Introduction to the Micromechanics of Composite Materials: 1st Edition (Paperback) book cover

Introduction to the Micromechanics of Composite Materials

1st Edition

By Huiming Yin, Yingtao Zhao

CRC Press

238 pages | 70 B/W Illus.

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Paperback: 9781138490499
pub: 2018-01-22
Hardback: 9781498707282
pub: 2016-02-09
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Presents Concepts That Can Be Used in Design, Processing, Testing, and Control of Composite Materials

Introduction to the Micromechanics of Composite Materials weaves together the basic concepts, mathematical fundamentals, and formulations of micromechanics into a systemic approach for understanding and modeling the effective material behavior of composite materials. As various emerging composite materials have been increasingly used in civil, mechanical, biomedical, and materials engineering, this textbook provides students with a fundamental understanding of the mechanical behavior of composite materials and prepares them for further research and development work with new composite materials.

Students will understand from reading this book:

  • The basic concepts of micromechanics such as RVE, eigenstrain, inclusions, and in homogeneities
  • How to master the constitutive law of general composite material
  • How to use the tensorial indicial notation to formulate the Eshelby problem
  • Common homogenization methods

The content is organized in accordance with a rigorous course. It covers micromechanics theory, the microstructure of materials, homogenization, and constitutive models of different types of composite materials, and it enables students to interpret and predict the effective mechanical properties of existing and emerging composites through microstructure-based modeling and design. As a prerequisite, students should already understand the concepts of boundary value problems in solid mechanics. Introduction to the Micromechanics of Composite Materials is suitable for senior undergraduate and graduate students.


"I am yet to read a book on micromechanics of composite materials with this level of description."

—Gangadhara Prusty, University of New South Wales, Australia

"This book would be appropriate for advanced students in materials science or mechanical engineering interested in modeling the micro-mechanical behavior of materials. It provides a good introduction to the subject…"

IEEE Electrical Insulation, January/February 2017

Table of Contents


Composite Materials

History of Micromechanics

A Big Picture of Micromechanics-Based Modeling

Basic Concepts of Micromechanics

Case Study: Holes Sparsely Distributed in a Plate


Vectors and Tensors

Cartesian Vectors and Tensors

Operations of Vectors and Tensors

Calculus of Vector and Tensor Fields

Potential Theory and Helmholtz’s Decomposition Theorem

Green’s Identities and Green’s Functions

Elastic Equations

General Solution and the Elastic Green’s Function


Spherical Inclusion and Inhomogeneity

Spherical Inclusion Problem

Introduction to the Equivalent Inclusion Method

Spherical Inhomogeneity Problem

Integrals of Φ, Ψ, Φp, Ψp and Their Derivatives in 3D Domain


Ellipsoidal Inclusion and Inhomogeneity

General Elastic Solution Caused By an Eigenstrain through Fourier Integral

Ellipsoidal Inclusion Problems

Equivalent Inclusion Method for Ellipsoidal Inhomogeneities


Volume Integrals and Averages in Inclusion and Inhomogeneity Problems

Volume Averages of Stress and Strain

Volume Averages in Potential Problems

Strain Energy in Inclusion and Inhomogeneity Problems


Homogenization for Effective Elasticity Based on the Energy Methods

Hill’s Theorem

Hill’s Bounds

Classical Variational Principles

Hashin–Shtrikman’s Variational Principle

Hashin–Shtrikman’s Bounds


Homogenization for Effective Elasticity Based on the Vectorial Methods

Effective Material Behavior and Material Phases

Micromechanics-Based Models for Two-Phase Composites


Homogenization for Effective Elasticity Based on the Perturbation Method


One-Dimensional Asymptotic Homogenization

Homogenization of a Periodic Composite


Defects in Materials: Void, Microcrack, Dislocation, and Damage






Boundary Effects on Particulate Composites

Fundamental Solution for Semi-Infinite Domains

Equivalent Inclusion Method for One Particle in a Semi-Infinite Domain

Elastic Solution for Multiple Particles in a Semi-Infinite Domain

Boundary Effects on Effective Elasticity of a Periodic Composite

Inclusion Based Boundary Element Method for Virtual Experiments of a Composite Sample



About the Authors

Huiming Yin is an associate professor in the Department of Civil Engineering and Engineering Mechanics at Columbia University, USA

Yingtao Zhao is an associate professor in the School of Aerospace Engineering at Beijing Institute of Technology, China

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mechanics / General