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 (Dou


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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 40 years of research experience. He has written over 250 journal articles and two prior books.

Affiliations and Expertise

Tel-Aviv University, Israel

Steven Arnold

Steven M. Arnold is Chief of the Mechanics and Life Prediction Branch within the Structures and Materials Division at NASA Glenn Research Center, Ohio, USA. He is the co-founder and director of NASA’s Multiscale Analysis Center of Excellence (MACE), an Abe Silverstein Award recipient, and is co-founder and current Chairman of the Material Data Management Consortium (MDMC). He has over 25 years of research experience resulting in 300 technical publications and two U.S. patents.

Affiliations and Expertise

Steven Arnold is Chief of the Mechanics and Life Prediction Branch within the Structures and Materials Division at NASA Glenn Research Center; co-founder and chairman of the Material Data Management Consortium (MDMC).

Brett Bednarcyk

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.

Affiliations and Expertise

Materials Research Engineer, Mechanics and Life Prediction Branch, Structures and Materials Division, NASA Glenn Research Center, Ohio, USA.