1st Edition

Introduction to the Micromechanics of Composite Materials

By Huiming Yin, Yingtao Zhao Copyright 2016
    238 Pages 70 B/W Illustrations
    by CRC Press

    238 Pages 70 B/W Illustrations
    by CRC Press

    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.

    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


    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

    "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