Random Theory of Deformation of Structured Media
In the last decade several theories have been proposed with the aim of modifying or extending classical continuum theory so that the deformation process of structured media can be described. The first theory considering the presence of a microstructure kn
- PDF / 3,494,199 Bytes
- 56 Pages / 481.885 x 691.641 pts Page_size
- 1 Downloads / 176 Views
D.R. AXELRAD McGILL UNIVERSITY MONTREAL
RANDOM THEORY OF DEFORMATION OF STRUCTURED MEDIA D.R. AXELRAD - J.W. PROVAN
THERMODYNAMICS OF DEFORMATION IN STRUCTURED MEDIA COURSE HELD AT THE DEPARTMENT OF MECHANICS OF SOLIDS J{"LY 1971
UDINE 1971
SPRINGER-VERLAG WIEN GMBH
Thia work is 8Uiject to copyright
All rigbts are reserved. whether the
wliole or part of the material is concemed
specifically those of translation, reprinting, re-uae of illustrations, broadcasting, reproduction by photocopying machine or llimilar me111111, and storage in data bank11.
©
1972 by Springer-Verlag Wien
Originally published by Springer- Verlag Wien- New York in 1972
ISBN 978-3-211-81175-7 DOI 10.1007/978-3-7091-2936-4
ISBN 978-3-7091-2936-4 (eBook)
D. R. AXELRAD
RANDOM THEORY OF DEFORMATION OF STRUCTURED MEDIA
P R E F A C E A theory of deformation of structured media derived from statistical mechanics and the theory of probability is introduced. The basic deformation kinematics of a simple model and a "material functional" that replaces the conventional constitutive relations are discussed. Functional analysis is used for the description of the field equations in the function space.
Udine, July 19?1
1. Introduction
In the last decade several theories have been proposed with the aim of modifying or extending classical continuum theory so that the deformation process of structured media can be described. The first theory considering the presence of a microstructure known as the theory of 'oriented media' is due to E.and F. Cosserat[t]. Iv this theory the deformation is described in terms of a position vector of an arbitrary point in the medium with respect to a fixed reference frame and a veetor called ''director'' associated with the position vector. The concept of using directors in continuum mechanics goes back to Duhem[zJ. The fundamental aspects of the deformation kinematics of such media were treated comprehensively by Truesdell and
Toupin[3]. Following the Cosserat approach, Mindlin[4] proposed a theory of elastic media possessing a microstructure -in which a physical point or ''unit cell'' was considered deformable, This theory can be reduced in the case of a homogeneous deformation to a model suggested by Ericksen and Truesdell[S],
which is
based on the concept of a Cosserat continuum. Another theoryextending the classical fonnulation is the ''couple stress theory'' treated in detail by Toupin[6]. This approach was later completed by Eringen and Suhubi[7].These researches also introduced a
6
Random Theory of Deformation •••
more general theory of microcontinuum that has been extended more recently to the continuum theory of ';micromorphic media'' Finally, Green and Rivlin[S]introduced the ''multipolar" continuum theory, which uses force and stress multipoles that are defined in terms of the velocity components and their spatial derivatives. The above theories mentioned briefly here, represent the major contributions towards a modification of classical continuum theory. However, it is the aim of this paper
Data Loading...
