Introduction to the micromechanics of composite materials / Huiming Yin, Columbia University, New York, New, USA, Yingtao Zhao, Beijing Institute of Technology, PR of China.

Format:

Book

Author/Creator:

Yin, Huiming, author.

Zhao, Yingtao, author.

Language:

English

Subjects (All):

Composite materials.

Micromechanics.

Composite construction--Fatigue.

Composite construction.

Physical Description:

xiii, 224 pages ; 26 cm

Place of Publication:

Boca Raton : CRC Press, Taylor & Francis Group, CRC Press is an imprint of the Taylor & Francis Group, an Informa business, [2016]

Summary:

This book 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. 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. It is suitable for senior undergraduate and graduate students. Book jacket.

Contents:

Chapter 1 Introduction 1

1.1 Composite Materials 1

1.2 History of Micromechanics 5

1.3 A Big Picture of Micromechanics-Based Modeling 6

1.4 Basic Concepts of Micromechanics 7

1.4.1 Representative Volume Element 7

1.4.2 Inclusion and Inhomogeneity 8

1.4.3 Eigenstrain 9

1.4.4 Eshelbys Equivalent Inclusion Method 10

1.5 Case Study: Holes Sparsely Distributed in a Plate 11

1.5.1 The Exact Solution to an Infinite Plate Containing a Circular Hole 11

1.5.2 Prediction of the Equivalent Property of an Infinite Plate Containing Periodic Holes 13

1.6 Exercises 15

Chapter 2 Vectors and Tensors 17

2.1 Cartesian Vectors and Tensors 17

2.1.1 Summation Convention in the Index Notation 17

2.1.2 Vector 18

2.1.3 Tensor 19

2.1.4 Special Tensors 20

2.2 Operation's of Vectors and Tensors 20

2.2.1 Multiplication of Vectors 20

2.2.2 Multiplication of Tensors 22

2.2.3 Isotropic Tensors and Stiffness Tensor 23

2.3 Calculus of Vector and Tensor Fields 25

2.3.1 Del Operator and Operations 25

2.3.1.1 Gradient 25

2.3.1.2 Divergence 26

2.3.1.3 Curl 26

2.3.2 Examples 27

2.3.3 The Gauss Theorem 27

2.3.4 Green's Theorem and Stokes' Theorem 28

2.4 Potential Theory and Helmholtz's Decomposition Theorem 28

2.4.1 Scalar and Vector Potentials 28

2.4.2 Helmholtz's Decomposition Theorem 29

2.5 Green's Identities and Green's Functions 30

2.5.1 Greens First and Second Identities 30

2.5.2 Green's Function for the Laplacian 30

2.5.3 Green's Function in the Space of Lower Dimensions 32

2.5.4 Example 34

2.6 Elastic Equations 35

2.6.1 Strain and Compatibility 35

2.6.2 Constitutive Law 37

2.6.3 Equilibrium Equation 37

2.6.4 Governing Equations 38

2.6.5 Boundary Value Problem 39

2.7 General Solution and the Elastic Green's Function 40

2.7.1 Papkovich-Neuber's General Solution 40

2.7.2 Kelvins Particular Solution 42

2.7.3 Elastic Green's Function 44

2.8 Exercises 46

Chapter 3 Spherical Inclusion and Inhomogeneity 49

3.1 Spherical Inclusion Problem 49

3.2 Introduction to the Equivalent Inclusion Method 52

3.3 Spherical Inhomogeneity Problem 55

3.3.1 Eshelby's Equivalent Inclusion Method 56

3.3.2 General Cases of Inhomogeneity with a Prescribed Eigenstrain 57

3.3.3 Interface Condition and the Uniqueness of the Solution 59

3.4 Integrals of φ ψ, φp. ψP, And Their Derivatives in 3D Domain 60

3.5 Exercises 62

Chapter 4 Ellipsoidal Inclusion and Inhomogeneity 63

4.1 General Elastic Solution Caused By an Eigenstrain Through Fourier Integral 63

4.1.1 An Eigenstrain in the Form of a Single Wave 63

4.1.2 An Eigenstrain in the Form of Fourier Series and Fourier Integral 65

4.1.3 Green's Function for Isotropic Materials 66

4.2 Ellipsoidal Inclusion Problems 69

4.2.1 Ellipsoidal Inclusion with a Uniform Eigenstrain 69

4.2.2 Ellipsoidal Inclusion with a Polynomial Eigenstrain 75

4.2.3 Ellipsoidal Inclusion with a Body Force 77

4.3 Equivalent Inclusion Method for Ellipsoidal in Homogeneities 79

4.3.1 Elastic Solution for a Pair of Ellipsoidal Inhomogeneities in the Infinite Domain 79

4.3.2 Equivalent Inclusion Method for Potential Problems of Ellipsoidal Inhomogeneities 81

4.4 Exercises 83

Chapter 5 Volume Integrals and Averages in Inclusion and Inhomogeneity Problems 85

5.1 Volume Averages of Stress and Strain 85

5.1.1 Average Stress and Strain for an Inclusion Problem 85

5.1.2 Average Stress and Strain for an Inhomogeneity Problem 86

5.1.3 Tanaka-Mori's Theorem 88

5.1.4 Image Stress and Strain for a Finite Domain 89

5.2 Volume Averages in Potential Problems 92

5.2.1 Average Magnetic Field and Flux for an Inclusion Problem 92

5.2.2 Average Magnetic Field and Flux for an Inhomogeneity Problem 93

5.3 Strain Energy in Inclusion and Inhomogeneity Problems 94

5.3.1 Strain Energy for an Inclusion in an Infinite Domain 94

5.3.2 Strain Energy for an Inclusion in a Finite Solid 96

5.3.3 Strain Energy for an Inclusion with Both an Eigenstrain and an Applied Load 98

5.3.4 Strain Energy for an Inhomogeneity Problem 100

5.4 Exercises 102

Chapter 6 Homogenization for Effective Elasticity Based on the Energy Methods 103

6.1 Hill's Theorem 103

6.2 Hill's Bounds 105

6.3 Classical Variational Principles 108

6.4 Hashin-Shtrikman's Variational Principle 110

6.5 Hashin-Shtrikman's Bounds 117

6.5.1 The Lower Bound 119

6.5.2 The Upper Bound 120

6.6 Exercises 120

Chapter 7 Homogenization for Effective Elasticity Based on the Vectorial Methods 123

7.1 Effective Material Behavior and Material Phases 123

7.2 Micromechanics-Based Models for Two-Phase Composites 125

7.2.1 The Voigt Model 125

7.2.2 The Reuss Model 126

7.2.3 The Dilute Model 127

7.2.4 The Mori-Tanaka Model 128

7.2.5 The Self-Consistent Model 129

7.2.6 The Differential Scheme 130

7.3 Exercises 132

Chapter 8 Homogenization for Effective Elasticity Based on the Perturbation Method 133

8.1 Introduction 133

8.2 One-Dimensional Asymptotic Homogenization 135

8.3 Homogenization of a Periodic Composite 139

8.4 Excercises 143

Chapter 9 Defects in Materials: Void, Microcrack, Dislocation, and Damage 145

9.1 Voids 145

9.2 Microcracks 147

9.2.1 Penny-Shape Crack 147

9.2.2 Slit-Like Crack 150

9.2.3 Flat Ellipsoidal Crack 152

9.2.4 Crack Opening Displacement, Stress Intensity Factor, and I-Integral 154

9.3 Dislocation 160

9.3.1 Introduction 160

9.3.2 Burgers Vector and Burgers Circuit 161

9.3.3 Continuum Model for Dislocation 161

9.4 Damage 163

9.4.1 Category 1 σ₁ > σ_cri > σ₂ > σ₃ 167

9.4.2 Category 2 σ₁ > σ₂ > σ_cri > σ₃ 168

9.4.3 Category 3 σ₁ > σ₂ > σ₃ > σ_cri 168

9.5 Exercises 170

Chapter 10 Boundary Effects on Particulate Composites 171

10.1 Fundamental Solution for Semi-Infinite Domains 172

10.2 Equivalent Inclusion Method for One Particle in a Semi-Infinite Domain 174

10.3 Elastic Solution for Multiple Particles in a Semi-Infinite Domain 189

10.4 Boundary Effects on Effective Elasticity of a Periodic Composite 192

10.4.1 Uniaxial Tensile Loading on the Boundary 194

10.4.2 Uniform Simple Shear Loading on the Boundary 197

10.5 Inclusion-Based Boundary Element Method for Virtual Experiments of a Composite Sample 201

10.6 Exercises 213.

Notes:

"A CRC title."

"A Spon Press book."

Includes bibliographical references (pages 215-218) and index.

ISBN:

9781498707282

1498707289

OCLC:

920672212

Publisher Number:

99971679593