Verfügbarkeit: Micromechanics of composite materials

Micromechanics of composite materials: a generalized multiscale analysis approach

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Bibliographische Detailangaben
Hauptverfasser:	Aboudi, Jacob (VerfasserIn), Arnold, Steven M. (VerfasserIn), Bednarcyk, Brett A. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam [u.a.] Elsevier, Butterworth-Heinemann 2013
Ausgabe:	1. ed.
Schlagworte:	Micromechanics Verbundwerkstoff Mikromechanik
Online-Zugang:	Inhaltsverzeichnis Klappentext
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XXII, 984 S., [12 Bl.] Ill., graph. Darst.
ISBN:	9780123970350

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adam_text	Contents Preface ..........................................................................................................xvii Acknowledgments ............................................................................................xix Acronyms ........................................................................................................xxi Chapter 1 Introduction ......................................................................................1 1.1 Fundamentals of Composite Materials and Structures .........................................2 1.2 Modeling of Composites .....................................................................................10 1.3 Description of the Book Layout ..........................................................................15 1.4 Suggestions on How to Use the Book ................................................................17 Chapter 2 Constituent Material Modeling ..........................................................19 2.1 Reversible Models ...............................................................................................25 2.1.1 Elasticity .....................................................................................................26 2.1.2 Ramberg-Osgood Nonlinear Elastic Constitutive Equations .....................33 2.1.3 Viscoelasticity .............................................................................................34 2.2 Irreversible Deformation Models ........................................................................46 2.2.1 Incremental Plasticity .................................................................................47 2.2.2 Power-Law Creep .......................................................................................49 2.2.3 Viscoplasticity .............................................................................................50 2.3 Damage/Life Models ...........................................................................................58 2.3.1 Continuum-Based Damage .........................................................................59 2.3.2 Interface Models .........................................................................................80 2.4 Concluding Remarks ...........................................................................................85 Chapter 3 Fundamentals of the Mechanics of Multiphase Materials ......................87 3.1 Introduction of Scales and Homogenization/Localization .................................88 3.2 Macromechanics versus Micromechanics ...........................................................90 3.3 Representative Volume Elements (RVEs) and Repeating Unit Cells (RUCs) ... 94 3.4 Volume Averaging ...............................................................................................95 3.5 Homogeneous Boundary Conditions ...................................................................96 3.6 Average Strain Theorem ......................................................................................96 vii viii Contents 3.7 Average Stress Theorem ......................................................................................97 3.8 Determination of Effective Properties .................................................................98 3.8.1 Effective Elastic Moduli .............................................................................98 3.8.2 Relations between Averages: A Direct Approach .....................................99 3.8.3 Energy Approach ......................................................................................101 3.9 Mechanics of Composite Materials ...................................................................103 3.9.1 The Voigt Approximation ......................................................................104 3.9.2 The Reuss Approximation .....................................................................105 3.9.3 Combined Voigt and Reuss Approximations ........................................105 3.9.4 Hill s Theorem .......................................................................................105 3.9.5 Bounding Theorems ...............................................................................108 3.9.6 The Dilute Approximation .....................................................................109 3.9.7 The Composite Spheres Assemblage Model ......................................... Ill 3.9.8 The Self-Consistent Scheme (SCS) .......................................................113 3.9.9 The Generalized Self-Consistent Scheme (GSCS) ...............................114 3.9.10 The Differential Scheme (DS) .............................................................116 3.9.11 The Mori-Tanaka (MT) Theory ...........................................................118 3.9.12 Eshelby Equivalent Inclusion Method .................................................121 3.9.13 The Strain Concentration Tensors for the Self-Consistent (SCS) and Differential Schemes (DS) .................................................125 3.9.14 The Strain Concentration Tensor for the Mori-Tanaka (MT) Method .................................................................................................126 3.9.15 Green s Function/Fourier Series ..........................................................129 3.9.16 Numerical Methods ..............................................................................130 3.10 Comparison of Various Micromechanics Methods for Continuous Reinforcement ..................................................................................................130 3.11 Levin s Theorem: Extraction of Effective СТЕ from Mechanical Effective Properties .........................................................................................................134 3.11.1 Multiphase Composite .........................................................................134 3.11.2 Two-Phase Composite .........................................................................136 3.11.3 The Generalization of Levin s Theorem: Transformation Fields .......138 3.12 The Self-Consistent Scheme (SCS) and Mori-Tanaka (MT) Method for Inelastic Composites ..................................................................................144 3.13 Concluding Remarks .......................................................................................145 Chapter 4 The Method of Cells Micromechanics ...............................................747 4.1 The MOC for Continuously Fiber-Reinforced Materials (Doubly Periodic)... 148 4.1.1 Thermomechanical Formulation ..............................................................149 4.1.2 Thermal Conductivities ............................................................................176 Contents ¡χ 4.1.3 Specific Heats ...........................................................................................178 4.1.4 MOC with Imperfect Bonding .................................................................180 4.2 The Method of Cells for Discontinuously Fiber-Reinforced Composites (Triply Periodic) ................................................................................................181 4.2.1 Thermomechanical Formulation ..............................................................181 4.2.2 Thermal Conductivity ...............................................................................187 4.3 Applications: Unidirectional Continuously Reinforced Composites ................189 4.3.1 Effective Elastic Properties ......................................................................189 4.3.2 Coefficients of Thermal Expansion ..........................................................195 4.3.3 Specific Heat .............................................................................................197 4.3.4 Yield Surfaces of Metal Matrix Composites ...........................................198 4.3.5 Inelastic Response of Metal Matrix Composites .....................................205 4.4 Applications: Discontinuously Reinforced (Short-Fiber) Composites .............212 4.4.1 Effective Elastic Properties ......................................................................212 4.5 Applications: Randomly Reinforced Materials .................................................217 4.6 Concluding Remarks .........................................................................................224 Chapter 5 The Generalized Method of Cells Micromechanics .............................227 5.1 GMC for Discontinuous Reinforced Composites (Triple Periodicity) .............229 5.1.1 Thermomechanical Formulation ..............................................................229 5.1.2 Thermal Conductivities ............................................................................243 5.1.3 Electric Conductivity ................................................................................243 5.1.4 Specific Heat .............................................................................................244 5.1.5 Computationally Efficient Reformulation ................................................246 5.2 Specialization of GMC to Continuously Reinforced Composites (Double Periodicity) ..........................................................................................259 5.3 Applications .......................................................................................................267 5.3.1 Effective Properties ...................................................................................267 5.3.2 Local Fields ..............................................................................................271 5.3.3 Response of Continuously Reinforced Unidirectional Composites ........277 5.3.4 Discontinuous Reinforced Composites ....................................................323 5.3.5 Modeling Woven PMC Composites .........................................................336 5.4 Concluding Remarks .........................................................................................349 Chapter 6 The High-Fidelity Generalized Method of Cells Micromechanics ..........351 6.1 Three-Dimensional (Triply Periodic) High-Fidelity Generalized Method of Cells with Imperfect Bonding Between the Phases .......................353 6.1.1 Governing Equations ................................................................................355 6.1.2 Displacement Expansion ..........................................................................358 χ Contents 6.1.3 Constitutive Equations ..............................................................................359 6.1.4 Determination of the Unknown Microvariables......................................360 6.1.5 Imperfect Bonding ....................................................................................363 6.1.6 Summary of Global Equations .................................................................364 6.2 Specialization to Double Periodicity (for Continuous Fibers, Anisotropie Constituents, and Imperfect Bonding) ..............................................................368 6.2.1 Governing Equations ................................................................................368 6.2.2 Displacement Expansion ..........................................................................371 6.2.3 Constitutive Equations ..............................................................................372 6.2.4 Determination of the Unknown Microvariables......................................373 6.2.5 Imperfect Bonding ....................................................................................374 6.2.6 Summary of Equations .............................................................................375 6.3 Reformulation of the Two-Dimensional (Doubly Periodic) HFGMC with Debonding and Inelasticity Effects ...................................................................376 6.3.1 Governing Equations ................................................................................377 6.3.2 Displacement Expansion ..........................................................................377 6.3.3 Constitutive Equations ..............................................................................378 6.3.4 The Determination of the Displacement s Microvariables in Terms of the Average Surface Displacements .........................................382 6.3.5 The Determination of the Average Surface Tractions in Terms of the Average Surface Displacements .........................................385 6.3.6 Perfect Bonding: Reduction of the Number of Unknowns .....................389 6.3.7 Imperfect Bonding ....................................................................................389 6.3.8 Computational Impact of Reformulation .................................................392 6.4 Contrast Between HFGMC and Finite Element Analysis (FEA) .....................395 6.5 Isoparametric Subcell Generalization ...............................................................396 6.6 Doubly Periodic HFGMC Applications ............................................................403 6.6.1 Effective Elastic Properties and Coefficient of Thermal Expansion (СТЕ) ........................................................................................................403 6.6.2 Local Fields: HFGMC versus Eshelby Solution ......................................406 6.6.3 Local Fields: HFGMC versus FEA ..........................................................409 6.6.4 Graphite/Aluminum Composite Global Response: HFGMC versus MCCM ......................................................................................................411 6.6.5 Titanium Composite (SiC/TIMETAL 2 IS) Response: Discretization Convergence Study ...................................................................................412 6.6.6 Fiber-Matrix Debonding ...........................................................................415 6.6.7 Woven Composite Example: 5HS SiC/SiC .............................................419 6.6.8 Progressive Damage/Failure of Polymeric Composite ............................423 6.7 Triply Periodic Applications .............................................................................431 Contents xi 6.7.1 Lattice Block/Open Cell ...........................................................................431 6.7.2 Micromechanical Analysis of Foams with Internal Pore Pressure ..........437 6.8 Concluding Remarks .........................................................................................444 Chapter 7 Multiscale Modeling of Composites ..................................................447 7.1 Introduction ........................................................................................................447 7.2 Multiscale Analysis Using Lamination Theory ................................................459 7.2.1 Transverse Tensile and Creep Response of an SiC/Ti Composite ..........465 7.2.2 Fatigue of SiC/Ti- 15-3..............................................................................472 7.2.3 High-Temperature Creep of a Woven Ceramic Matrix Composite .........477 7.2.4 Progressive Failure of PMC Laminates ...................................................481 7.3 HyperMAC .........................................................................................................488 7.3.1 Progressive Failure of a T-Stiffened Composite Panel ............................489 7.3.2 Fatigue Life Prediction of a Foam Core Sandwich Beam .......................491 7.4 Multiscale Generalized Method of Cells (MSGMC) ........................................498 7.4.1 Micro Scale (Constitutive Modeling) .......................................................501 7.4.2 Meso Scale (Multiphase Material) ...........................................................501 7.4.3 Macro Scale (Weave) ...............................................................................503 7.4.4 Sensitivity Study of PMC Parameters across Scales ...............................505 7.4.5 Triaxially Braided PMC ...........................................................................518 7.5 FEAMAC ...........................................................................................................522 7.5.1 Stochastic Fiber Breakage of a Longitudinally Reinforced SiC/Ti Metal Matrix Composite (MMC) .................................................523 7.5.2 Progressive Failure of a Notched Composite Laminate Plate .................533 7.5.3 Delamination Modeling ............................................................................536 7.6 Concluding Remarks .........................................................................................539 Chapter 8 Fully Coupled Thermomicromechanical Analysis of Multiphase Composites ...................................................................................541 8.1 Introduction ........................................................................................................541 8.2 Classical Thermomicromechanical Analysis ....................................................542 8.2.1 The Homogenization Procedure ...............................................................542 8.2.2 Solution of the Repeating Unit Cell Problem ..........................................547 8.3 Fully Coupled Thermomicromechanical Analysis ...........................................550 8.3.1 The Energy Equation ................................................................................551 8.3.2 The Homogenized Energy Equation ........................................................552 8.3.3 The Fully Coupled Thermomechanical Solution of the Repeating Unit Cell Problem .....................................................................................557 8.4 Applications .......................................................................................................560 xii Contents 8.4.1 Monolithic Aluminum Subjected to Cyclic Loading ..............................565 8.4.2 AI2O3/AI Subjected to Axial Cyclic Loading ..........................................566 8.4.3 AI2O3/AI Subjected to Transverse Cyclic Loading .................................568 8.4.4 AI2O3/AI Subjected to Axial and Transverse Shear Cyclic Loading ......571 8.4.5 Full Thermomechanical Coupling with Damage .....................................574 8.5 Concluding Remarks .........................................................................................576 Chapter 9 Finite Strain Micromechanica/ Modeling of Multiphase Composites .....577 9.1 Introduction ........................................................................................................578 9.2 Finite Strain Generalized Method of Cells (FSGMC) ......................................581 9.2.1 Material Representation of the Monolithic Thermoelastic Material .......581 9.2.2 FSGMC Formulation for Thermoelastic Composites ..............................585 9.3 Applications Utilizing FSGMC .........................................................................592 9.3.1 Porous Material Undergoing Large Deformation Subjected to Hydrostatic Loading .................................................................................592 9.3.2 Class I—Harmonic Material ....................................................................594 9.3.3 Class II ......................................................................................................595 9.3.4 Class III — Generalized Varga Material ....................................................596 9.3.5 Discontinuous Reinforced Composites ....................................................597 9.3.6 Continuous Reinforced Composites .........................................................598 9.4 Finite Strain High-Fidelity Generalized Method of Cells (FSHFGMC) for Thermoelastic Composites ...........................................................................599 9.4.1 The Homogenization Procedure ...............................................................600 9.4.2 Method of Solution of the RUC Problem ................................................603 9.5 Applications Utilizing FSHFGMC ....................................................................608 9.5.1 Hyperelastic Matrix Composites Exhibiting the Mullins Damage Effect ..........................................................................................608 9.5.2 Thermoelastic Composites .......................................................................617 9.5.3 Viscoelastic Composites ...........................................................................620 9.5.4 Thermoviscoelastic Composites ...............................................................639 9.5.5 Thermoelastoplastic Composites ..............................................................653 9.5.6 Elastoplastic Composites with Evolving Damage ...................................659 9.5.7 Thermoviscoplastic Composites ...............................................................669 9.5.8 Optimization of Porous Microstructures ..................................................675 9.6 Concluding Remarks .........................................................................................676 Chapter 10 Micromechanical Analysis of Smart Composite Materials .................677 10.1 Introduction ......................................................................................................678 10.2 Electro-Magneto-Thermo-Elastic Composites ................................................680 Contents xiii 10.2.1 Effective Behavior of Unidirectional Electro-Magneto- Thermo-Elastic Composites via GMC .................................................680 10.2.2 Effective Behavior of Unidirectional Electro-Magneto- Thermo-Elastic Composites via the High-Fidelity Generalized Method of Cells (HFGMC) ..................................................................695 10.2.3 Thermo-Electro-Magneto-Elasto-Plastic Lamination Theory .............699 10.3 Hysteresis Behavior of Ferroelectric Fiber Composites .................................706 10.3.1 The Modeling of the Monolithic Ferroelectric Material .....................707 10.3.2 Incremental Micromechanics Analysis ................................................712 10.4 The Response of Electrostrictive Composites ................................................714 10.4.1 The Modeling of the Monolithic Electrostrictive Material .................715 10.4.2 Incremental Micromechanical Analysis ..............................................717 10.5 Analysis of Magnetostrictive Composites .......................................................718 10.6 Nonlinear Electro-Magneto-Thermo-Elastic Composites ...............................718 10.7 Shape Memory Alloy Fiber Composites .........................................................720 10.7.1 Constitutive Models for SMA Response .............................................721 10.8 Shape Memory Alloy Fiber Composites Undergoing Large Deformations... 731 10.8.1 Finite-Strain Shape Memory Alloy Constitutive Equations ................731 10.8.2 Finite-Strain Constitutive Equations for SMA Fiber Composites .......736 10.9 Applications .....................................................................................................737 10.9.1 Piezoelectric Effective Constants ..........................................................737 10.9.2 Electromagnetic Effective Constants ....................................................739 10.9.3 Multiscale Analysis of a Hybrid Smart/Metal Matrix Composite Laminate ................................................................................................740 10.9.4 Macroscopic Hysteresis Response of Ferroelectric Fiber Composites ...................................................................................748 10.9.5 Porous Lead Magnesium Niobáte (PMN) Electrostrictive Material Behavior ................................................................................................751 10.9.6 Nonlinear Electro-Magneto-Thermo-Elastic LiNbCb/PVDF Composite Response .............................................................................754 10.9.7 Unidirectional SMA Fiber Composite Response Using Lagoudas (and Coworkers) Model ........................................................................755 10.9.8 Response of SMA/Epoxy Unidirectional Composite Using Auricchio (and Coworkers) Model .......................................................759 10.9.9 Response of SMA/Epoxy Unidirectional Composite Using the Two-Way Shape Memory Effect Model ...............................................760 10.9.10 Response of SMA/A1 Unidirectional Composite Undergoing Large Deformations .............................................................................763 10.9.11 Dynamic Response of SMA Composite Plates ..................................765 xiv Contents 10.9.12 Thermal Buckling of Activated SMA Composite Plates .................767 10.10 Concluding Remarks .....................................................................................770 Chapter 11 Higher-Order Theory for Functionally Graded Materials ..................773 11.1 Background and Motivation ............................................................................775 11.2 Generalized Three-Directional HOTFGM ......................................................779 1.2.1 Model Overview ...................................................................................779 1.2.2 Thermal Analysis ..................................................................................781 1.2.3 Mechanical Analysis ............................................................................786 1.2.4 Higher-Order Theory versus Finite Element Analysis ........................793 11.3 Specialization of the Higher-Order Theory ....................................................794 1.3.1 Two-Directional HOTFGM ..................................................................795 1.3.2 One-Directional HOTFGM ..................................................................798 1.4 Higher-Order Theory for Cylindrical Functionally Graded Materials (HOTCFGM) ...................................................................................................801 1.4.1 Thermal Analysis ..................................................................................802 1.4.2 Mechanical Analysis ............................................................................804 1.5 HOTFGM Applications ...................................................................................805 1.5.1 Finite Element Validation .....................................................................806 1.5.2 Microstructural Effects .........................................................................814 1.5.3 Microstructural Tailoring ......................................................................833 1.5.4 Microstructural Optimization ...............................................................840 1.5.5 Internally Cooled Plate .........................................................................848 1.5.6 Smart Materials in HOTFGM ..............................................................855 11.6 HOTCFGM Applications ................................................................................863 1.6.1 Case I: Thin-Walled Cylinder Subjected to Internal Pressure ............864 1.6.2 Case II: Thin-Walled Cylinder Subjected to Temperature Gradient... 865 1.6.3 Case III: Transient Thermal Loading ...................................................865 1.6.4 Thrust Cell Liner Response ..................................................................867 11.7 Concluding Remarks .......................................................................................876 Chapter 12 Wave Propagation in Multiphase and Porous Materials ...................879 12.1 Full Three-Dimensional Theory ......................................................................880 12.2 Specialization to Two-Dimensional Theory for Thermoelastic Materials .....893 12.3 The Inclusion of Inelastic Effects ...................................................................902 12.4 Two-Dimensional Wave Propagation with Full Thermoelastic Coupling ......905 12.5 Applications .....................................................................................................910 12.5.1 Acoustic Evaluation of Foam Sandwich Panels ..................................910 12.5.2 Acoustic Evaluation of Heterogeneous Panels ....................................913 Contents xv 12.5.3 Temperature Field Induced by Dynamic Stresses on a Cracked Composite .............................................................................................916 12.6 Concluding Remarks .......................................................................................928 Chapter 13 Micromechanics Software .............................................................929 13.1 Accessing the Software ...................................................................................930 13.2 Method of Cells Source Code .........................................................................930 13.2.1 Method of Cells Source Code Example Problem ................................932 13.3 MAC/GMC 4.0................................................................................................932 13.3.1 Getting Started ......................................................................................933 13.3.2 Executing MAC/GMC 4.0 Problems ...................................................933 13.3.3 Format of the MAC/GMC 4.0 Input File .............................................935 13.3.4 MAC/GMC 4.0 Example Problem .......................................................936 13.3.5 MAC/GMC 4.0 Example Problem Input .............................................937 13.4 Concluding Remarks .......................................................................................941 References ....................................................................................................943 Index ............................................................................................................973 MECHANICAL ENGINEERING / MATERIALS MICROMECHANICS OF COMPOSITE MATERIALS A GENERALIZED MULTISCALE ANALYSIS APPROACH Reliably and efficiently model and analyze composites with this practical digest of a lifetime s research by recognized leaders in the field • Brings together for the first time the findings of a lifetime of research by Jacob Aboudi, a leading authority in the area and the originator of the generalized method of cells family of micromechanics theories • Provides a comprehensive overview of primary micromechanics formulations in use today and offers a unified approach for multiscale analysis and design of multi-phased composite materials, considering both small strain and large strain formulations • Demonstrates the applicability and utility of these methods over a wide range of topics including finite deformation, two-way thermomechanical coupling, smart composites, functionally graded materials, impact and wave propagation, and multiscale implementations. Micromechanics of Composite Materials brings together comprehensive background information on the multiscale nature of composites, constituent material behavior, damage models and key techniques for multiscale modeling, as well as presenting the key findings and methods of three leading experts in the field. A unified approach is provided, along with corresponding software, for conducting analysis and design of conventional and smart composite materials and structures, with numerous examples to illustrate use and application involving linear and nonlinear material behavior. Modeling composite behavior is a key challenge in research and industry. When done efficiently and reliably it can save weight, money, decrease time to market with new innovations and prevent component failure. Micromechanics of Composite Materials provides tools and knowledge from the cutting edge of aerospace structures and materials technologies, allowing researchers and engineers within academia, industry and government to improve results and streamline development workflows. About the authors Jacob Aboudi is a Professor Emeritus at the School of Mechanical Engineering, Tel Aviv University. Israel. He was formerly Head of the university s Department of Solid Mechanics. Materials and Structures, and Dean of their Faculty of Engineering. He has held visiting appointments internationally and has written two books and more than 250 journal articles during his 40 years in research. Steven M. Arnold is Chief of the Mechanics and Life Prediction Branch within the Structures and Materials Division at NASA Glenn Research Center, as well as Co-founder and Director of NASA s Multiscale Analysis Center of Excellence (MACE). He has over 25 years of research experience resulting in 300 technical publications, two U.S. patents, and an Abe Silverstein Award. Brett A. Bednarcyk is a Senior Research Engineer and Discipline Lead for Analytical and Computational Mechanics in the Mechanics and Life Prediction Branch of the Structures and Materials Division. NASA Glenn Research Center. Ohio, USA. He has over 15 years of research experience. 140 technical publications, and is the primary developer of NASA s MAC/GMC software. Web link to the companion site: http://booksite.elsevier.com/9780123970350 Related titles from Elsevier Hull & Bacon \| Introduction to Dislocations і ISBN 9780080966724 Lee at al i Metal Failure Analysis Handbook \| ISBN 9780123852045 Vasiliev & Morozov \| Advanced Mechanics of Composite Materials \| ISBN 9780080453729 ISBN 978-0-12-397035-0 ELSEYIER ACADEMIC PRESS An imprint of Elsevier store.elsevier.com 9 780123 970350
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id	DE-604.BV040587312
illustrated	Illustrated
indexdate	2024-07-10T00:26:44Z
institution	BVB
isbn	9780123970350
language	English
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physical	XXII, 984 S., [12 Bl.] Ill., graph. Darst.
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publisher	Elsevier, Butterworth-Heinemann
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spelling	Aboudi, Jacob Verfasser aut Micromechanics of composite materials a generalized multiscale analysis approach Jacob Aboudi ; Steven M. Arnold ; Brett A. Bednarcyk 1. ed. Amsterdam [u.a.] Elsevier, Butterworth-Heinemann 2013 XXII, 984 S., [12 Bl.] Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Micromechanics Verbundwerkstoff (DE-588)4062670-2 gnd rswk-swf Mikromechanik (DE-588)4205811-9 gnd rswk-swf Verbundwerkstoff (DE-588)4062670-2 s Mikromechanik (DE-588)4205811-9 s DE-604 Arnold, Steven M. Verfasser aut Bednarcyk, Brett A. Verfasser aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025415337&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025415337&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	Aboudi, Jacob Arnold, Steven M. Bednarcyk, Brett A. Micromechanics of composite materials a generalized multiscale analysis approach Micromechanics Verbundwerkstoff (DE-588)4062670-2 gnd Mikromechanik (DE-588)4205811-9 gnd
subject_GND	(DE-588)4062670-2 (DE-588)4205811-9
title	Micromechanics of composite materials a generalized multiscale analysis approach
title_auth	Micromechanics of composite materials a generalized multiscale analysis approach
title_exact_search	Micromechanics of composite materials a generalized multiscale analysis approach
title_full	Micromechanics of composite materials a generalized multiscale analysis approach Jacob Aboudi ; Steven M. Arnold ; Brett A. Bednarcyk
title_fullStr	Micromechanics of composite materials a generalized multiscale analysis approach Jacob Aboudi ; Steven M. Arnold ; Brett A. Bednarcyk
title_full_unstemmed	Micromechanics of composite materials a generalized multiscale analysis approach Jacob Aboudi ; Steven M. Arnold ; Brett A. Bednarcyk
title_short	Micromechanics of composite materials
title_sort	micromechanics of composite materials a generalized multiscale analysis approach
title_sub	a generalized multiscale analysis approach
topic	Micromechanics Verbundwerkstoff (DE-588)4062670-2 gnd Mikromechanik (DE-588)4205811-9 gnd
topic_facet	Micromechanics Verbundwerkstoff Mikromechanik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025415337&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025415337&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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