Nonlinear Continuum Mechanics and Large Inelastic Deformations
The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular
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SOLID MECHANICS AND ITS APPLICATIONS Volume 174
Series Editors:
G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity.
For other titles published in this series, go to www.springer.com/series/6557
Yuriy I. Dimitrienko
Nonlinear Continuum Mechanics and Large Inelastic Deformations
123
Prof. Yuriy I. Dimitrienko Bauman Moscow State Technical University 2nd Baumanskaya St. 5 105005 Moscow Russia [email protected]
ISSN 0925-0042 ISBN 978-94-007-0033-8 e-ISBN 978-94-007-0034-5 DOI 10.1007/978-94-007-0034-5 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010938719 c Springer Science+Business Media B.V. 2011 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Cover design: SPi Publisher Services Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Nonlinear continuum mechanics is the kernel of the general course ‘Continuum Mechanics’, which includes kinematics of continua, balance laws, general nonlinear theory of constitutive equations, relations at singular surfaces. Moreover, in the course of nonlinear continuum mechanics one also considers the theory of solids at finite (arbitrary) deformations. This arbitrariness of deformations makes the equations describing the behavior of continua extremely complex – nonlinear (so that sometimes the term ‘strongly nonlinear’ is used), as the relationships contained in them cannot always be expressed in an explicit analytical way. If we drop the condition of the arbitrariness of continuum de
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