Advanced Computational Materials Modeling E-Book

• Herausgeber: Wiley-VCH
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 686

Veröffentlichungsjahr: 2011

Beschreibung

With its discussion of strategies for modeling complex materials using new numerical techniques, mainly those based on the finite element method, this monograph covers a range of topics including computational plasticity, multi-scale formulations, optimization and parameter identification, damage mechanics and nonlinear finite elements.

Leseprobe

Contents

Cover

Half Title page

Title page

Copyright page

Preface

List of Contributors

Chapter 1: Materials Modeling – Challenges and Perspectives

1.1 Introduction

1.2 Modeling Challenges and Perspectives

1.3 Concluding Remarks

Acknowledgments

References

Chapter 2: Local and Nonlocal Modeling of Ductile Damage

2.1 Introduction

2.2 Continuum Damage Mechanics

2.3 Lemaitre’s Ductile Damage Model

2.4 Modified Local Damage Models

2.5 Nonlocal Formulations

2.6 Numerical Analysis

2.7 Concluding Remarks

Acknowledgments

References

Chapter 3: Recent Advances in the Prediction of the Thermal Properties of Metallic Hollow Sphere Structures

3.1 Introduction

3.2 Methodology

3.3 Finite Element Analysis on Regular Structures

3.4 Finite Element Analysis on Cubic-Symmetric Models

3.5 LMC Analysis of Models of Cross Sections

3.6 Computed Tomography Reconstructions

3.7 Conclusions

References

Chapter 4: Computational Homogenization for Localization and Damage

4.1 Introduction

4.2 Continuous–Continuous Scale Transitions

4.3 Continuous–Discontinuous Scale Transitions

4.4 Closing Remarks

References

Chapter 5: A Mixed Optimization Approach for Parameter Identification Applied to the Gurson Damage Model

5.1 Introduction

5.2 Gurson Damage Model

5.3 Parameter Identification

5.4 Optimization Methods – Genetic Algorithms and Mathematical Programming

5.5 Sensitivity Analysis

5.6 A Mixed Optimization Approach

5.7 Examples of Application

5.8 Concluding Remarks

Acknowledgments

References

Chapter 6: Semisolid Metallic Alloys Constitutive Modeling for the Simulation of Thixoforming Processes

6.1 Introduction

6.2 Semisolid Metallic Alloys Forming Processes

6.3 Rheological Aspects

6.4 Numerical Background in Large Deformations

6.5 State-of-the-Art in FE-Modeling of Thixotropy

6.6 A Detailed One-Phase Model

6.7 Numerical Applications

6.8 Conclusion

References

Chapter 7: Modeling of Powder Forming Processes; Application of a Three-invariant Cap Plasticity and an Enriched Arbitrary Lagrangian–Eulerian FE Method

7.1 Introduction

7.2 Three-Invariant Cap Plasticity

7.3 Arbitrary Lagrangian–Eulerian Formulation

7.4 Enriched ALE Finite Element Method

7.5 Conclusion

Acknowledgments

References

Chapter 8: Functionally Graded Piezoelectric Material Systems – A Multiphysics Perspective

8.1 Introduction

8.2 Piezoelectricity

8.3 Functionally Graded Piezoelectric Materials

8.4 Finite Element Method for Piezoelectric Structures

8.5 Influence of Property Scale in Piezotransducer Performance

8.6 Influence of Microscale

8.7 Conclusion

Acknowledgments

References

Chapter 9: Variational Foundations of Large Strain Multiscale Solid Constitutive Models: Kinematical Formulation

9.1 Introduction

9.2 Large Strain Multiscale Constitutive Theory: Axiomatic Structure

9.3 The Multiscale Model Definition

9.4 Specific Classes of Multiscale Models: The Choice of

9.5 Models with Stress Averaging in the Deformed RVE Configuration

9.6 Problem Linearization: The Constitutive Tangent Operator

9 7 Time-Discrete Multiscale Models

9.8 The Infinitesimal Strain Theory

9.9 Concluding Remarks

Appendix

Acknowledgments

References

Chapter 10: A Homogenization-Based Prediction Method of Macroscopic Yield Strength of Polycrystalline Metals Subjected to Cold-Working

10.1 Introduction

10.2 Two-Scale Modeling and Analysis Based on Homogenization Theory

10.3 Numerical Specimens: Unit Cell Models with Crystal Plasticity

10.4 Approximate Macroscopic Constitutive Models

10.5 Macroscopic Yield Strength after Three-Step Plastic Forming

10.6 Application for Pilger Rolling of Steel Pipe

10.7 Conclusion

References

Index

Edited byMiguel Vaz Júnior,Eduardo A. de Souza Neto, andPablo A. Muñoz-Rojas

Advanced Computational Materials Modeling

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The Editors

Prof. Miguel Vaz JúniorState Univ. of Santa CatarinaDept. of Mech. EngineeringUniv. Campus Avelino Marcante89223-100 Joinville SCBrasil

Prof. Eduardo A. de Souza NetoSwansea UniversityCivil & Comp. Eng. CentreSingleton ParkSwansea SA2 8PPUnited Kingdom

Prof. Dr. Pablo A. Muñoz-RojasState Univ. of Santa CatarinaCtr. Techn. SciencesUniv. Campus Avelino Marcante89223-100 Joinville SCBrasil

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for

British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibli- ografie; detailed bibliographic data are available on the Internet at <http://dnb.d-nb.de>.

© 2011 WILEY-VCH Verlag & Co. KGaA, Boschstr. 12, 69469 Weinheim, Germany

All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law.

Print ISBN: 978-3-527-32479-8 ePdf ISBN: 978-3-527-63232-9 ePub ISBN: 978-3-527-63233-6 Mobi ISBN: 978-3-527-64215-1

Preface

The systematic analysis of solid mechanics problems using numerical techniques can be traced back to the 1960s and 1970s following the development of the finite element method. The early approaches to elastic materials and, to a certain extent, inelastic problems, paved the way to an all-encompassing discipline known today as computational materials modelling.

As computer technologies have evolved, placing portable computers on the desk of virtually every university staff and graduate student, numerical techniques and algorithms have experienced extraordinary advances in a wide range of engineering fields. The development of new computational modelling strategies, especially those based on the finite element method, has prompted new applications such as crystal plasticity, damage and multi-scale formulations, semi-solid, particulate, porous and functionally graded materials amongst others.

This book was conceived in an attempt to congregate innovative modelling approaches so that graduate students and researchers, both from academia and industry, can use it as a springboard to further advancements. It is also important to say that this book is by no means exhaustive on the subject of materials modelling and some advanced readers would probably have appreciated the inclusion of further details on the underlying mathematical formulations. For the sake of objectivity, we have focussed on topics which show not only new and innovative modelling strategies, but also on sound physical foundations and both promising and direct application to engineering problems. Emphasis is placed on computational modelling rather than materials processing, although illustrative examples featuring some process applications are also included. A review of the state-of-the-art modelling approaches as well as a discussion on future trends and advancements is also presented by the contributors.

Finally we would like to sincerely thank all the authors for their time and commitment to produce such high quality chapters. We really appreciate their contribution.

July 2010

Miguel Vaz Jr.Eduardo A. de Souza NetoPablo A. Muñoz-Rojas

List of Contributors

Masayoshi AkiyamaKyoto Institute of TechnologyDepartment of MechanicalEngineeringGosho-Kaido-choMatsugasakiSakyo-kuKyoto 606-8585Japan

Filipe Xavier Costa AndradeUniversity of PortoFaculty of EngineeringRua Dr. Roberto Frias4200-465 PortoPortugal

Irina V. BelovaUniversity of NewcastleUniversity Centre for Mass andThermal Transport inEngineering MaterialsPriority Research Centre forGeotechnical and MaterialsModellingSchool of EngineeringCallaghan, NSW 2308Australia

Eduardo L. CardosoState University ofSanta CatarinaDepartment of MechanicalEngineering Centre forTechnological SciencesCampus Universitário Prof.Avelino MarcanteSanta Catarina89223-100 – JoinvilleBrazil

José Manuel de Almeida César de SáUniversity of PortoFaculty of EngineeringRua Dr. Roberto Frias4200-465 PortoPortugal

Guillermo Juan CreusFederal University ofRio Grande do SulDepartment of Civil EngineeringCentre for Computational andApplied MechanicsRua Osvaldo Aranha90035-190 – Porto Alegre99, Rio Grande do SulBrazil

Luiz Antonio B. da CundaFederal University of RioGrande FoundationSchool of EngineeringRua Alfredo Huch96201-900 – Rio Grande475, Rio Grande do SulBrazil

Raúl A. FeijóoLaboratorio Nacional deComputação Científica(LNCC/MCT) & InstitutoNacional de Ciência e Tecnologiaem Medicina Assistida porComputação Científica(INCT-MACC) Av.Getúlio Vargas 333QuitandinhaCEP 25651-070Petrópolis – RJBrazil

Thomas FiedlerUniversity of NewcastleUniversity Centre for Mass andThermal Transport inEngineering MaterialsPriority Research Centre forGeotechnical and MaterialsModellingSchool of EngineeringCallaghan, NSW 2308Australia

Marc G. D. GeersEindhoven University ofTechnologyDepartment of MechanicalEngineeringP.O. Box 5135600 MBEindhovenNetherlands

Amir R. KhoeiSharif University of TechnologyDepartment of Civil EngineeringCenter of Excellence in Structuresand Earthquake EngineeringP.O. Box. 11365-9313TehranIran

Shigemitsu KimuraPipe & Tube CompanySumitomo MetalIndustries Ltd.1 Higashi-mukoujimaAmagasakiHyogo 660-0856Japan

Roxane KoeuneUniversity of LiègeAerospace and MechanicalEngineering Department1 Chemin des ChevreuilsB4000 LiègeBelgium

Varvara KouznetsovaEindhoven University ofTechnologyDepartment of MechanicalEngineeringP.O. Box 5135600 MBEindhovenNetherlands

Kouichi KurodaCorporate R & D LaboratoriesSumitomo Metal Industries Ltd.1-8 Fuso-cho, AmagasakiHyogo 660-0891Japan

Thierry J. MassartUniversité Libre deBruxelles (ULB)Building Architectureand Town PlaningCP 194/2Av. F.-D. Roosevelt 501050 BrusselsBelgium

Pablo Andreś Muñoz-RojasSanta Catarina StateUniversity - UDESCDepartment of MechanicalEngineeringCentre for Technological SciencesCampus Universitário Prof.Avelino Marcante89223-100, JoinvilleSanta CatarinaBrazil

Graeme E. MurchUniversity of NewcastleUniversity Centre for Mass andThermal Transport inEngineering MaterialsPriority Research Centre forGeotechnical and MaterialsModellingSchool of EngineeringCallaghan, NSW 2308Australia

Eduardo A. de Souza NetoSwansea UniversityCivil and ComputationalEngineering CentreSchool of EngineeringSingleton ParkSA2 8PPSwanseaUK

Gláucio Hermogenes PaulinoUniversity of Illinois atUrbana-ChampaignNewmark LaboratoryDepartment of Civil andEnvironment Engineering205 North Mathews Av.UrbanaIL 61801USA

Ron H. J. PeerlingsEindhoven University ofTechnologyDepartment of MechanicalEngineeringP.O. Box 5135600 MB EindhovenNetherlands

Francisco Manuel Andrade PiresUniversity of PortoFaculty of EngineeringRua Dr. Roberto Frias4200-465 PortoPortugal

Jean-Philippe PonthotUniversity of LiègeAerospace and MechanicalEngineering Department1 Chemin des ChevreuilsB4000 LiègeBelgium

Wilfredo Montealegre RubioNational University of ColombiaSchool of Mechatronic ofthe Faculty of MineCarrera 80 No. 65-223bloque M8, oficina 113Medellin, AntioquiaColombia

Emílio Carlos Nelli SilvaUniversity of São PauloDepartment of Mechatronics andMechanical Systems EngineeringAv. Prof. Mello Moraes2231 - Cidade UniversitáriaSão Paulo05508-900Brazil

Kenjiro TeradaTohoku UniversityDepartment ofCivil EngineeringAza-Aoba 6-6-06AramakiAoba-kuSendai 980-8579Japan

Sandro Luis VatanabeUniversity of São PauloDepartment of Mechatronics andMechanical Systems EngineeringAv. Prof. Mello Moraes2231 - Cidade UniversitáriaSão Paulo05508-900Brazil

Miguel Vaz Jr.Santa Catarina StateUniversity - UDESCDepartment of MechanicalEngineeringCentre for Technological SciencesCampus Universitário Prof.Avelino Marcante89223-100 JoinvilleSanta CatarinaBrazil

Ikumu WatanabeNational Institute forMaterials ScienceStructural Metals CenterSengen 1-2-1TsukubaIbaraki 305-0047Japan

Andreas ÖchsnerTechnical University of MalaysiaDepartment of AppliedMechanicsFaculty of MechanicalEngineeringSkudaiJohor81310 UTMMalaysia

andUniversity of NewcastleUniversity Centre for Mass andThermal Transport inEngineering MaterialsPriority Research Centre forGeotechnical and MaterialsModellingSchool of EngineeringCallaghan, NSW 2308Australia

Chapter 1

Materials Modeling – Challenges and Perspectives

Miguel Vaz Jr., Eduardo A. de Souza Neto, Pablo Andreś Muñoz-Rojas

1.1 Introduction

The development of materials modeling has experienced a huge growth in the last 10 years. New mathematical approaches (formulations, concepts, etc.), numerical techniques (algorithms, solution strategies, etc.), and computing methods (parallel computing, multigrid techniques, etc.), allied to the ever-increasing computational power, have fostered the research growth observed in recent times. Numerical implementation of some modeling concepts, such as multiscale formulations and optimization procedures, were severally restricted two decades ago due to limitation of computing resources. What were once perspectives of new advancements have become a reality in the last few years and longstanding difficulties have been overcome.

It is important to emphasize that materials modeling is not a recent concept or a new research topic. Some material descriptions widely accepted and used these days were actually proposed in the late eighteenth century. For instance, within the framework of modeling inelastic deformation of metals, the French engineer Henri Tresca (1814–1884), professor at the Conservatoire National des Arts et Métiers (CNAM) in Paris, was the first to define distinct rules for the onset of plastic flow in ductile solids [1]. Tresca’s groundbreaking studies established a material-dependent critical plastic threshold given by the maximum shear stress. The apparently simple concept gave rise to a completely new approach to studying deformation of solid materials, and, today, his principle is known as Tresca’s yield criterion. It is interesting to mention that, in spite of many years of proposition, numerical implementation of Tresca’s criterion is not straightforward because of the sharp corners of the yield locus and its association with the plastic-normality flow rule [2, 3].

The search for alternate modeling descriptions is also not a new endeavor. For similar problems, Maksymilian Tytus Huber (1872–1950), a Polish engineer, postulated that material strength depends upon the spatial state of stresses and not on a single component of the stress tensor [4]. Independently, the Austrian mathematician and engineer, Richard von Mises (1883–1953), indicated that plastic deformation of solids is associated with some measure of an equivalent stress state [5]. The assumption indicates that plastic deformation is initiated when the second deviatoric stress invariant reaches a critical value. A few years later, the German engineer, Heinrich Hencky (1885–1952), still within the criterion introduced by Huber and von Mises, suggested that the onset of plastic deformation takes place when the elastic energy of distortion reaches a critical value [6]. An alternate physical interpretation was proposed by Roš and Eichinger, who demonstrated that the critical distortional energy principle is equivalent to defining a critical shear stress on the octahedral plane [7], generally known as maximum octahedral shear stress criterion. The aforementioned elastic–plastic modeling assumptions are known today as the Huber–Mises–Hencky yield criterion. A brief review of the early works on modeling of plastic deformation of metals illustrates the drive toward understanding the physics of material behavior and its translation into mathematical descriptions.1

Despite the fact that the principles of plasticity theory have long been established, application to realistic problems or advanced materials using only mathematical tools is difficult or even impossible. Following the example on deformation of metals, when addressing computational modeling of elastic–plastic deformation at finite strains, the solution requires a physical/material description (e.g., the classical Huber–Mises–Hencky equation), a mathematical formulation able to handle geometrical and material nonlinearity (e.g., multiplicative decomposition of the gradient of deformation tensor into elastic and plastic components), and a computational approximation/discretization of the physical and mathematical problem (e.g., iterative procedures such as the Newton–Raphson and arc-length methods). This class of problems has already been exhaustively investigated in the last 30 years, and the literature shows a wide variety of strategies (see, for instance, Ref. [11] and references therein).

The illustration on the development of physical/mathematical/numerical formulations of elastic–plastic deformation of ductile solids shows that a proper material modeling requires

1) understanding of the physics involved in the problem;

2) comprehensive theoretical and mathematical treatment of the phenomena;

3) sound and consistent numerical approximation/discretization of the governing and constitutive equations; and

4) adequate computing resources.

These principles are extensive to modeling and simulation of any materials-processing operation. In a broader context of materials modeling, the literature has shown an increasing pace in the evolution of each one of the aspects mentioned in items (1–4). Advancements in mathematical and numerical tools have prompted investigation in areas of materials modeling ranging from electronic and atomistic level to complex structures within the continuum realm [12]. Despite this considerable progress, there are still pressing challenges to be overcome, mainly those associated with more realistic materials-processing operations or simulation of complex materials structures. This chapter highlights some modeling issues under current and intense scrutiny by researchers and does not intend to be exhaustive. The other chapters of this book present deeper insights into materials modeling and simulation of some class of problems that, in a way, we hope, will serve as a springboard for further realistic applications.