| Description |
1 online resource (xvi, 489 pages) |
| Contents |
Half Title; Title Page; Copyright; Contents; Preface; Introduction; 1.1 Motivation for the Work; 1.2 Geometry Models; 1.2.1 Single Inclusion; 1.2.2 Finite Arrays of Inclusions; 1.2.3 Composite Band and Layer; 1.2.4 Representative Unit Cell (RUC) Model; 1.3 Method of Solution; 1.4 Homogenization Problem: Volume vs. Surface Averaging; 1.4.1 Conductivity; 1.4.2 Elasticity; 1.5 Scope and Structure of the Book; Potential Fields of Interacting Spherical Inclusions; 2.1 Background Theory; 2.1.1 Scalar Spherical Harmonics; 2.1.2 Selected Properties of Solid Spherical Harmonics |
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2.1.3 Spherical Harmonics vs. Multipole Potentials2.2 General Solution for a Single Inclusion; 2.2.1 Multipole Expansion Solution; 2.2.2 Far Field Expansion; 2.2.3 Resolving Equations; 2.3 Particle Coating vs. Imperfect Interface; 2.4 Re-Expansion Formulas for the Solid Spherical Harmonics; 2.4.1 Equally Oriented Coordinate Systems; 2.4.2 Multipole Expansion Theorem; 2.4.3 Arbitrarily Oriented Coordinate Systems; 2.5 Finite Cluster Model (FCM); 2.5.1 Superposition Principle; 2.5.2 FCM Boundary-Value Problem; 2.5.3 Convergence Proof; 2.5.4 Modified Maxwell Method for Effective Conductivity |
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2.6 Composite Sphere2.6.1 Outer Boundary Condition; 2.6.2 Interface Conditions; 2.6.3 RSV and Effective Conductivity of Composite; 2.7 Half-Space FCM; 2.7.1 Double Fourier Transform of Solid Spherical Harmonics; 2.7.2 Homogeneous Half-Space; 2.7.3 Superposition Sum; 2.7.4 Half-Space Boundary Condition; 2.7.5 Interface Conditions; Periodic Multipoles: Application to Composites; 3.1 Composite Layer; 3.1.1 2P Fundamental Solution of Laplace Equation; 3.1.2 2P Solid Harmonics; 3.1.3 Heat Flux Through the Composite Layer; 3.2 Periodic Composite as a Sandwich of Composite Layers |
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3.3 Representative Unit Cell Model3.4 3P Scalar Solid Harmonics; 3.4.1 Direct Summation; 3.4.2 Hasimoto's Approach; 3.4.3 2P Harmonics-Based Approach; 3.5 Local Temperature Field; 3.6 Effective Conductivity of Composite; Elastic Solids with Spherical Inclusions; 4.1 Vector Spherical Harmonics; 4.1.1 Vector Surface Harmonics; 4.1.2 Vector Solid Harmonics; 4.2 Scalar and Vector Solid Spherical Biharmonics; 4.3 Partial Solutions of Lame Equation; 4.3.1 Definition; 4.3.2 Properties of Spherical Lame Solutions; 4.4 Single Inclusion in Unbounded Solid; 4.4.1 Far Field Expansion |
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4.4.2 Resolving Set of Linear Equations4.4.3 Single Inclusion in Viscous Fluid (Stokes's Problem); 4.5 Application to Nanocomposite: Gurtin & Murdoch Theory; 4.5.1 Imperfect Interface Conditions; 4.5.2 Formal Solution; 4.5.3 Single Cavity Under Hydrostatic Far Field Load; 4.5.4 Single Cavity Under Uniaxial Far Field Load; 4.6 Re-Expansion Formulas for the Vector Harmonics and Biharmonics; 4.6.1 Translation of Scalar Biharmonics; 4.6.2 Translation of Vector Harmonics; 4.6.3 Translation of Vector Biharmonics; 4.6.4 Translation of Lame Solutions; 4.6.5 Re-Expansion Due to Rotation |
| Summary |
Micromechanics 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 |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Composite materials -- Mechanical properties
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TECHNOLOGY & ENGINEERING -- Material Science.
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Composite materials -- Mechanical properties
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| Form |
Electronic book
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| ISBN |
9780124076600 |
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0124076602 |
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1299610404 |
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9781299610408 |
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