based, however, on possibly simple models of media, and on the lowest possible nurober of additional assumptions, material constants, etc., in order to obtain solutions which could successf•1.1ly be compared with certain experimental results which cannot be explained on the basis of classical theories of elastic media. The so- called theory of bodies with constrained rotations offers a good opportunity forthist
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