lecture notes in applied and computational mechanics

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Lecture Notes in Applied and Computational Mechanics

Prof. Dr.-Ing. Friedrich Pfeiffer Prof. Dr.-Ing. Peter Wriggers

Volume 55

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For other titles published in this series, go to

Multiscale Methods inComputational Mechanics

Ekkehard RammRené de Borst •Editors

Progress and Accomplishments

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Department of Mechanical Engineering

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Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

René de BorstEditors

EindhovenThe Netherlands

Eindhoven University of Technology

R.d.Borst@tue.nl

Ekkehard Ramm

University of StuttgartInstitute of Structural Mechanics

StuttgartGermany

ISSN 1613-7736 e-ISSN 1860-0816ISBN 978-90-481-9808-5 e-ISBN 978-90-481-9809-2DOI 10.1007/978-90-481-9809-2

Cover design: eStudio Calamar S.L.

Library of Congress Control Number: 2010935928

Table of Contents

Preface ix

List of Authors xi

Part 1: Computational Fluid Dynamics

Residual-Based Variational Multiscale Theory of LES Turbulence Modeling 3Y. Bazilevs, V.M. Calo, T.J.R. Hughes and G. Scovazzi

A Posteriori Error Estimation for Computational Fluid Dynamics.The Variational Multiscale Approach 19G. Hauke, M.H. Doweidar and D. Fuster

Advances in Variational Multiscale Methods for Turbulent Flows 39P. Gamnitzer, V. Gravemeier and W.A. Wall

Variational Germano Approach for Multiscale Formulations 53I. Akkerman, S.J. Hulshoff, K.G. van der Zee and R. de Borst

Dissipative Structure and Long Term Behavior of a Finite ElementApproximation of Incompressible Flows with Numerical Subgrid ScaleModeling 75R. Codina, J. Principe and S. Badia

Large-Eddy Simulation of Multiscale Particle Dynamics at High VolumeConcentration in Turbulent Channel Flow 95B.J. Geurts

Part 2: Materials with Microstructure

An Incremental Strategy for Modeling Laminate Microstructures in FinitePlasticity – Energy Reduction, Laminate Orientation and Cyclic Behavior 117K. Hackl and D.M. Kochmann

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vi Table of Contents

The Micromorphic versus Phase Field Approach to Gradient Plasticity andDamage with Application to Cracking in Metal Single Crystals 135O. Aslan and S. Forest

Homogenization and Multiscaling of Granular Media for DifferentMicroscopic Constraints 155C. Miehe, J. Dettmar and D. Zäh

Effective Hydraulic and Mechanical Properties of Heterogeneous Mediawith Interfaces 179L. Dormieux, L. Jeannin and J. Sanahuja

An Extended Finite Element Method for the Analysis of Submicron HeatTransfer Phenomena 195P. Lee, R. Yang and K. Maute

Part 3: Composites, Laminates and Structures: Optimization

Multiscale Modeling and Simulation of Composite Materials andStructures 215J. Fish

Multiscale Modelling of the Failure Behavior of Fibre-ReinforcedLaminates 233M.V. Cid Alfaro, A.S.J. Suiker and R. de Borst

Improved Multiscale Computational Strategies for Delamination 261O. Allix, P. Gosselet and P. Kerfriden

Damage Propagation in Composites – Multiscale Modeling andOptimization 281E. Ramm, A. Erhart, T. Hettich, I. Bruss, F. Hilchenbach and J. Kato

Computational Multiscale Model for NATM Tunnels: Micromechanics-Supported Hybrid Analyses 305S. Scheiner, B. Pichler, C. Hellmich and H.A. Mang

Optimization of Corrugated Paperboard under Local and Global BucklingConstraints 329T. Flatscher, T. Daxner, D.H. Pahr and F.G. Rammerstorfer

Framework for Multi-Level Optimization of Complex Systems 347A. de Wit and F. van Keulen

Table of Contents vii

Part 4: Coupled Problems and Porous Media

Multiscale/Multiphysics Model for Concrete 381B.A. Schrefler, F. Pesavento and D. Gawin

Swelling Phenomena in Electro-Chemically Active Hydrated Porous Media 405W. Ehlers, B. Markert and A. Acartürk

Propagating Cracks in Saturated Ionized Porous Media 425F. Kraaijeveld and J.M. Huyghe

Author Index 443

Subject Index 445

Preface

For a long time limited computational resources restricted the scale of observationand modeling of physical systems mostly to one scale in time and space. This modusoperandi was accepted although it was well known that the response at the level ofpractical interest is to a large extent determined by processes that occur at scaleswhich are one to several orders of a magnitude smaller, namely the meso, microor even nanoscales. The rapid increase in computer power and the development ofefficient computational methods allow coming closer to the human dream of a con-tinuous model through all spatial and temporal scales. However seeking solutionsusing numerical models simultaneously at the various length scales has proven to bebeyond current computational capabilities. This perception is the starting point forthe development of Multiscale Methods which is currently one of the hot researchtopics all over the world. Multiscale Methods either derive properties at the levelof observation by repeated numerical homogenization of more fundamental physicalproperties several scales below (upscaling), or they devise concurrent schemes wherethose parts of the domain that are of interest are computed with a higher resolutionthan parts that are of less interest or where the solution is varying only slowly.

The present volume contains selected papers presented at the InternationalColloquium on Multiscale Methods in Computational Mechanics in Rolduc, theNetherlands, on 11–13 March 2009 (MMCM 2009). The contributions in the firstpart address multiscale methods in Computational Fluid Dynamics; in particularturbulence modeling applying the Variational Multiscale Method is described. Thesecond part deals with materials having a distinct microstructure such as single- andpoly-crystals, granular materials, aggregates embedded in a matrix, micro-laminatesand nano-composites. Part three focuses on materials and structures and the interac-tion between their behavior on micro/meso- and macro-scales. Failure of compositesand laminates, material modeling of shotcrete in tunnels, buckling of paperboard ondifferent scales as well as material and structural optimization are investigated. Thefourth part concentrates on coupled problems and porous media like concrete andcharged hydrated materials.

The mentioned colloquium was organized by the German–Dutch Research Unit“Multiscale Methods in Computational Mechanics”, in which a group of scientistsin Germany at Universität Stuttgart and TU München and in the Netherlands at TU

ix

x Preface

Delft and TU Eindhoven have joined forces in order to address a variety of problemareas and computational solution strategies for multiscale methods in mechanics ofstructures, materials and flows. This joint project, which serves as a prototype forresearch cooperations within Europe, was financially supported by the German Re-search Foundation (Deutsche Forschungsgemeinschaft, DFG FOG 509), The Neth-erlands Technology Foundation (STW) and The Netherlands Organization for Sci-entific Research (NWO). This support is very much appreciated.

We also would like to thank the authors very much for their valuable contribu-tions. Furthermore our thanks go to Springer for taking over the publication of thisvolume in its LNACM series.

January 2010René de Borst, Technische Universiteit EindhovenEkkehard Ramm, Universität Stuttgart

List of Authors

Acartürk, Ayhan Y.Universität Stuttgart, Institut für Mechanik (Bauwesen), Stuttgart, Germanyacar@mechbau.uni-stuttgart.de

Akkerman, IdoUniversity of California, San Diego, Department of Structural Engineering, USAIAkkerman@ucsd.edu

Allix, OlivierL.M.T., ENS de Cachan, Franceallix@lmt.ens-cachan.fr

Aslan, OzgurMines ParisTech, Centre des Matériaux, Evry, Franceozgur.aslan@ensmp.fr

Badia, SantiagoUniversitat Politècnica de Catalunya, International Center for Numerical Methods inEngineering (CIMNE), Barcelona, Spainsbadia@cimne.upc.edu

Bazilevs, YuriUniversity of California, San Diego, Department of Structural Engineering, USAyuri@ucsd.edu

de Borst, RenéEindhoven University of Technology, Department of Mechanical Engineering,Eindhoven, The NetherlandsR.d.Borst@tue.nl

xi

xii List of Authors

Bruss, IngridUniversität Stuttgart, Institut für Baustatik und Baudynamik, Stuttgart, Germanybruss@ibb.uni-stuttgart.de

Calo, Victor M.KAUST, Earth and Environmental Science and Engineering, Saudi Arabiavictor.calo@kaust.edu.sa

Cid Alfaro, Marcela V.Corus, IJmuiden, The Netherlands

Codina, RamonUniversitat Politècnica de Catalunya, Departament de Resistencia de Materials iEstructures a l’Enginyeria, Barcelona, Spainramon.codina@upc.edu

Daxner, ThomasCAE Simulations & Solutions, Wien, Austriadaxner@ilsb.tuwien.ac.at

Dettmar, JoachimUniversität Stuttgart, Institut für Mechanik (Bauwesen), Stuttgart, Germany

Dormieux, LucÉcole Nationale des Ponts et Chaussées, Laboratoire des Matériaux et Structures duGénie Civil (LMSGC), Champs-sur-Marne, Francedormieux@lmsgc.enpc.fr

Doweidar, Mohamed H.Centro PolitCcnico Superior de Zaragoza, Área de Mecánica de Fluidos, Zaragoza,Spain

Ehlers, WolfgangUniversität Stuttgart, Institut für Mechanik (Bauwesen), Stuttgart, Germanyehlers@mechbau.uni-stuttgart.de

Erhart, AndreaDYNAmore, Stuttgart, Germanyandrea.erhart@dynamore.de

Fish, JacobRensselaer Polytechnic Institute, Multiscale Science and Engineering Center,Troy, NY, USAfishj@rpi.edu

List of Authors xiii

Flatscher, ThomasTechnische Universität Wien, Institut für Leichtbau und Struktur-Biomechanik,Wien, Austriaflatscher@ilsb.tuwien.ac.at

Forest, SamuelMines ParisTech, Centre des Matériaux, Evry, Francesamuel.forest@ensmp.fr

Fuster, DanielCentro Politécnico Superior de Zaragoza, Área de Mecánica de Fluidos, Zaragoza,Spain

Gamnitzer, PeterTechnische Universität München, Lehrstuhl für Numerische Mechanik, München,Germanygamnitzer@lnm.mw.tum.de

Gawin, DariuszTU Lodz, Department of Building Physics and Building Materials, Lodz, Polandgawindar@p.lodz.pl

Geurts, Bernard J.University of Twente, Mathematical Sciences, Enschede; Eindhoven University ofTechnology, Department of Applied Physics, Eindhoven, The Netherlandsb.j.geurts@utwente.nl

Gosselet, PierreL.M.T., ENS de Cachan, Francegosselet@lmt.ens-cachan.fr

Gravemeier, VolkerTechnische Universität München, Lehrstuhl für Numerische Mechanik, München,Germanyvgravem@lnm.mw.tum.de

Hackl, KlausRuhr-Universität Bochum, Lehrstuhl für Allgemeine Mechanik, Bochum, Germanyklaus.hackl@rub.de

Hauke, GuillermoCentro Politécnico Superior de Zaragoza, Área de Mecánica de Fluidos, Zaragoza,Spainghauke@unizar.es

xiv List of Authors

Hellmich, ChristianTechnische Universität Wien, Institut für Mechanik der Werkstoffe und Strukturen,Wien, Austriachristian.hellmich@tuwien.ac.at

Hettich, Thomas M.Mahle GmbH, Stuttgart, Germany

Hilchenbach, FrédéricUniversität Stuttgart, Institut für Baustatik und Baudynamik, Stuttgart, Germanyhilchenbach@ibb.uni-stuttgart.de

Hughes, Thomas J.R.The University of Texas at Austin, Institute for Computational Engineering andSciences, Austin, USAhughes@ices.utexas.edu

Hulshoff, Steven J.Delft University of Technology, Aerospace Engineering, Delft, The Netherlandss.j.hulshoff@tudelft.nl

Huyghe, Jacques M.R.Eindhoven University of Technology, Department of Biomedical Engineering,Eindhoven, The Netherlandsj.m.r.huyghe@tue.nl

Jeannin, LaurentGaz de France (GDF), France

Kato, JunjiUniversität Stuttgart, Institut für Baustatik und Baudynamik, Stuttgart, Germanykato@ibb.uni-stuttgart.de

Kerfriden, PierreL.M.T., ENS de Cachan, Francekerfriden@lmt.ens-cachan.fr

Kochmann, Dennis M.Ruhr-Universität Bochum, Lehrstuhl für Allgemeine Mechanik, Bochum, Germanydennis.kochmann@rub.de

Kraaijeveld, FamkeEindhoven University of Technology, Eindhoven, The Netherlandsf.kraaijeveld@tue.nl

List of Authors xv

Lee, PilhwaUniversity of Colorado at Boulder, Department of Mechanical Engineering,Boulder, USApilhwa.lee@colorado.edu

Mang, HerbertTechnische Universität Wien, Institut für Mechanik der Werkstoffe und Strukturen,Wien, Austriaherbert.mang@tuwien.ac.at

Markert, BerndUniversität Stuttgart, Institut für Mechanik (Bauwesen), Stuttgart, Germanymarkert@mechbau.uni-stuttgart.de

Maute, KurtUniversity of Colorado at Boulder, Department of Aerospace Engineering Sciences,Boulder, USAmaute@colorado.edu

Miehe, ChristianUniversität Stuttgart, Institut für Mechanik (Bauwesen), Stuttgart, Germanycm@mechbau.uni-stuttgart.de

Pahr, Dieter H.Technische Universität Wien, Institut für Leichtbau und Struktur-Biomechanik,Wien, Austriapahr@ilsb.tuwien.ac.at

Pesavento, FrancescoUniversità degli Studi di Padova, Dipartimento di Costruzioni e Trasporti,Padova, Italyfrancesco.pesavento@unipd.it

Pichler, BernhardTechnische Universität Wien, Institut für Mechanik der Werkstoffe und Strukturen,Wien, Austriabernhard.pichler@tuwien.ac.at

Principe, JavierUniversitat Politécnica de Catalunya, International Center for Numerical Methods inEngineering (CIMNE), Barcelona, Spainprincipe@cimne.upc.edu

xvi List of Authors

Ramm, EkkehardUniversität Stuttgart, Institut für Baustatik und Baudynamik, Stuttgart, Germanyramm@ibb.uni-stuttgart.de

Rammerstorfer, Franz G.Technische Universität Wien, Institut für Leichtbau und Struktur-Biomechanik,Wien, Austriara@ilsb.tuwien.ac.at

Sanahuja, JulienElectricité de France (EDF), Department of Materials and Mechanics ofComponents, Moret-sur-Loing, Francejulien.sanahuja@edf.fr

Schrefler, Bernhard A.Università degli Studi di Padova, Dipartimento di Costruzioni e Trasporti,Padova, Italybernhard.schrefler@unipd.it

Scheiner, StefanThe University of Western Australia, Computer Science and Software Engineering,Crawley, Perth, Western Australiastefan.scheiner@csse.uwa.edu.au

Scovazzi, GuglielmoSandia National Laboratories, Albuquerque, USAgscovaz@sandia.gov

Suiker, Akke S.J.Delft University of Technology, Aerospace Engineering, Delft, The Netherlandsa.s.j.suiker@tudelft.nl

van der Zee, KrisThe University of Texas at Austin, Institute for Computational Engineering andSciences, Austin, USA

van Keulen, FredDelft University of Technology, Department of Precision and MicrosystemsEngineering, Delft, The Netherlandsa.vankeulen@tudelft.nl

Wall, Wolfgang A.Technische Universität München, Lehrstuhl für Numerische Mechanik,München, Germanywall@lnm.mw.tum.de

List of Authors xvii

de Wit, Albert J.Dutch National Aerospace Laboratory (NLR), Amsterdam, The Netherlandsadewit@nlr.nl

Yang, RongguiUniversity of Colorado at Boulder, Department of Mechanical Engineering,Boulder, USAronggui.yang@colorado.edu

Zäh, DominicUniversität Stuttgart, Institut für Mechanik (Bauwesen), Stuttgart, Germanyzaeh@mechbau.uni-stuttgart.de