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BOOK EXCERPT:
The term "dislocation" is used in several different senses in the literature of mechanics. In the elassic work of VOLTERRA, WEINGARTEN, and SOMIGLIANA, it refers to particular solutions of the equations of linear elasticity, in which a con tinuous field of strain does not correspond, globally, to a continuous field of dis placement. The configuration of the body so obtained, even when that body is free of all load, is subject to interior stress that does not vanish, and in general no deformation of the body as a wh oIe can bring it into a stress-free configuration. Nevertheless, if any sufficiently sm all part of the body is considered by itself, a configuration for it in which the stress is everywhere zero may be found at once. In this work constitutiL"e assumptions provide the basic data. These consist in prescribed stress-free configurations for each material point and in prescribed elastic moduli governing the response to deformation from the stress-free configuration at each material point. Everything follows from these data, ineluding the dislocations present, if any. In particular, the common boundary-value problems of linear elasticity may be set and solved for the dislocated body.
Product Details :
Genre |
: Science |
Author |
: W. Noll |
Publisher |
: Springer Science & Business Media |
Release |
: 2012-12-06 |
File |
: 187 Pages |
ISBN-13 |
: 9783642859922 |
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BOOK EXCERPT:
A First Course in Rational Continuum Mechanics V1
Product Details :
Genre |
: Mathematics |
Author |
: |
Publisher |
: Academic Press |
Release |
: 1992-02-03 |
File |
: 417 Pages |
ISBN-13 |
: 9780080873879 |
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BOOK EXCERPT:
Product Details :
Genre |
: Science |
Author |
: Chao-Chen Wang |
Publisher |
: Springer |
Release |
: 2013-12-19 |
File |
: 39 Pages |
ISBN-13 |
: 9783662383155 |
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BOOK EXCERPT:
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
Product Details :
Genre |
: Mathematics |
Author |
: Reuven Segev |
Publisher |
: Springer Nature |
Release |
: 2023-10-31 |
File |
: 410 Pages |
ISBN-13 |
: 9783031356551 |
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BOOK EXCERPT:
This book presents a collection of papers giving the flavor of current research activities in continuum mechanics, fluid mechanics, thermodynamics and the mathematical analysis related to these topics. Written by leading experts in the field, all the papers in this collection have been carefully refereed according to the standards of the "Archive for Rational Mechanics and Analysis."
Product Details :
Genre |
: Science |
Author |
: Bernard D. Coleman |
Publisher |
: Springer Science & Business Media |
Release |
: 2012-12-06 |
File |
: 536 Pages |
ISBN-13 |
: 9783642615986 |
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BOOK EXCERPT:
Product Details :
Genre |
: Science |
Author |
: Chao-cheng Wang |
Publisher |
: Springer Science & Business Media |
Release |
: 1973-12-31 |
File |
: 578 Pages |
ISBN-13 |
: 9001937101 |
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BOOK EXCERPT:
This second part of Continuum Thermodynamics is designed to match almost one-to-one the chapters of Part I. This is done so that the reader studying thermodynamics will have a deepened understanding of the subjects covered in Part I. The aims of the book are in particular: the illustration of basic features of some simple thermodynamical models such as ideal and viscous fluids, non-Newtonian fluids, nonlinear solids, interactions with electromagnetic fields and diffusive porous materials. A further aim is the illustration of the above subjects by examples and simple solutions of initial and boundary problems as well as simple exercises to develop skills in the construction of interdisciplinary macroscopic models.
Product Details :
Genre |
: Science |
Author |
: Bettina Albers |
Publisher |
: World Scientific |
Release |
: 2014-11-12 |
File |
: 482 Pages |
ISBN-13 |
: 9789814412384 |
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BOOK EXCERPT:
The scope of this book is based on the keynote lectures delivered during the Inter national Symposium on Anisotropic Behaviour of Damaged Materials ABDM, held in Krakow-Przegorzaiy, Poland, September 9-11, 2002. The Symposium was organized by the Solid Mechanics Division of the Institute of Mechanics and Machine Design - Cracow University of Technology, under aus pices of the Dean of the Faculty of Mechanical Engineering, Cracow University of Technology, Prof. S. Michalowski. The Co-organizers of the ABDM Symposium were: • Martin-Luther-Universitat Halle-Wittenberg, • Centre of Excellence for Advanced Materials and Structures AMAS at the In stitute of Fundamental Technological Research of the Polish Academy of Sci ences, Warsaw, • Committee of Mechanics of the Polish Academy of Sciences, Warsaw. Ten chapters of this book in their present form essentially exceed lectures de livered at the Symposium. They should rather be read as not only author's recent achievements in the field, but also the state of art and synthesis done by the lead ers in the mechanics community. The mixed formula of the Symposium, namely: the invited lectures and presentations of the original papers by the participants was used. 23 original papers, published in the Symposium Proceedings on CD, exhaust the full scope of the ABDM Symposium. The present book provides a survey of various damage models focusing on the damage response in anisotropic materials as well as damage-induced anisotropy.
Product Details :
Genre |
: Technology & Engineering |
Author |
: Jacek J. Skrzypek |
Publisher |
: Springer Science & Business Media |
Release |
: 2012-11-27 |
File |
: 370 Pages |
ISBN-13 |
: 9783540364184 |
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BOOK EXCERPT:
This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models — ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts.The book is the first presentation of continuum thermodynamics in which foundations of continuum mechanics, microscopic foundations and transition to extended thermodynamics, applications of extended thermodynamics beyond ideal gases, and thermodynamic foundations of various material theories are exposed in a uniform and rational way. The book may serve both as a support for advanced courses as well as a desk reference.
Product Details :
Genre |
: Science |
Author |
: Wilmanski |
Publisher |
: World Scientific |
Release |
: 2008 |
File |
: 416 Pages |
ISBN-13 |
: 9789812835567 |
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BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: F. Bloom |
Publisher |
: Springer |
Release |
: 2006-11-15 |
File |
: 217 Pages |
ISBN-13 |
: 9783540350453 |