Multiscale Methods in Computational Mechanics Progress and Accomplis
Many features in the behaviour of structures, materials and flows are caused by phenomena that occur at one to several scales below common levels of observation. Multiscale methods account for this scale dependence: They either derive properties at the le
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Series Editors Prof. Dr.-Ing. Friedrich Pfeiffer Prof. Dr.-Ing. Peter Wriggers
For other titles published in this series, go to www.springer.com/series/4623
René de Borst • Ekkehard Ramm Editors
Multiscale Methods in Computational Mechanics Progress and Accomplishments
Editors René de Borst Department of Mechanical Engineering Eindhoven University of Technology Eindhoven The Netherlands [email protected]
Ekkehard Ramm Institute of Structural Mechanics University of Stuttgart Stuttgart Germany
e-ISSN 1860-0816 ISSN 1613-7736 ISBN 978-90-481-9808-5 e-ISBN 978-90-481-9809-2 DOI 10.1007/978-90-481-9809-2 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2010935928 © 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: eStudio Calamar S.L. Printed on acid-free paper
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Table of Contents
Preface
ix
List of Authors
xi Part 1: Computational Fluid Dynamics
Residual-Based Variational Multiscale Theory of LES Turbulence Modeling Y. Bazilevs, V.M. Calo, T.J.R. Hughes and G. Scovazzi A Posteriori Error Estimation for Computational Fluid Dynamics. The Variational Multiscale Approach G. Hauke, M.H. Doweidar and D. Fuster
3
19
Advances in Variational Multiscale Methods for Turbulent Flows P. Gamnitzer, V. Gravemeier and W.A. Wall
39
Variational Germano Approach for Multiscale Formulations I. Akkerman, S.J. Hulshoff, K.G. van der Zee and R. de Borst
53
Dissipative Structure and Long Term Behavior of a Finite Element Approximation of Incompressible Flows with Numerical Subgrid Scale Modeling R. Codina, J. Principe and S. Badia Large-Eddy Simulation of Multiscale Particle Dynamics at High Volume Concentration in Turbulent Channel Flow B.J. Geurts
75
95
Part 2: Materials with Microstructure An Incremental Strategy for Modeling Laminate Microstructures in Finite Plasticity – Energy Reduction, Laminate Orientation and Cyclic Behavior K. Hackl and D.M. Kochmann
v
117
vi
Table of Contents
The Micromorphic versus Phase Field Approach to Gradient Plasticity and Damage with Application to Cracking in Metal Single Crystals O. Aslan and S. Forest
135
Homogenization and Multiscaling of Granular Media for Different Microscopic Constraints C. Miehe, J. Dettmar and D. Zäh
155
Effective Hydraulic and Mechanical Properties of Heterogeneous Media with Interfaces L. Dormieux, L. Jeannin and J. Sanahuja
179
An Extended Finite Element Method for the Analysis of Submicron Heat Transfer Phenomena P. Lee, R. Yang and K. Maute
195
Part 3: Composites, Laminates, and Structures: Optimization Multiscale Modeling and S
