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Micromechanics of Composites
Multipole Expansion Approach
- 1st Edition - May 13, 2013
- Author: Volodymyr Kushch
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 4 0 7 6 8 3 - 9
- eBook ISBN:9 7 8 - 0 - 1 2 - 4 0 7 6 6 0 - 0
Micromechanics of Composites: Multipole Expansion Approach is the first book to introduce micromechanics researchers to a more efficient and accurate alternative to comput… Read more
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Request a sales quoteMicromechanics of Composites: Multipole Expansion Approach is the first book to introduce micromechanics researchers to a more efficient and accurate alternative to computational micromechanics, which requires heavy computational effort and the need to extract meaningful data from a multitude of numbers produced by finite element software code. In this book Dr. Kushch demonstrates the development of the multipole expansion method, including recent new results in the theory of special functions and rigorous convergence proof of the obtained series solutions. The complete analytical solutions and accurate numerical data contained in the book have been obtained in a unified manner for a number of the multiple inclusion models of finite, semi- and infinite heterogeneous solids. Contemporary topics of micromechanics covered in the book include composites with imperfect and partially debonded interface, nanocomposites, cracked solids, statistics of the local fields, and brittle strength of disordered composites.
- Contains detailed analytical and numerical analyses of a variety of micromechanical multiple inclusion models, providing clear insight into the physical nature of the problems under study
- Provides researchers with a reliable theoretical framework for developing the micromechanical theories of a composite’s strength, brittle/fatigue damage development and other properties
- Includes a large amount of highly accurate numerical data and plots for a variety of model problems, serving as a benchmark for testing the applicability of existing approximate models and accuracy of numerical solutions
A multidisciplinary audience consisting of researchers, professionals and graduate students in materials science, mechanics, engineering, applied mathematics, physics and related areas dealing with heterogeneous solids
Preface
Chapter 1. Introduction
1.1 Motivation for the Work
1.2 Geometry Models
1.3 Method of Solution
1.4 Homogenization Problem: Volume vs. Surface Averaging
1.5 Scope and Structure of the Book
References
Part I: Particulate Composites
Chapter 2. Potential Fields of Interacting Spherical Inclusions
2.1 Background Theory
2.2 General Solution for a Single Inclusion
2.3 Particle Coating vs. Imperfect Interface
2.4 Re-Expansion Formulas for the Solid Spherical Harmonics
2.5 Finite Cluster Model (FCM)
2.6 Composite Sphere
2.7 Half-Space FCM
References
Chapter 3. Periodic Multipoles: Application to Composites
3.1 Composite Layer
3.2 Periodic Composite as a Sandwich of Composite Layers
3.3 Representative Unit Cell Model
3.4 3P Scalar Solid Harmonics
3.5 Local Temperature Field
3.6 Effective Conductivity of Composite
References
Chapter 4. Elastic Solids with Spherical Inclusions
4.1 Vector Spherical Harmonics
4.2 Scalar and Vector Solid Spherical Biharmonics
4.3 Partial Solutions of Lame Equation
4.4 Single Inclusion in Unbounded Solid
4.5 Application to Nanocomposite: Gurtin & Murdoch Theory
4.6 Re-Expansion Formulas for the Vector Harmonics and Biharmonics
4.7 Finite Array of Inclusions (FCM)
4.8 Isotropic Solid with Anisotropic Inclusion
4.9 Effective Stiffness of Composite: Modified Maxwell Approach
4.10 Elastic Composite Sphere
4.11 RSV and Effective Elastic Moduli
References
Chapter 5. Elasticity of Composite Half-Space, Layer, and Bulk
5.1 Vector Harmonics and Biharmonics for Half-Space
5.2 Vector Lame Solutions for Half-Space
5.3 FCM for Elastic Half-Space
5.4 Doubly Periodic Models
5.5 Triply Periodic Vector Multipoles
5.6 RUC Model of Elastic Spherical Particle Composite
5.7 Numerical Study
References
Chapter 6. Conductivity of a Solid with Spheroidal Inclusions
6.1 Scalar Spheroidal Solid Harmonics
6.2 Single Inclusion: Conductivity Problem
6.3 Re-Expansion Formulas for Spheroidal Solid Harmonics
6.4 Finite Cluster Model of Spheroidal Particle Composite
6.5 Double Fourier Integral Transform of Spheroidal Harmonics
6.6 Doubly Periodic Harmonics
6.7 Triply Periodic Harmonics
6.8 Heat Conduction in Periodic Composite
6.9 Numerical Examples
References
Chapter 7. Elastic Solid with Spheroidal Inclusions
7.1 Background Theory
7.2 Single-Inclusion Problem
7.3 Re-Expansion Formulas for the Spheroidal Lame Solutions
7.4 Finite Cluster Model of Composite with Spheroidal Inclusions
7.5 Half-Space Problem
7.6 RUC Model of Elastic Spheroidal Particle Composite
References
Chapter 8. Composites with Transversely Isotropic Constituents
8.1 Transversely Isotropic Conductivity
8.2 Transversely Isotropic Elastic Solid with Spherical Inclusions
8.3 RUC Model
8.4 Numerical Examples
References
Part II: Fibrous Composites: Two-Dimensional Models
Chapter 9. Circular Fiber Composite with Perfect Interfaces
9.1 In-Plane Conductivity and Out-of-Plane Shear: The Governing Equations
9.2 Finite Array of Circular Inclusions
9.3 Half Plane with Circular Inclusions
9.4 Infinite Arrays of Circular Inclusions
9.5 Representative Unit Cell Model
9.6 Finite Array of Circular Inclusions: In-Plane Elasticity Problem
9.7 Circular Inclusions in Half-Plane
9.8 RUC Model of Fibrous Composite: Elasticity
9.9 Statistics of Microstructure, Peak Stress and Interface Damage in Fibrous Composite
References
Chapter 10. Fibrous Composite with Interface Cracks
10.1 General Solution for a Single, Partially Debonded Inclusion
10.2 Finite Array of Partially Debonded Inclusions
10.3 Conductivity of Fibrous Composite with Interface Damage
10.4 In-Plane Elasticity: General Form of the Displacement Solution
10.5 Displacement Solution for the Partially Debonded Inclusion
10.6 A Finite Number of Interacting Inclusions withInterface Cracks
10.7 RUC Model of Fibrous Composite with Interface Cracks
References
Chapter 11. Solids with Elliptic Inclusions
11.1 Single Elliptic Inclusion in an Inhomogeneous Far Field
11.2 Re-Expansion Formulas for the Elliptic Solid Harmonics
11.3 Finite Array of Inclusions
11.4 Half-Space Containing a Finite Array of Elliptic Fibers
11.5 Periodic Complex Potentials
11.6 Micromechanical Model of Cracked Solid
11.7 Numerical Examples
References
Chapter 12. Fibrous Composite with Anisotropic Constituents
12.1 Out-of-Plane Shear
12.2 Periodic Complex Potentials
12.3 Plane Strain
12.4 Effective Stiffness Tensor
References
Appendix A. Sample Fortran Codes
A.1 FCM Conductivity Problem (Chapter 2)
A.2 RUC Conductivity Problem for Spherical Particle Composite (Chapter 3)
A.3 FCM Elasticity Problem (Chapter 4)
A.4 RUC Elasticity Problem for Spherical Particle Composite (Chapter 5)
A.5 RUC Conductivity and Elasticity Problems for Fibrous Composite (Chapter 9)
A.6 Standard Lattice Sums
References
Bibliography
Index
- No. of pages: 512
- Language: English
- Edition: 1
- Published: May 13, 2013
- Imprint: Butterworth-Heinemann
- Hardback ISBN: 9780124076839
- eBook ISBN: 9780124076600
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Volodymyr Kushch
Prof. Volodymyr Kushch is Leading Research Scientist, Institute for Superhard Materials of the National Academy of Sciences of Ukraine. He is the author of Micromechanics of Composites as well as dozens of peer-reviewed papers. He has over thirty years of research and industry experience in micromechanics of composites and computational mechanics, with research interests that include advanced analytical and numerical methods in mechanics of heterogeneous solids, suspensions and bubbly liquids, computational materials science, mathematical physics, and more.
Affiliations and expertise
Head of Laboratory, Institute for Superhard Materials, The National Academy of Sciences of UkraineRead Micromechanics of Composites on ScienceDirect