This text is a guide how to solve problems in which viscoelasticity is present using existing commercial computational codes. The book gives information on codes’ structure and use, data preparation and output interpretation and verification. The first part of the book introduces the reader to the subject, and to provide the models, equations and notation to be used in the computational applications. The second part shows the most important Computational techniques: Finite elements formulation, Boundary elements formulation, and presents the solutions of Viscoelastic problems with Abaqus.
SpringerBriefs in Applied Sciences and Technology Computational Mechanics
For further volumes: http://www.springer.com/series/8886
Severino P. C. Marques Guillermo J. Creus •
Computational Viscoelasticity
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Severino P. C. Marques Centro de Tecnologia Universidade Federal de Alagoas Maceió, Alagoas Brazil e-mail:
[email protected]
ISSN 2191-5342 ISBN 978-3-642-25310-2 DOI 10.1007/978-3-642-25311-9
Guillermo J. Creus ILEA Universidade Federal do Rio Grande do Sul Porto Alegre Rio Grande do Sul Brazil e-mail:
[email protected]
e-ISSN 2191-5350 e-ISBN 978-3-642-25311-9
Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011943323 Ó The Author(s) 2012 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To my wife, Dilze, and my children, Fernando, Gustavo and Clarissa S. P. C. Marques To my wife, Susana, and my children, Guillermo, Tomás, Amalia and Ana G. J. Creus
Preface
This book develops a presentation of viscoelasticity theory oriented toward numerical applications. It is our hope that it will be useful both as a textbook for graduate courses and as a reference volume for engineers and researchers.The book is structured in twelve chapters. The first eight chapters introduce basic concepts and theoretical ideas about the viscoelastic response of solids. They cover constitutive relations in integral and differential form, influence of temperature, age and finite strain. These topics were selected aiming to make the access to the computational viscoelastic formulations easier. It is assumed that the reader has a background in mathematics and mechanics at the undergraduate level. In the last five chapters a more advanced experience may be needed. The remaining chapters address the numerical formulation of viscoelastic problems using finite element, boundary element and finite volume methods. Chapter 9 presents viscoelastic finite element procedures formulated on a total Lagrangian description for large displacements and rotations with small strains. Two alternative bou