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E-raamat: Introduction to the Micromechanics of Composite Materials

(Columbia University, New York, New York, USA), (Beijing Institute of Technology, PR of China)
  • Formaat: 238 pages
  • Ilmumisaeg: 27-Jan-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498707305
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Introduction to the Micromechanics of Composite MaterialsSuurem pilt
  • Formaat: 238 pages
  • Ilmumisaeg: 27-Jan-2016
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781498707305
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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.

Arvustused

"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

Preface, xi
Acknowledgments, xiii
Chapter 1 Introduction 1(16)
1.1 Composite Materials
1(4)
1.2 History Of Micromechanics
5(1)
1.3 A Big Picture Of Micromechanics-Based Modeling
6(1)
1.4 Basic Concepts Of Micromechanics
7(4)
1.4.1 Representative Volume Element
7(1)
1.4.2 Inclusion and Inhomogeneity
8(1)
1.4.3 Eigenstrain
9(1)
1.4.4 Eshelby's Equivalent Inclusion Method
10(1)
1.5 Case Study: Holes Sparsely Distributed In A Plate
11(4)
1.5.1 The Exact Solution to an Infinite Plate Containing a Circular Hole
11(2)
1.5.2 Prediction of the Equivalent Property of an Infinite Plate Containing Periodic Holes
13(2)
1.6 Exercises
15(2)
Chapter 2 Vectors And Tensors 17(32)
2.1 Cartesian Vectors And Tensors
17(3)
2.1.1 Summation Convention in the Index Notation
17(1)
2.1.2 Vector
18(1)
2.1.3 Tensor
19(1)
2.1.4 Special Tensors
20(1)
2.2 Operations Of Vectors And Tensors
20(5)
2.2.1 Multiplication of Vectors
20(2)
2.2.2 Multiplication of Tensors
22(1)
2.2.3 Isotropic Tensors and Stiffness Tensor
23(2)
2.3 Calculus Of Vector And Tensor Fields
25(3)
2.3.1 Del Operator and Operations
25(2)
2.3.1.1 Gradient
25(1)
2.3.1.2 Divergence
26(1)
2.3.1.3 Curl
26(1)
2.3.2 Examples
27(1)
2.3.3 The Gauss Theorem
27(1)
2.3.4 Green's Theorem and Stokes' Theorem
28(1)
2.4 Potential Theory And Helmholtz's Decomposition Theorem
28(2)
2.4.1 Scalar and Vector Potentials
28(1)
2.4.2 Helmholtz's Decomposition Theorem
29(1)
2.5 Green's Identities And Green's Functions
30(5)
2.5.1 Green's First and Second Identities
30(1)
2.5.2 Green's Function for the Laplacian
30(2)
2.5.3 Green's Function in the Space of Lower Dimensions
32(2)
2.5.4 Example
34(1)
2.6 Elastic Equations
35(5)
2.6.1 Strain and Compatibility
35(2)
2.6.2 Constitutive Law
37(1)
2.6.3 Equilibrium Equation
37(1)
2.6.4 Governing Equations
38(1)
2.6.5 Boundary Value Problem
39(1)
2.7 General Solution And The Elastic Green's Function
40(6)
2.7.1 Papkovich-Neuber's General Solution
40(2)
2.7.2 Kelvin's Particular Solution
42(2)
2.7.3 Elastic Green's Function
44(2)
2.8 Exercises
46(3)
Chapter 3 Spherical Inclusion And Inhomogeneity 49 (14)
3.1 Spherical Inclusion Problem
49(3)
3.2 Introduction To The Equivalent Inclusion Method
52(3)
3.3 Spherical Inhomogeneity Problem
55(5)
3.3.1 Eshelby's Equivalent Inclusion Method
56(1)
3.3.2 General Cases of Inhomogeneity with a Prescribed Eigenstrain
57(2)
3.3.3 Interface Condition and the Uniqueness of the Solution
59(1)
3.4 Integrals Of φ, ψ, φP, ΨP And Their Derivatives In 3D Domain
60(2)
3.5 Exercises
62(1)
Chapter 4 Ellipsoidal Inclusion And Inhomogeneity 63(22)
4.1 General Elastic Solution Caused By An Eigenstrain Through Fourier Integral
63(6)
4.1.1 An Eigenstrain in the Form of a Single Wave
63(2)
4.1.2 An Eigenstrain in the Form of Fourier Series and Fourier Integral
65(1)
4.1.3 Green's Function for Isotropic Materials
66(3)
4.2 Ellipsoidal Inclusion Problems
69(10)
4.2.1 Ellipsoidal Inclusion with a Uniform Eigenstrain
69(6)
4.2.2 Ellipsoidal Inclusion with a Polynomial Eigenstrain
75(2)
4.2.3 Ellipsoidal Inclusion with a Body Force
77(2)
4.3 Equivalent Inclusion Method For Ellipsoidal Inhomogeneities
79(4)
4.3.1 Elastic Solution for a Pair of Ellipsoidal Inhomogeneities in the Infinite Domain
79(2)
4.3.2 Equivalent Inclusion Method for Potential Problems of Ellipsoidal Inhomogeneities
81(2)
4.4 Exercises
83(2)
Chapter 5 Volume Integrals And Averages In Inclusion And Inhomogeneity Problems 85(18)
5.1 Volume Averages Of Stress And Strain
85(7)
5.1.1 Average Stress and Strain for an Inclusion Problem
85(1)
5.1.2 Average Stress and Strain for an Inhomogeneity Problem
86(2)
5.1.3 Tanaka-Mori's Theorem
88(1)
5.1.4 Image Stress and Strain for a Finite Domain
89(3)
5.2 Volume Averages In Potential Problems
92(2)
5.2.1 Average Magnetic Field and Flux for an Inclusion Problem
92(1)
5.2.2 Average Magnetic Field and Flux for an Inhomogeneity Problem
93(1)
5.3 Strain Energy In Inclusion And In Homogeneity Problems
94(8)
5.3.1 Strain Energy for an Inclusion in an Infinite Domain
94(2)
5.3.2 Strain Energy for an Inclusion in a Finite Solid
96(2)
5.3.3 Strain Energy for an Inclusion with Both an Eigenstrain and an Applied Load
98(2)
5.3.4 Strain Energy for an Inhomogeneity Problem
100(2)
5.4 Exercises
102(1)
Chapter 6 Homogenization For Effective Elasticity Based On The Energy Methods 103 (20)
6.1 Hill's Theorem
103(2)
6.2 Hill's Bounds
105(3)
6.3 Classical Variational Principles
108(2)
6.4 Hashin-Shtrikman's Variational Principle
110(7)
6.5 Hash In-Shtrikman's Bounds
117(3)
6.5.1 The Lower Bound
119(1)
6.5.2 The Upper Bound
120(1)
6.6 Exercises
120(3)
Chapter 7 Homogenization For Effective Elasticity Based On The Vectorial Methods 123(10)
7.1 Effective Material Behavior And Material Phases
123(2)
7.2 Micromechanics-Based Models For Two-Phase Composites
125(7)
7.2.1 The Voigt Model
125(1)
7.2.2 The Reuss Model
126(1)
7.2.3 The Dilute Model
127(1)
7.2.4 The Mori-Tanaka Model
128(1)
7.2.5 The Self-Consistent Model
129(1)
7.2.6 The Differential Scheme
130(2)
7.3 Exercises
132(1)
Chapter 8 Homogenization For Effective Elasticity Based On The Perturbation Method 133 (12)
8.1 Introduction
133(2)
8.2 One-Dimensional Asymptotic Homogenization
135(4)
8.3 Homogenization Of A Periodic Composite
139(4)
8.4 Excercises
143(2)
Chapter 9 Defects In Materials: Void, Microcrack, Dislocation, And Damage 145(26)
9.1 Voids
145(2)
9.2 Microcracks
147(13)
9.2.1 Penny-Shape Crack
147(3)
9.2.2 Slit-Like Crack
150(2)
9.2.3 Flat Ellipsoidal Crack
152(2)
9.2.4 Crack Opening Displacement, Stress Intensity Factor, and J-Integral
154(6)
9.3 Dislocation
160(3)
9.3.1 Introduction
160(1)
9.3.2 Burgers Vector and Burgers Circuit
161(1)
9.3.3 Continuum Model for Dislocation
161(2)
9.4 Damage
163(7)
9.4.1 Category 1 σ1 > σcri > σ2 > σ3
167(1)
9.4.2 Category 2 σ1 > σ2 > σcri > σ3
168(1)
9.4.3 Category 3 σ1 > σ2 > σ3 > σcri
168(2)
9.5 Exercises
170(1)
Chapter 10 Boundary Effects On Particulate Composites 171(44)
10.1 Fundamental Solution For Semi-Infinite Domains
172(2)
10.2 Equivalent Inclusion Method For One Particle In A Semi-Infinite Domain
174(15)
10.3 Elastic Solution For Multiple Particles In A Semi-Infinite Domain
189(3)
10.4 Boundary Effects On Effective Elasticity Of A Periodic Composite
192(9)
10.4.1 Uniaxial Tensile Loading on the Boundary
194(3)
10.4.2 Uniform Simple Shear Loading on the Boundary
197(4)
10.5 Inclusion-Based Boundary Element Method For Virtual Experiments Of A Composite Sample
201(12)
10.6 Exercises
213(2)
References, 215(4)
Index, 219
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
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