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Micromechanics of Composite Materials - 1st Edition - ISBN: 9780123970350, 9780123977595

Micromechanics of Composite Materials

1st Edition

A Generalized Multiscale Analysis Approach

Authors: Jacob Aboudi Steven Arnold Brett Bednarcyk
eBook ISBN: 9780123977595
Paperback ISBN: 9780128101278
Hardcover ISBN: 9780123970350
Imprint: Butterworth-Heinemann
Published Date: 1st November 2012
Page Count: 1006
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With composites under increasing use in industry to replace traditional materials in components and structures, the modeling of composite performance, damage and failure has never been more important.

Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach brings together comprehensive background information on the multiscale nature of the composite, constituent material behaviour, damage models and key techniques for multiscale modelling, as well as presenting the findings and methods, developed over a lifetime’s research, of three leading experts in the field.

The unified approach presented in the book for conducting multiscale analysis and design of conventional and smart composite materials is also applicable for structures with complete linear and nonlinear material behavior, with numerous applications provided to illustrate use.

Modeling composite behaviour is a key challenge in research and industry; when done efficiently and reliably it can save money, decrease time to market with new innovations and prevent component failure. This book provides the tools and knowledge from leading micromechanics research, allowing researchers and senior engineers within academia and industry with to improve results and streamline development workflows.

Key Features

  • Brings together for the first time the findings of a lifetime’s research in micromechanics by recognized leaders in the field
  • Provides a comprehensive overview of all micromechanics formulations in use today and a unified approach that works for the multiscale analysis and design of multi-phased composite materials, considering both small strain and large strain formulations
  • Combines otherwise disparate theory, code and techniques in a step-by-step manner for efficient and reliable modeling of composites


Academic professionals and practicing engineers in the field of composite mechanics, including members of ASME, AIAA and SAE; Aerospace and automotive engineers wanting to design and analyze composite materials; Advanced students and graduates

Table of Contents





Chapter 1. Introduction

1.1 Fundamentals of Composite Materials and Structures

1.2 Modeling of Composites

1.3 Description of the Book Layout

1.4 Suggestions on How to Use the Book

Chapter 2. Constituent Material Modeling

2.1 Reversible Models

2.2 Irreversible Deformation Models

2.3 Damage/Life Models

2.4 Concluding Remarks

Chapter 3. Fundamentals of the Mechanics of Multiphase Materials

3.1 Introduction of Scales and Homogenization/Localization

3.2 Macromechanics versus Micromechanics

3.3 Representative Volume Elements (RVEs) and Repeating Unit Cells (RUCs)

3.4 Volume Averaging

3.5 Homogeneous Boundary Conditions

3.6 Average Strain Theorem

3.7 Average Stress Theorem

3.8 Determination of Effective Properties

3.9 Mechanics of Composite Materials

3.10 Comparison of Various Micromechanics Methods for Continuous Reinforcement

3.11 Levin’s Theorem: Extraction of Effective CTE from Mechanical Effective Properties

3.12 The Self-Consistent Scheme (SCS) and Mori-Tanaka (MT) Method for Inelastic Composites

3.13 Concluding Remarks

Chapter 4. The Method of Cells Micromechanics

4.1 The MOC for Continuously Fiber-Reinforced Materials (Doubly Periodic)

4.2 The Method of Cells for Discontinuously Fiber-Reinforced Composites (Triply Periodic)

4.3 Applications: Unidirectional Continuously Reinforced Composites

4.4 Applications: Discontinuously Reinforced (Short-Fiber) Composites

4.5 Applications: Randomly Reinforced Materials

4.6 Concluding Remarks

Chapter 5. The Generalized Method of Cells Micromechanics

5.1 GMC for Discontinuous Reinforced Composites (Triple Periodicity)

5.2 Specialization of GMC to Continuously Reinforced Composites (Double Periodicity)

5.3 Applications

5.4 Concluding Remarks

Chapter 6. The High-Fidelity Generalized Method of Cells Micromechanics

6.1 Three-Dimensional (Triply Periodic) High-Fidelity Generalized Method of Cells with Imperfect Bonding Between the Phases

6.2 Specialization to Double Periodicity (for Continuous Fibers, Anisotropic Constituents, and Imperfect Bonding)

6.3 Reformulation of the Two-Dimensional (Doubly Periodic) HFGMC with Debonding and Inelasticity Effects

6.4 Contrast Between HFGMC and Finite Element Analysis (FEA)

6.5 Isoparametric Subcell Generalization

6.6 Doubly Periodic HFGMC Applications

6.7 Triply Periodic Applications

6.8 Concluding Remarks

Chapter 7. Multiscale Modeling of Composites

7.1 Introduction

7.2 Multiscale Analysis Using Lamination Theory

7.3 HyperMAC

7.4 Multiscale Generalized Method of Cells (MSGMC)


7.6 Concluding Remarks

Chapter 8. Fully Coupled Thermomicromechanical Analysis of Multiphase Composites

8.1 Introduction

8.2 Classical Thermomicromechanical Analysis

8.3 Fully Coupled Thermomicromechanical Analysis

8.4 Applications

8.5 Concluding Remarks

Chapter 9. Finite Strain Micromechanical Modeling of Multiphase Composites

9.1 Introduction

9.2 Finite Strain Generalized Method of Cells (FSGMC)

9.3 Applications Utilizing FSGMC

9.4 Finite Strain High-Fidelity Generalized Method of Cells (FSHFGMC) for Thermoelastic Composites

9.5 Applications Utilizing FSHFGMC

9.6 Concluding Remarks

Chapter 10. Micromechanical Analysis of Smart Composite Materials

10.1 Introduction

10.2 Electro-Magneto-Thermo-Elastic Composites

10.3 Hysteresis Behavior of Ferroelectric Fiber Composites

10.4 The Response of Electrostrictive Composites

10.5 Analysis of Magnetostrictive Composites

10.6 Nonlinear Electro-Magneto-Thermo-Elastic Composites

10.7 Shape Memory Alloy Fiber Composites

10.8 Shape Memory Alloy Fiber Composites Undergoing Large Deformations

10.9 Applications

10.10 Concluding Remarks

Chapter 11. Higher-Order Theory for Functionally Graded Materials

11.1 Background and Motivation

11.2 Generalized Three-Directional HOTFGM

11.3 Specialization of the Higher-Order Theory

11.4 Higher-Order Theory for Cylindrical Functionally Graded Materials (HOTCFGM)

11.5 HOTFGM Applications

11.6 HOTCFGM Applications

11.7 Concluding Remarks

Chapter 12. Wave Propagation in Multiphase and Porous Materials

12.1 Full Three-Dimensional Theory

12.2 Specialization to Two-Dimensional Theory for Thermoelastic Materials

12.3 The Inclusion of Inelastic Effects

12.4 Two-Dimensional Wave Propagation with Full Thermoelastic Coupling

12.5 Applications

12.6 Concluding Remarks

Chapter 13. Micromechanics Software

13.1 Accessing the Software

13.2 Method of Cells Source Code

13.3 MAC/GMC 4.0

13.4 Concluding Remarks

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1st November 2012
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About the Authors

Jacob Aboudi

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 at the University of Strathclyde, Northwestern University, Virginia Tech, and the University of Virginia, and has over 45 years of research experience. He has written over 300 journal articles and 2 prior books.

Affiliations and Expertise

Professor Emeritus, School of Mechanical Engineering, Tel Aviv University, Tel Aviv, Israel

Steven Arnold

Steven M. Arnold is the Technical Lead for Multiscale Modeling within the Materials and Structures Division at NASA Glenn Research Center, Ohio, USA. He was awarded NASA’s Exceptional Service Medal in 2019, the ASC/DEStech Award in Composites for 2015, NASA’s Exceptional Technology Achievement Medal in 2014, and the NASA Glenn Abe Silverstein outstanding research award in 2004. He is co-founder and current Chairman of the Material Data Management Consortium (MDMC), an ASM International Fellow and has over 30 years of research experience resulting in over 440 technical publications and 2 U.S. patents.

Affiliations and Expertise

Technical Lead for Multiscale Modeling, Materials and Structures Division, NASA Glenn Research Center, Cleveland, Ohio, USA

Brett Bednarcyk

Brett A. Bednarcyk is a Senior Research Engineer in the Materials and Structures Division at NASA Glenn Research Center, Ohio, USA. He serves as a composite expert for NASA Space Launch Systems (SLS) projects and the NASA Engineering and Safety Center Structures Technical Discipline Team. He has held visiting appointments at the RWTH Aachen University (Germany) and the University of Virginia. He was awarded the NASA Glenn Abe Silverstein outstanding research award in 2015 and NASA’s Exceptional Achievement Medal in 2013. He has over 20 years of research experience, over 300 technical publications, and is the primary developer of NASA’s MAC/GMC composites software.

Affiliations and Expertise

Senior Research Engineer, Materials and Structures Division, NASA Glenn Research Center, Cleveland, Ohio, USA

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