1st Edition
Introduction to the Micromechanics of Composite Materials
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
