Multiscale Modeling in Solid Mechanics Computational Approaches

Transcription

1 Multiscale Modeling in Solid Mechanics Computational Approaches

2 Computational and Experimental Methods in Structures Series Editor: Ferri M. H. Aliabadi (Imperial College London, UK) Vol. 1 Vol. 2 Vol. 3 Buckling and Postbuckling Structures: Experimental, Analytical and Numerical Studies edited by B. G. Falzon and M. H. Aliabadi (Imperial College London, UK) Advances in Multiphysics Simulation and Experimental Testing of MEMS edited by A. Frangi, C. Cercignani (Politecnico di Milano, Italy), S. Mukherjee (Cornell University, USA) and N. Aluru (University of Illinois at Urbana Champaign, USA) Multiscale Modeling in Solid Mechanics: Computational Approaches edited by U. Galvanetto and M. H. Aliabadi (Imperial College London, UK)

3 Computational and Experimental Methods in Structures Vol. 3 Multiscale Modeling in Solid Mechanics Computational Approaches Editors Ugo Galvanetto M H Ferri Aliabadi Imperial College London, UK ICP Imperial College Press

4 Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore USA office: 27 Warren Street, Suite , Hackensack, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Computational and Experimental Methods in Structures Vol. 3 MULTISCALE MODELING IN SOLID MECHANICS Computational Approaches Copyright 2010 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN ISBN X Desk Editor: Tjan Kwang Wei Typeset by Stallion Press enquiries@stallionpress.com Printed in Singapore.

5 PREFACE This unique volume presents the state of the art in the field of multi-scale modelling in solid mechanics with particular emphasis on computational approaches. Contributions from leading experts in the field and younger promising researchers are reunited to give a comprehensive description of recently proposed techniques and of the engineering problems which can be tackled with them. The first four chapters provide a detailed introduction to the theories on which different multi-scale approaches are based, Chapters 5 6 present advanced applications of multi-scale approaches used to investigate the behaviour of non-linear structures. Finally Chapter 7 introduces the novel topic of materials with self-similar structure. All chapters are self-contained and can be read independently. Chapter 1 by V. G. Kouznetsova, M. G. D. Geers and W. A. M. Brekelmans is a concise but comprehensive introduction to the problem of mechanical multi-scale modelling in the general non-linear environment. This chapter presents a computational homogenization strategy, which provides a rigorous approach to determine the macroscopic response of heterogeneous materials with accurate account for microstructural characteristics and evolution. The implementation of the computational homogenization scheme in a Finite Element framework is discussed. Chapter 2 by Qi-Zhi Xiao and Bhushan Lai Karihaloo is limited to linear problems: higher order homogenization theory and corresponding consistent solution strategies are fully described. Modern high performance Finite Element Methods, which are powerful for the solution of sub-problems from homogenization analysis, are also discussed. Chapter 3 by G. K. Sfantos and M. H. Aliabadi presents a multiscale modelling of material degradation and fracture based on the use of the Boundary Element method. Both micro and macro-scales are being modelled with the boundary element method. Additionally, a scheme for coupling the micro-bem with a macro-fem is presented. Chapter 4 by J. C. Michel and P. Suquet is devoted to the Nonuniform Transformation Field Analysis which is a reduction technique introduced v

6 vi Preface in the field of multi-scale problems in Nonlinear Solid Mechanics. The flexibility and accuracy of the method are illustrated by assessing the lifetime of a plate subjected to cyclic four-point bending. Chapter5byM.Lefik,D.Boso,and B. A. Schrefler presents a multiscale approach for the thermo-mechanical analysis of hierarchical structures. Both linear and non-linear material behaviours are considered. The case of composites with periodic microstructure is dealt with in detail and an example shows the capability of the method. It is also shown how Artificial Neural Networks can be used either to substitute the overall material relationship or to identify the parameters of the constitutive relation. Chapter 6 by P. B. Lourenço, on recent advances in masonry modelling: micro-modelling and homogenization, addresses the issue of mechanical data necessary for advanced non-linear analysis first, with a set of recommendations. Then, the possibilities of using micro-modelling strategies replicating units and joints are addressed, with a focus on an interface finite element model for cyclic loading and a limit analysis model. Finally Chapter 7 by R. C. Picu and M. A. Soare deals with the mechanics of materials with self-similar hierarchical microstructure. Many natural materials have hierarchical microstructure that extends over a broad range of length scales. Performing efficient design of structures made from such materials requires the ability to integrate the governing equations of the respective physics on supports with complex geometry.

7 CONTENTS Preface Contributors Computational Homogenisation for Non-Linear Heterogeneous Solids 1 V. G. Kouznetsova, M. G. D. Geers and W. A. M. Brekelmans Two-Scale Asymptotic Homogenisation-Based Finite Element Analysis of Composite Materials 43 Qi-Zhi Xiao and Bhushan Lal Karihaloo Multi-Scale Boundary Element Modelling of Material Degradation and Fracture 101 G. K. Sfantos and M. H. Aliabadi Non-Uniform Transformation Field Analysis: A Reduced Model for Multiscale Non-Linear Problems in Solid Mechanics 159 Jean-Claude Michel and Pierre Suquet Multiscale Approach for the Thermomechanical Analysis of Hierarchical Structures 207 Marek J. Lefik, Daniela P. Boso and Bernhard A. Schrefler v ix Recent Advances in Masonry Modelling: Micromodelling and Homogenisation 251 Paulo B. Lourenço vii

8 viii Contents Mechanics of Materials With Self-Similar Hierarchical Microstructure 295 R.C.PicuandM.A.Soare Index 333

9 CONTRIBUTORS Prof. Wing Kam Liu Director of NSF Summer Institute on Nano Mechanics and Materials Northwestern University Department of Mechanical Engineering 2145 Sheridan Rd., Evanston, IL Prof. Ian Hutchings University of Cambridge Institute for Manufacturing Mill Lane, Cambridge CB2 1RX Prof.dr.ir. R. Huiskes (Rik) Eindhoven University of Technology Biomedical Engineering, Materials Technology Eindhoven, The Netherlands Prof. Manuel Doblare Structural Mechanics, Department of Mechanical Engineering Director of the Aragon Institute of Engineering Research Maria de Luna, Zaragoza (Spain) Prof. David Hills Lincoln College, Oxford University Oxford, UK Prof. Paulo Sollero University of Campinas Sao Paulo, Brasil ix

10 x Contributors Prof. Brian Falzon Department of Aeronautics, Monash University Australia Prof. K. Nikbin Department of Mechanical Engineering Imperial College London, UK Dr. M. Denda Department of Mechanical and Aerospace Engineering Rutgers University New Jersey, USA Prof. Ramon Abascal Escuela Superior de Ingenieros Camino de los descubrimientos s/n Sevilla, Spain Prof. K.J. Bathe Massachusetts Institute of Technology Boston, USA Prof. Ugo Galvanetto Department Engineering, Padova University Padova, Italy Prof. J.C.F. Telles COPPE, Brasil Prof. M Edirisinghe Department of Engineering University College London, UK Prof. Spiros Pantelakis Laboratory of Technology and Strength of Materials Department of Mechanical, Engineering and Aeronautics University of Patras, Greece

11 Contributors xi Prof. Eugenio Onate Director of CIMNE, UPC Barcelona, Spain Prof.J.Woody Department of Civil and Environmental Engineering UCLA, Los Angeles, CA, , USA Prof. Jan Sladek Slovak Academy of Sciences Slovakia Prof. Ch-Zhang University of Siegen Germany Prof. Mario Gugalinao University of Milan Italy Prof. B. Abersek University of Maribor Slovenia Dr.P.Dabnichki Department of Engineering Queen Mary, University of London Prof. Alojz Ivankovic Head of Mechanical Engineering UCD School of Electrical Electronic and Mechanical Engineering University College, Dublin, Ireland Prof. A. Chan Department of Engineering University of Birmingham, UK

12 xii Contributors Prof. Carmine Pappalettere Department of Engineering Bari University, Italy Prof. H. Espinosa Mechanical Engineering Northwestern University, USA Prof. Kon-Well Wang The Pennsylvania State University University Park, PA USA Prof. Ole Thybo Thomsen Department of Mechanical Engineering Aalborg University Aalborg East, Denmark Prof. Herbert A. Mang Technische Universität Wien Vienna University of Technology Institute for Mechanics of Materials and Structures Karlsplatz 13/202, 1040, Wien Austria Prof. Peter Gudmundson Department of Solid Mechanics KTH Engineering Sciences SE , Stockholm, Sweden Prof. Pierre Jacquot Nanophotonics and Metrology Laboratory Swiss Federal Institute of Technology Lausanne CH Lausanne, Switzerland

13 Contributors xiii Prof. K. Ravi-Chandar Department of Aerospace Engineering and Engineering Mechanics University of Texas at Austin, USA A. Sellier LadHyX. Ecole Polytechnique Palaiseau Cedex, France