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

238 Pages
by CRC Press

Also available as eBook on:

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.

Introduction
Composite Materials
History of Micromechanics
A Big Picture of Micromechanics-Based Modeling
Basic Concepts of Micromechanics
Case Study: Holes Sparsely Distributed in a Plate
Exercise

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
Exercise

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
Exercise

Ellipsoidal Inclusion and Inhomogeneity
General Elastic Solution Caused By an Eigenstrain through Fourier Integral
Ellipsoidal Inclusion Problems
Equivalent Inclusion Method for Ellipsoidal Inhomogeneities
Exercise

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
Exercise

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
Exercise

Homogenization for Effective Elasticity Based on the Vectorial Methods
Effective Material Behavior and Material Phases
Micromechanics-Based Models for Two-Phase Composites
Exercise

Homogenization for Effective Elasticity Based on the Perturbation Method
Introduction
One-Dimensional Asymptotic Homogenization
Homogenization of a Periodic Composite
Exercise

Defects in Materials: Void, Microcrack, Dislocation, and Damage
Voids
Microcracks
Dislocation
Damage
Exercise

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
Exercise
References

### Biography

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